Managerial Economics

(1)

(2)

Managerial Economics

Syllabus

Lecture 1 Notes

Lecture 2 Notes Problem Set 1 Problem Set 1Key Lecture 3 Notes Problem Set 2 Problem Set 2 Key Lecture 4 Notes

Lecture 5 Notes Lecture 6 Notes

Lecture 7 Notes Problem Set 3 Problem Set 3 Key Lecture 8 Notes

Lecture 9 Notes

Lecture 12 Notes

Test 1 Review Outline

Lecture 17 Notes Problem Set 7 Problem 7 Key Lecture 18 Notes

(3)

Lecture 19 Notes Problem Set 8 Problem 8 Key Lecture 20 Notes

Lecture 21 Notes Problem Set 9 Problem 9 Key Lecture 22 Notes Problem Set 10 Problem 10 Key Lecture 23 Notes Problem Set 11 Problem 11 Key Lecture 24 Notes

Lecture 27 Notes Problem 12 Lecture 28 Notes

Lecture 29 Notes

Lecture 30 Notes Problem 13 NEW Problem 13 Key Test 2 Review Outline

Lecture 33 Notes Problem 14 Problem 14 Key Lecture 34 Notes

Lecture 35 Notes

Lecture 36 Problem 15 Problem 15 Key (CORRECTED) Lecture 37

Lecture 38

(4)

Review Outline for Final Examination

I. Chapter 1. The Fundamentals of Managerial Economics A. Definition of Topic.

1. Economics

2. Managerial Decisions

B. Components of Effective Decision Making

1. Identify Goals and Constraints:

2. Recognize the Nature and Importance of Profits: Economic profits differ from

Accounting profits. . Good decision-making involves the maximization of economic profits.

3. Understanding Incentives. .Compensation and the structure of organizations

affects importantly organizations.

a. Organizational Incentives

b. Incentives for Motivating Individuals

4. Understand Markets. Market forces represent a series of rivalries. In any

problem, you must appreciate your position relative to other agents. 5. Recognize the Time Value of Money

6. Appreciate Marginal Analysis. Marginal decisions are an easy way to optimize totals. Calculus is just a formal expression of marginal analysis.

a. Discrete Decisions.

b. Continuous Decisions and the calculus c. Incremental Analysis

1. Pay attention to incremental costs and incremental benefits. 2. Ignore sunk costs. .

II. Chapter Market Forces: Demand and Supply A. Introduction and Overview.

1. Overview

2. The structure of the supply and demand model.

B. The Demand Side.

1. Motivation: Diminishing marginal utility: 2. Definition of Demand Curve

3. Determinants of Demand.

4. Changes in demand vs. changes in qty demanded. 5. The Notion of Consumer Surplus

6. An Analytical Example

C. The Supply Side.

1. Driving Force. The Law of Diminishing Returns 2. Definition of Supply Curve

(5)

4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus.

6. An Analytical Example.

D. Equilibrium. Putting Supply and Demand Together

1. Definition.

2. Binding the market. Price floors Price Ceilings

E. Comparative Statics.

1. Supply or Demand Shifts 2. Supply and Demand Shifts

III. Quantitative Demand Analysis A. Price Elasticity of Demand

1. Motivation 2. Calculations

a. Arc price elasticity of demand b. Point price elasticity of demand c. Percentage Changes

3. A Graphical Interpretation of Price Elasticity. 4. Some Observations about Price Elasticity of Demand

a. Most Demand curves have elastic and inelastic segments b. Exceptions

c. Elasticity and the Slope of Demand Curves 5. Price Elasticity, MR and TR.

6. Determinants of price elasticity of demand

B. Other Demand Elasticities 1. Cross Price Elasticities

2. Income Elasticities 3.Other Elasticites.

C. Elasticities and demand functions

1. Linear Demand functions. 2. Logrithmic Demand.

D. Estimating Demand: Regression Analysis.

1. Interpreting the significance of individual parameter estimates 2. Forecasting

(6)

IV. Chapter 5. The Production Process and Costs A. Introduction

B. The Production Function

1. Short Run Production.

a. Diminishing Marginal Productivity and Marginal Product b. Relationships between Productivity Measures.

c. Optimal Use of a single input.

2. Long Run Production (Optimal use of multiple inputs) 3. Returns to scale: Given a production function of the form

F(K,L) = KLα

The function exhibits increasing returns to scale if α>.5 constant returns to scale if α=.5 decreasing returns to scale if α<.5 C. Costs.

1. The relationship of production functions to cost functions. 2. Short run costs.

a. Cost curves

b. Sunk vs. Variable Costs c. Algebraic forms of cost curves 3. Long-Run Costs

a. Long Run Average Costs b. Economics of Scale 4. Multiple Output Cost functions

a. Economies of Scope b. Cost complementarities

V. Chapter 6. The Organization of the Firm. A. Overview and Motivation.

B. Optimal Methods of Obtaining Inputs

1. Options a. Spot b. Contract

c. Internal Production

2. Factors affecting choice of the optimal method a. Costly Bargaining

b. Underinvestment c. The Hold-up Problem.

(7)

C. Managerial Compensation and the Principal-Agent Problem.

1. The Principal-Agent Problem.

2. Structuring Contracts for Managers (review). 3. The Manager/Worker Problem.

a. Profit Sharing. b. Revenue Sharing. c. Piece Rates.

d. Time clocks and time checks

VI. Chapter 8. Managing in Competitive, Monopolistic and Monopolistically Competitive Markets.

A. Introductory Comments on Chapter 7. B. Competition.

1. Assumptions

2. Optimal short run decisions a. Graphically

b. Analytically (set P = MR = MC) 3. Long run decisions.

C. Monopoly

1. Assumptions, Sources of monopoly power. 2. Characterization:

a. Graphically b. Analytically

Q* is where MR = MC P* is the demand curve at Q* Profits are TR - TC

3. Observations: Social Costs of Monopoly

D. Monopolistic Competition

. 1. Assumptions

2. Characterization: 3. Optimizing decisions. 4. Observations.

(8)

VII. Chapter 11. Pricing Strategies.

A. Basic Pricing Strategies for Firms with Market Power

1. Optimal Pricing for a monopolist or monopolistic competitor a. Basic Case

b. Imperfect Demand Information

P = MC/[1+1/η].

B. Strategies that yield higher profits

1. Price Discrimination

a. Perfect (1st_{degree) price discrimination}

i. Calculating gains ii. Necessary conditions

b. Price List (2nd_{degree) price discrimination}

c. Group Division (3rd_{degree) price discrimination.}

2. Two part pricing. 3. Commodity Bundling 4. Peak Load Pricing

1. Economics

2. Managerial Decisions

a. Organizational Incentives

b. Incentives for Motivating Individuals

6. Appreciate Marginal Analysis. Marginal decisions are an easy way to optimize totals. Calculus is just a formal expression of marginal analysis.

a. Discrete Decisions.

b. Continuous Decisions and the calculus c. Incremental Analysis

(9)

1. Pay attention to incremental costs and incremental benefits. 2. Ignore sunk costs. .

1. Overview

1. Motivation: Diminishing marginal utility: 2. Definition of Demand Curve

3. Determinants of Demand.

4. Changes in demand vs. changes in qty demanded. 5. The Notion of Consumer Surplus

6. An Analytical Example

1. Driving Force. The Law of Diminishing Returns 2. Definition of Supply Curve

3. Determinants of supply:

4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus.

6. An Analytical Example.

1. Definition.

2. Binding the market. Price floors Price Ceilings

E. Comparative Statics.

1. Supply or Demand Shifts 2. Supply and Demand Shifts

III. Quantitative Demand Analysis A. Price Elasticity of Demand

1. Motivation 2. Calculations

a. Arc price elasticity of demand b. Point price elasticity of demand c. Percentage Changes

3. A Graphical Interpretation of Price Elasticity. 4. Some Observations about Price Elasticity of Demand

a. Most Demand curves have elastic and inelastic segments b. Exceptions

(10)

c. Elasticity and the Slope of Demand Curves 5. Price Elasticity, MR and TR.

6. Determinants of price elasticity of demand

B. Other Demand Elasticities 1. Cross Price Elasticities

2. Income Elasticities 3.Other Elasticites.

C. Elasticities and demand functions

1. Linear Demand functions. 2. Logrithmic Demand.

D. Estimating Demand: Regression Analysis.

1. Interpreting the significance of individual parameter estimates 2. Forecasting

(11)

IV. Chapter 5. The Production Process and Costs A. Introduction

B. The Production Function

1. Short Run Production.

a. Diminishing Marginal Productivity and Marginal Product b. Relationships between Productivity Measures.

c. Optimal Use of a single input.

2. Long Run Production (Optimal use of multiple inputs) 3. Returns to scale: Given a production function of the form

F(K,L) = KLα

The function exhibits increasing returns to scale if α>.5 constant returns to scale if α=.5 decreasing returns to scale if α<.5 C. Costs.

1. The relationship of production functions to cost functions. 2. Short run costs.

a. Cost curves

b. Sunk vs. Variable Costs c. Algebraic forms of cost curves 3. Long-Run Costs

a. Long Run Average Costs b. Economics of Scale 4. Multiple Output Cost functions

a. Economies of Scope b. Cost complementarities

V. Chapter 6. The Organization of the Firm. A. Overview and Motivation.

B. Optimal Methods of Obtaining Inputs

1. Options a. Spot b. Contract

c. Internal Production

2. Factors affecting choice of the optimal method a. Costly Bargaining

b. Underinvestment c. The Hold-up Problem.

(12)

C. Managerial Compensation and the Principal-Agent Problem.

1. The Principal-Agent Problem.

2. Structuring Contracts for Managers (review). 3. The Manager/Worker Problem.

a. Profit Sharing. b. Revenue Sharing. c. Piece Rates.

d. Time clocks and time checks

VI. Chapter 8. Managing in Competitive, Monopolistic and Monopolistically Competitive Markets.

A. Introductory Comments on Chapter 7. B. Competition.

1. Assumptions

2. Optimal short run decisions a. Graphically

b. Analytically (set P = MR = MC) 3. Long run decisions.

C. Monopoly

1. Assumptions, Sources of monopoly power. 2. Characterization:

a. Graphically b. Analytically

Q* is where MR = MC P* is the demand curve at Q* Profits are TR - TC

3. Observations: Social Costs of Monopoly

D. Monopolistic Competition

. 1. Assumptions

2. Characterization: 3. Optimizing decisions. 4. Observations.

(13)

VII. Chapter 11. Pricing Strategies.

A. Basic Pricing Strategies for Firms with Market Power

1. Optimal Pricing for a monopolist or monopolistic competitor a. Basic Case

b. Imperfect Demand Information

P = MC/[1+1/η].

B. Strategies that yield higher profits

1. Price Discrimination

a. Perfect (1st_{degree) price discrimination}

i. Calculating gains ii. Necessary conditions

b. Price List (2nd_{degree) price discrimination}

c. Group Division (3rd_{degree) price discrimination.}

2. Two part pricing. 3. Commodity Bundling 4. Peak Load Pricing

Lecture 1

I. Chapter 1. The Fundamentals of Managerial Economics Preview:

A. Definition of Topic. 1. Economics

2. Managerial Decisions

Lecture_______________________________________________

A. Definition of Topic.

A first topic involves defining the scope of the course:

1. Economics: The study of how societies and individuals allocate scarce resources

(14)

Observation: This is a study of allocation decisions. It applies widely to an immense variety of topics. It is not, for example, particularly focused on the decisions of businesses. It applies to profit as well as to non profit institutions.

2. The Manager. A person who directs resources to achieve a stated goal.

Observation: Again, this is a very broad definition. Clearly, you manage your own lives. In business or organizational contexts, managers control resources other than their own time and energy such as

a. The efforts of others b. Input acquisition and use c. Output/Pricing decisions

3. Managerial Economics: The study of how to direct scarce resources in the way that

most efficiently achieves a managerial goal.

Observation: The difference between this course and, say microeconomics is that it is

policy oriented. That is, we focus on giving you tools to make decisions, rather than

describing how a market or an economy as a whole works.

B. Effective Management from an Economic Perspective. Economic “tools” are guides to good allocative decision-making. Elements of good decision-making can be divided into six categories

1. Identify Goals and Constraints: This is critical for defining the dimension of the

problem.

Objectives are simply what you would like to accomplish. Constraints are the natural (and perhaps unfortunate) consequence of scarcity.

a. Having a well-defined objective in mind when making an allocative decision is critical. (Very concretely, imagine how one might decide to allocate time to this course if it were uncertain whether your intention was to get a good grade or to merely pass)

b. Also, it is necessary to evaluate the constraints available in the decision process. (For example, time is typically the constraint in making personal allocative decisions. Most of our applications will focus on the decisions of a profit-maximizing firm. Here the objective is typically profits. Constraints arise in the form of pricing limitations, and production considerations.)

2. Recognize the Nature and Importance of Profits: When discussing the firm, profits

take on a special role. However, when making allocative decisions you must have the correct definition of profits in mind.

a. Accounting Profits

(15)

b. Economic Profits

πE = TR - (TCA +TCI)

The difference in the definitions is implicit costs. Implicit costs are measured in terms of foregone alternatives. Economic costs are the sum of implicit and implicit costs.

Economic costs can be measured in terms of choices foregone, or opportunity costs.

Observations

a) The function of economic profits. Accounting profits are not an incorrect definition of profits, just inappropriate for the purpose of making allocative decisions.

Example: Suppose you consider opening a T.J. Cinnamon Franchise in a storefront you

own in the VA Center Commons, North of Richmond. Suppose the franchise fee is $20,000 per year, and you must pay $80,000 per year for materials and help. How much must you earn to realize an accounting profit?

Suppose that you must work in the store (and quit your job paying $25,000 per year). Also you could rent the store slot for $1000 per month. If you expected revenues of $120,000 per year, would this be a good allocation of resources?

b) The difficulty of collecting implicit cost information. In fact, it is relatively difficult get good information pertaining to opportunity costs. A legitimate (and important) function of the manager is to do as good a job as possible in collecting this information.

Lecture 2

1. Economics

2. Managerial Decisions

2. Recognize the Nature and Social Role of Profits:

a. Defining Economic Profits Economic profits differ from Accounting

profits. . Good decision-making involves the maximization of economic profits. Preview__________________________________________________________

(16)

b. Understanding the Social Role of Profits.

a. Organizational Incentives

b. Incentives for Motivating Individuals

6. Appreciate Marginal Analysis Marginal decisions are an easy way to optimize totals. Calculus is just a formal expression of marginal analysis.

Lecture_____________________________________________________________

b) The social role of profits. The 1980’s are popularly called “the decade of

greed.” A popular depiction of attitudes in the 80’s was the film “Wall Street” where Michael Douglas gives a lecture to shareholders extolling the virtues of selfishness. This is passe, of course, but, even at its height, it was a caricature of the role of profits in society.

Profits serve a valuable social function if certain assumptions regarding competitive performance are satisfied. These assumptions include:

-many buyers and sellers. This is referred to as the structural assumption. Violations

cause problems of monopoly or oligopoly.

-perfect information about both product quality and price. This an informational assumption: Violations are of the form of “lemon’s markets” problems, as well as

“Diamond Paradox”

-pure privacy in consumption and production. The privacy assumption. Violations cause “free-riding” and “externalities.

If these assumptions are met, then the signals sent by profits channel resources into their most efficient use. To quote Smith (1776)

“It is not out of the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.”

Profits send signals about entry, exit, expansion and innovation.

Example: The computer industry in the 1980s was very dynamic. The number of firms

increased substantially. As a consequence, prices fell, and also the quality of computers increased. More recently, computers have become a more commodity-like product. The number of firms has decreased, and production runs have increased.

(17)

If competitive assumptions are satisfied, economic profits are a temporary phenomenon, attributable to a new idea, product develop or change in consumer tastes. Entry will dissipate these profits. On the other hand, if competitive assumptions are not satisfied (because, a firm has a patent, or unique license) then they are permanent, and not socially beneficial.

3. Understanding Incentives. If profits restrict the behavior of firms via incentives, in the

market, it is also important to understand the effects of incentives within the firm. a. Institutional organization affects performance. The way an institution is organized often puts incredible limitations on the power of personalities to exert

influence. Sometimes this is healthy (e.g., in the U.S. government, laws severely restrict the power of the presidency.) In other environments institutional restrictions are an important handicap. For example, the recent scandals at Enron and WorldCom are not a consequence of “bad guys”. Rather the institutional structure of these firms, and the oversight process for these firms, not only allowed, but encouraged illegal behavior. Reorganizing the structure of an institution, as well as the laws regulating the oversight process, can make firms more reliable and more efficient.

b. The way people are rewarded can influence their incentive to work

Example: Suppose you pay someone $75,000 to manage your restaurant. Would this

person do better than someone paid $50,000? There is no particular reason to suppose that the answer should be in the affirmative. A compensation package that more nearly aligns the interests of the owner and the manager would be one that provided incentives to the manager that paralleled the interests of the owner. (e.g., a profit-sharing

arrangement.)

This type of problem is called a principle-agent problem. It is a common problem in many firms. Particularly in publicly-held firms, where the stockholders have only limited control over the decisions of the CEO.

4. Understand Markets. Markets are the regulating force for firms, and the source of incentives for their activities. These incentives arise via transactions, and are the consequence of competing interests. For every transaction, there are two parties. a. Consumer-Producer Rivalry: Consumers and producers are simultaneously trying to take advantage of each other. They are limited by reputation and bargaining skills. As a consequence of bargaining, each gets less than they want, but not more than it is worth, or less than it costs.

b. Consumer-Consumer Rivalry: Consumers compete with each other for products. In the process, the purchasing consumer pays more than (s)he wants, but not more than it is worth to him or her. (Example: This is most clearly seen in auctions for specialized consumer goods, such as antiques. Bidding by rival potential purchasers drives up the price.)

c. Producer-Producer Rivalry: Producers compete with each other, and as a consequence, offer better quality, and higher quantities at a lower price than they would like. (Again, this is most directly seen in a procurement auction)

(18)

d. The Role of Government: Provided that the conditions that I mentioned above are satisfied, there is no need for the government to intervene. However, when one or more of these assumptions fails, the Government frequently intervenes to restore the balance.

5. Recognize the Time Value of Money. It is important to realize that money earned in the

future is not valued the same as money earned today. Allocative decisions should be adjusted accordingly.

a. Present Value Analysis.

Suppose that the interest rate is 10%. Then it would take $1.10 next year to equal $1 today. In general

PV(1+i) = FV

Similarly, for two years hence

PV(1+i)2 ₌ _FV

and in general

PV = FV

(1+i)n

Often times we are interested in a stream of earnings. PV = ∑ FVt

(19)

In valuing a stream of earnings relative to a cost. (As is typical for any investment decision) It is important to consider the net present value

NPV = ∑ FVt - Co

(1+i)t

Example: Suppose you are given the opportunity to purchase a new high-speed lathe

that will reduce the costs of producing cedar wooden eggs by $2 per egg. At current prices, you sell 10,000 per year for each of the next 4 years. If the interest rate is 10%, and the machine costs $65,000 is it a good purchase?

20,000/(1.1) + 20,000/(1.1)2₊_20,000/(1.1)3 _{+ 2 0,000/(1.1)}4

= 18,182 + 16258 + 15026+ 13660 = 63,397

No. The NPV is -$1,603.

Lecture 3

Problems: Collect Problem Set 1

REVIEW___________________________________________________: I. Chapter 1. The Fundamentals of Managerial Economics

b. Incentives for Motivating Individuals.

Example: What is the best way to motivate Meg Whitman, CEO of Ebay? 5. Recognize the Time Value of Money.

a. Discounting the Future.

b. Calculating Net Present Value of a Project

Example: Suppose that a firm expects to net an extra $10,000 in yearly

earnings from the production of a machine for each of the next 3 years. Suppose that the interest rate is 8%. If the machine costs $20,000 is it a good purchase? Preview__________________________________________________________

c. The present value of a firm/ Discounting over an infinite horizon

6. Appreciate Marginal Analysis Marginal decisions are an easy way to optimize totals. Calculus is just a formal expression of marginal analysis.

LECTURE______________________________________________

c. The present value of a firm. The discounting equation used last lecture can be

(20)

PV = ∑ πt

(1+i)t

Accounting for indefinite life. There is, however, one important complication. Unlike a

piece of equipment, firms are not expected to be finitely lived. In this case, the summation in the present value formula becomes infinite, e.g.,

PV = π0 + π1 + π2 + π 3 + …

(1+i)1 _(1+i)2 _(1+i)3

We can still come up with a finite present value if we assume that the stream of revenues each period is fixed. That is, consider a “perpetuity” e.g,. a constant cash flow (“CF”) that, starting one year from today, will be paid to you the first day of each year, forever. The present value of that flow is

PV = CF + CF + CF + …

(1+i)1 _(1+i)2 _(1+i)3

Notice, that as long as i > 0, terms get smaller as we get further into the future. It is well known that the present value of such a perpetuity can be expressed simply as

PV = CF/i

Similarly, for a firm generating a constant profit

PV = π/i

Notice that the above PV formula excludes a payment received now (e.g., at time 0).The PV of a stream of returns starting today is

PV = π/i + π= [(1+i) π]/i

You must always be careful to stipulate the timing of the first payment when doing PV calculations.

Note: Your text discusses extensions of this model. In this class you will be responsible only for the material covered above.

6. Using Marginal Analysis. A final principle in intelligent decision-making pertains to

the unit of analysis used. One can often cut through a very difficult optimization process by confining attention to incremental changes.

a. Discrete Decisions. Example. Suppose you were faced with the problem of trying to allocate study time between two courses for a test on the same day. If you had a total of 6 hours to study, you might have the following possibilities.

(21)

Econ Math

Hours score Hours score

0 0 0 0 1 30 1 40 2 55 2 65 3 75 3 77 4 93 4 86 5 98 5 94 6 100 6 100

(22)

One way to approach this problem would be to consider all combinations of all totals that were available:

Scores

Total

Econ

Math

Econ

Math

0 6 0 100 100 1 5 30 94 124 2 4 55 86 141 3 3 75 77 152 4 2 93 65 158 5 1 98 40 138 6 0 100 0 100

An equivalent solution, however, is obtained by considering just the marginal changes A marginal change is the change in the total associated with studying an extra hour. Econ Math

Hour score marginal increase

hour score marginal increase 0 0 0 0 1 30 30 1 40 40 2 55 25 2 65 25 3 75 20 3 77 12 4 93 18 4 86 9 5 98 5 5 94 8 6 100 2 6 100 6

Note: This process has the advantage that it requires less information.

Lecture 4 Problems: Return Problem Set 1,

Problem Set 2 – due Monday. REVIEW

I. Chapter 1. The Fundamentals of Managerial Economics B. Components of Effective Decision Making

5. Recognize the Time Value of Money.

a. Discounting the Future.

b. Calculating Net Present Value of a Project

Comment: Recall problem 1. A student asked if in deciding whether to

undertake a project, it made a difference if the net present value if a project was less than the cost the project. I ERRED IN MY RESPONSE. The correct answer is: ANY

(23)

To see this, suppose you are given the chance to invest $100,000 in a project that will yield $60,000 for each of the next two years. If i=.10, then the PV of the returns is

60,000/1.1 + 60,000/1.12

=54,540 + 49,587 =104,132.

The Net Present value is 104,132-100,000 = 4,132. (That is, you end up with 4,132 MORE than 100,000 in present value terms.)

Suppose, alternatively, that you took the 100,000 and put it in the bank for two years. If i = .10, you would have 110,000 after one year, and $121, 000 after two years. The present value of that money is (by definition) $121,000/(1.1)2_{= 100,000}

c. The present value of a firm/ Discounting over an infinite horizon. With the first payment coming in one year,

PV = π/i

If the first payment is tomorrow,

PV = π/i + π= [(1+i) π]/i

Example: Suppose you can purchase a share of a firm that will pay a dividend of $10 each year, starting one year from today. If the discount rate is . 05, what is the present value of this stock?

10/.05 = $200.

How would your answer change if the first payment came tomorrow?

10/.05 + 10 = $210.

5. Appreciate Marginal Analysis. Marginal decisions are an easy way to

optimize totals that require less information in the decision-making process.

a. Discrete Decisions

- Allocating time for a test

Preview__________________________________________________________

5. Marginal Analysis Continued - Comparing TR to TC b. Continuous Decisions

(24)

5. Using Marginal Analysis. A final principle in intelligent decision-making pertains to

the unit of analysis used. One can often cut through a very difficult optimization process by confining attention to incremental changes.

a. Discrete Decisions. Example. Suppose you were faced with the problem of trying to allocate study time between two courses for a test on the same day. If you had a total of 6 hours to study, you might have the following possibilities.

Econ Math

Hours score Hours score

0 0 0 0 1 30 1 40 2 55 2 65 3 75 3 77 4 93 4 86 5 98 5 94 6 100 6 100

(25)

One way to approach this problem would be to consider all combinations of all totals that were available:

Scores

Total

Econ

Math

Econ

Math

0 6 0 100 100 1 5 30 94 124 2 4 55 86 141 3 3 75 77 152 4 2 93 65 158 5 1 98 40 138 6 0 100 0 100

An equivalent solution, however, is obtained by considering just the marginal changes A marginal change is the change in the total associated with studying an extra hour. Econ Math

Hour score marginal increase

hour score marginal increase 0 0 0 0 1 30 30 1 40 40 2 55 25 2 65 25 3 75 20 3 77 12 4 93 18 4 86 9 5 98 5 5 94 8 6 100 2 6 100 6

Note: This process has the advantage that it requires less information.

More generally, we might consider a situation in which there were both costs and benefit (for example the case of profit maximization, where

π = TR - TC Control Variable

TB

TC

NB

MB

MC

MNB

0 0 0 0 1 90 10 80 90 10 80 2 170 30 140 80 20 60 3 240 60 180 70 30 40 4 300 100 200 60 40 20 5 350 150 200 50 50 0 6 390 210 180 40 60 -20 7 420 280 140 30 70 -40 8 440 360 80 20 80 -60 9 450 450 0 10 90 -80

(26)

10 450 550 -100 0 100 -100

Definition: The Marginal Principle: To maximize net benefits, the manager should increase the managerial control variable to the point where marginal benefit equals marginal costs.

Graphically, this can be illustrated both by graphs of totals and of marginal changes: Total changes 0 100 200 300 400 500 600 0 1 2 3 4 5 6 7 8 9 10 Output T C T B 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 Output M B , M C

Observe the role of marginals and totals.

(Notice that the totals and marginal lines should not line up exactly. There are two points of total maximization. This is due to the discreteness of decisions here. )

Lecture 5 Problems: Problem Set 2 – due Monday.

(27)

5. Appreciate Marginal Analysis. a. Discrete Decisions

- Allocating time for a test. (Recall the point, making the best incremental decisions at each step in a sequence will drive you to the maximum total.

- Comparing TR and TC

On a graph, the point where π is maximized is where the difference between TR and TC is maximized. This is also the point where MR =MC. The DISTANCE between TR and TC equals the AREA above MC and below MR (We will use this to show that equilibrium is efficient in Chapter 2.)

Note, however, in your homework that your marginals never quite line up. This is a problem with discrete analysis. Your rule in such a case is to take (produce) the last unit such that MR>MC. Example: Q TR TC TNB MR MC MNB 0 0 1 -1 1 19 3 16 19 2 17 2 36 9 27 17 6 11 3 51 19 32 15 10 5 4 64 33 31 13 14 -1 5 75 51 24 11 18 -7 6 84 73 11 9 22 -13

If you plot this you will see that MR and MC never equal, given we are restricted to discrete changes. In a continuous world, we could find an exact answer..

Preview__________________________________________________________

5. Marginal Analysis Continued b. Continuous Decisions c. Incremental Decisions

LECTURE______________________________________________

b. Continuous Decisions. Notice that in some circumstances, it is possible to make adjustments more continuously

Notice in my graphical analysis that my graphs are always a bit off. This is a problem of discreteness.

(28)

More generally, we might consider a situation in which there were both costs and benefit (for example the case of profit maximization, where

π = TR - TC

Now, suppose that I tell you that in the problem in the introduction that TR = 20Q – Q2

and that TC = 1 + 2Q2 _{I could come closer to finding the optimum if I used a finer grid.}

For example, suppose I reduce Q steps to .5

Q TR TC TNB MR MC MNB 0 0 1 -1 0.5 9.75 1.5 8.25 9.75 0.5 9.25 1 19 3 16 9.25 1.5 7.75 1.5 27.75 5.5 22.25 8.75 2.5 6.25 2 36 9 27 8.25 3.5 4.75 2.5 43.75 13.5 30.25 7.75 4.5 3.25 3 51 19 32 7.25 5.5 1.75 3.5 57.75 25.5 32.25 6.75 6.5 0.25 4 64 33 31 6.25 7.5 -1.25

What if I wanted to find the exact maximum? I could do this by taking a infinitesimal changes. Let’s do this in parts. Start with the Total Revenue relationship.

TR = 20Q -Q2

Consider the slope of the line tangent to the curve at Q=4.

Q TR 0 0 1 19 2 36 3 51 4 64 Graphically,

(29)

0 20 40 60 80 100 120 0 2 4 6 8

Consider the slope of the line tangent to the curve at Q =4. We could estimate this by calculating the average slope over progressively narrower ranges, e.g.,

(64 - 0 )/(4 - 0) = 64/4 = 16 (64 - 19 )/(4 - 1) = 45/3 = 15 (64 -36 )/(4 - 2) = 28/2 = 14 (64 -51)/(4 - 3) = 13/1 = 13

If we really wanted the slope of the line tangent to the curve, we must take an infinitesimally small change -h. Then

64 - [20(4-h) - (4-h)2_] 4 -(4-h) = 64 - 80 + 20h +16 – 8h + h2 h = _Q 2_+12h h

and as h → 0 this becomes 12.

This is the idea of a derivative. The only difference between taking limits, and the rules of derivation that you learned is that the rules are just a shorthand, for example,

TR = 20Q -Q2

TR' = MR =20 - 2Q At Q = 4, TR'= 12.

(30)

You could do the same thing for costs TC = 1+2Q2

TC = MC = 4Q

This is the slope of the line tangent to the TC curve To maximize profits, set MR = MC

TR = 20 – 2Q = 4Q = TC

Q = 20/6 = 3.33

Comments

a) I assume that you all have been exposed to simple differential calculus. The above development was done only to complete a little intuition pertaining to calculus. In the event that your calculus is a bit rusty, I can assure you that with only a few exceptions, our derivatives will be restricted to the following functional forms.

Derivative of a constant f(x) = a; f’(x) = 0

Derivative of a linear equation f(x)= ax; f’’(x) = a

Derivative of an exponential function f(x) = xn_{; f’(x) nx}n-1

You may also find it useful to recall the following: f(x) = g(x) + h(x); f’(x) = g’(x) + h’(x)

f(x) = g(x)h(x); f’(x) = g’(x)h(x) + h’(x) g(x) f(x) = g(h(x)) = g’(h(x))h’(x)

b) Finally, in your homework, I would like for you to report your marginal revenue and marginal costs as derivates, rather than as incremental changes.

Lecture 6 Problems: Collect Problem Set 2.

(Other review problem, 2, 3, 5, 8, 10)

(31)

5. Appreciate Marginal Analysis. a. Discrete Decisions b. Continuous Decisions

TR = 10Q – Q2_{and that TC = .25Q}2 _{(In problem 2). I can see the relationship of}

marginals to the totals on the marginals graph, as well as on a totals graph. But we also learned the idea of a derivative, which is just a slope over an infinitesimally small range. Derivative of a constant

f(x) = a; f’(x) = 0

Derivative of a linear equation f(x)= ax; f’’(x) = a

Derivative of an exponential function f(x) = xn_{; f’(x) nx}n-1

You may also find it useful to recall the following: f(x) = g(x) + h(x); f’(x) = g’(x) + h’(x)

f(x) = g(x)h(x); f’(x) = g’(x)h(x) + h’(x) g(x) f(x) = g(h(x)) = g’(h(x))h’(x)

Preview__________________________________________________________

c. Incremental Decisions Some review problems.

LECTURE______________________________________________

Incremental analysis: For many (if not most) decisions, the manager must make a binary

(yes or no) choice. In that case, the tools described above are appropriate. However, rather than considering the entire set of possibilities, consider only the changes from the status quo, and determine whether the incremental change is desirable. The trick to this

incremental analysis is to attend only to the things that actually change with the decision,

and ignore the rest.

One practical way express this is the following:

a) In making a decision pay attention to marginal costs and marginal benefits b) In making a decision, pay attention only to marginal costs and marginal benefits (That is, ignore sunk costs)

Example, suppose you wait in a line in a grocery store. Another line opens up. What

(32)

Example; Suppose you have a 12 month lease on an apartment. You must pay $700 per

month. If you get a new job in May that forces you to leave town in May and if your lease runs through August, how much, at a minimum must you get to sublease the apartment? (Answer, you must cover any variable costs, and nothing more!)

Example: A more involved example. Suppose you manufacture umbrellas, and you are

deciding whether or not to purchase a new “game day” golf umbrella, which is big enough to keep the entire family dry in a halftime downpour.

The new machine costs $40,000. For simplicity, we assume that the machine lasts one year, and is then useless. You can put the machine in a slot where a now defunct standard machine sits. Old machine removal and recycling costs are $5,000, and must be borne independent of whether or not you buy the new machine.

Installation costs for the new machine are $4,000. Variable costs for the new umbrellas are $8 per umbrella for materials and energy and $4 per umbrella for labor. Suppose that you can reasonably expect to sell 2000 of these umbrellas next year, at $35 each. Is the machine a good investment?

Incremental revenues are ($35)(2000) = $70,000 Incremental Costs are

$40,000 new machine $4,000 installation

$24,000 variable expenses ($12)(2000) $68,000

Result: Yes, purchase the machine. Notice, however, that the $5,000 removal expenses should not be considered in this analysis.

Lecture 7

REVIEW___________________________________________________:

c. Incremental Decisions

In attempting to optimize, two rules:

- Attend to marginal benefits, attend to marginal benefits and marginal costs. -Attend only to marginal benefits and marginal costs. (Ignore sunk costs) Preview__________________________________________________________

1. Overview

(33)

1. Motivation: Diminishing marginal utility:

2. Definition of Demand Curve 3. Determinants of Demand.

4. Changes in demand vs. changes in qty demanded.

LECTURE______________________________________________

A. Introduction and Overview.

1. Overview. The purpose of this chapter. Economics proceeds via models. A model is

an abstraction from reality, done for the purpose of explanation, or prediction. It is important to emphasize that these models are necessarily unrealistic. A “model” that captured all the complexity of reality wouldn’t be useful at all. Rather the

oversimplification of a model is useful if it serves effectively an explanatory or predictive function.

For example, the first model presented in this class was the present value characterization of the firm, introduced in chapter 1. This model, of course misses many elements,

including the uncertainty of returns over time, as well as the possibility that interest rates may change. Nevertheless, it is useful in that it provides some insight into the issues relevant to considering the inter-temporal value of a firm.

This chapter presents a second model, the theory of price and quantity

determination. This model should be a review for most of you. Nevertheless, it is of prominent importance. The purpose of this model is both explanatory and predictive. It is the primary tool that you can use to infer the effects of market impacts on prices and outputs. You are expected to master the mechanics of this model.

A second function of this review is to present this model in simple algebraic terms. This presentation should help “acclimatize” you to the type of analysis we will do in this course.

a. Overview. In this model, we divide people into two groups

i. Households: Who attempt to maximize utility, they face diminishing marginal

utility, and are subject to a budget constraint.

ii Firms: Attempt to maximize profits. Firms fact cost constraints, and are subject

to a law of diminishing returns in production.

We will look at Demand (household behavior) Supply (firm behavior) and equilibrium, the interaction of these parts that generates price and output predictions

1. Motivation: Consider an example of consuming a good. Suppose that it’s 100 degrees

(34)

jump in the car, turn the heater up to full blast, and drive 3 hours in the sun. At the end of all this, you 1/2 dozen chili peppers. Now stop at a gas station and purchase cans of Sprite, one by one. Consider how much you would pay, for the first can, for the second, the third, and etc. The fact that you are gradually getting full is the notion of

diminishing marginal utility.

Diminishing marginal utility: In a given time frame, consumption

of additional units of a good yields decreasing increments to total well being due to relative satiation (fullness).

2. Definition (for output market):

The Demand Curve: A curve indicating varying quantities of a good or service that

consumers are ready, willing and able to purchase at varying prices, per unit of time, other things constant. Demand is down-sloping due to the diminishing marginal utility of consumption.

There are a number of important components in this decision

a. Price/Quantity relationship: Price is the most important determinant of Quantity

b. Ready, willing and able: Defines the market.

Ready - in the market. Willing - desires the good. Able - has the wherewithal.

c. Per unit of time: Time must be specified, as it affects diminishing marginal utility.

d. Other things constant. A number of things aside from the price affect qty purchased (including substitutes, complements, and advertising, and etc.)

e. Down-sloping due to diminishing marginal utility (Fullness). This is the reason that there is an inverse relationship between price and quantity.

3. Determinants of Demand. Things that affect the Marginal Utility of purchasers in

the market. In addition to price, determinants include: Ps -Price of substitutes

Pc Price of complements

I Income (Normal goods or Inferior goods) E Expectations (regarding relative future prices B Number of buyers (population)

4. Changes in demand vs. changes in qty demanded. When one of the non-price

determinants of demand changes, it is necessary to draw a new demand schedule. This is known as a change in demand (schedule). When there is a change in price, other things held constant, this is called a change in quantity demand (a movement along a schedule)

(35)

Example, consider Qd = f(P, Ps, Pc, I)

This is a demand function. It is a relationship between quantity demanded, and the entire collection of elements that determine sales quantity. The demand curve is a relationship between price and quantity alone, holding all other elements constant.

Suppose income increases. Then it would be necessary to shift the demand schedule. Note: The one thing that CANNOT change demand (curve) is a change in the price of the good!

Lecture 8

REVIEW___________________________________________________:

1. Overview

2. The structure of the supply and demand model. B. The Demand Side.

1. Motivation: Diminishing marginal utility:

2. Definition of Demand Curve 3. Determinants of Demand.

4. Changes in demand vs. changes in qty demanded.

Preview__________________________________________________________

5. The Notion of Consumer Surplus 6. An Analytical Example

LECTURE______________________________________________

4. Changes in demand vs. changes in qty demanded. When one of the non-price

determinants of demand changes, it is necessary to draw a new demand schedule. This is known as a change in demand (schedule). When there is a change in price, other things held constant, this is called a change in quantity demand (a movement along a schedule)

Example, consider Qd = f(P, Ps, Pc, I)

(36)

This is a demand function. It is a relationship between quantity demanded, and the entire collection of elements that determine sales quantity. The demand curve is a relationship between price and quantity alone, holding all other elements constant.

Suppose income increases. Then it would be necessary to shift the demand schedule. Note: The one thing that CANNOT change demand (curve) is a change in the price of the good!

5. The Notion of Consumer Surplus In markets where all consumers pay a uniform price

for a good, most of the consumers who purchase the good place a higher value on the product than the purchase price. This difference between purchase price and value is termed consumer surplus.

P $8

Consumer Surplus for unit Q1

$5

D Q1 10 Q

For example, a consumer who values unit Q1 at $8 and pays $5 for the unit enjoys a

consumer surplus of $3. Notice that the entire consumer surplus for the market is the area between the demand curve and the price.

Notice that in some contexts, it is possible for a seller to collect some of the consumer surplus realized in a single-price market. In particular, the seller may sell “packages” of units at a higher price than single quantities of the same unit, to achieve a given sales total. (We will discuss this later in the semester.

6. An analytical example

Consider the following, simple demand function. Qd = 10 - 2P + .33I.

Suppose I=30, then the demand curve can be written as Qd = 20 - 2P

Or inverse demand: P = 10 - Q/2

This is shown as D on the figure below D

(37)

0 2 4 6 8 10 12 14 16 0 5 10 15 20 25 D D' If I increases to 60 then Qd = 10 - 2P+ .333(60) Qd = 30-2P So inverse demand is

P= 15-Q/2, illustrated as D’ in the above figure.

Suppose that the price is $5. How much consumer surplus to consumers receive at that price?

When 15-Q/2 = 5, Q = 20. So the area of the C.S. triangle is (.5)(15-5)(20) = 100

(38)

0 2 4 6 8 10 12 14 16 0 5 10 15 20 25 D D' 15-5 20 Lecture 9 REVIEW___________________________________________________:

II. Chapter Market Forces: Demand and Supply B. The Demand Side.

5. The Notion of Consumer Surplus 6. An Analytical Example

Preview__________________________________________________________

1. Driving Force. The Law of Diminishing Returns

2. Definition of Supply Curve

3. Determinants of supply:

4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus.

LECTURE______________________________________________

C. The Supply Side. In output market, this defines the behavior of sellers,

1. Initial assumption. Firms are motivated by the profit incentive, but constrained by

(39)

Example, consider conditions under which you would produce for sale quartz lamps from your uncle's shack in Southern Montana. As the amount of variable inputs (quartz, and workers) increases, the room should become “crowded,” and unit costs should increase as more variable inputs (labor) becomes “imbed” in each unit of output. This, we would expect, there would be a direct relationship

2. Definition

The supply curve: A schedule of intentions indicating varying quantities of a good

or service that sellers are ready, willing and able to place on the market at varying prices, per unit of time, other things constant. The supply curve is upsloping due to the law of diminishing returns (“crowding”)

Important elements

a. Schedule of intentions: An estimate

b. Price/Quantity relationship: Price is the most important determinant of quantity.

c. Ready, willing and able: Defines the market of relevant suppliers. Ready: Has access to market.

Willing: Is a reasonable use of resources, Able: Has productive means

d. Per unit of time: Time must be specified, as it affects LDR. e. other things constant.

f. Upsloping due to the law of diminishing returns (crowdedness)

3. Determinants of supply: Things other than the price that affect how r.w. and a. sellers

are to offer goods to the market. As a class, these are things that affect production costs Technology

Factor prices.

NUMBER OF SELLERS.

Price expectations (e.g. hold grain in silo if price is expected to increase next year).

Taxes (excise or ad valorem)

4. Changes in supply vs. changes in quantity supplied.

Definition. (As with demand): A change in quantity supplied occurs in response to a change in the price of a good, all other things held constant.

A change in supply occurs in response to a change in something other than price. Again, price is, by definition, the one thing that cannot change supply.

(40)

a. Definition Symmetric to the notion of consumer surplus, in a market where a single price is charged for all transactions, producers typically receive more from a sale than is necessary to induce them to offer a unit to the market.

P

S $5

Producer Surplus for unit Q1

$3 D Q1 10 Q

The producer surplus for unit Q1 is $5 - $3 = $2. The producer surplus for the market is

the triangle bounded by the vertical axis, the production cost, and the price. b. Observations

-Producer surplus is not the same as profit. We will talk about this more later, when we discuss the theory of the firm.

-There are ways for a savvy purchaser to extract producer surplus in making purchasing decisions. Similar to demand, this is typically accomplished via bulk purchases.

Lecture 10

REVIEW___________________________________________________:

II. Chapter Market Forces: Demand and Supply C. The Supply Side.

1. Driving Force. The Law of Diminishing Returns

2. Definition of Supply Curve

3. Determinants of supply:

4. Changes in supply vs. changes in quantity supplied. 5. Producer Surplus.

Preview__________________________________________________________ 6. An Analytical Example.

D. Equilibrium. Putting Supply and Demand Together 1. Definition.

(41)

2. Binding the market. Price floors Price ceilings

LECTURE______________________________________________

6. An analytical example. Consider the market supply schedule for small laser-light

paper erasers. The supply function is given by Qs = -44 + 20P - 4W - 2M, where

P = the price of the erasers

W = the average hourly wage for labor M = an index measuring materials costs.

If W = 10 and M = 8, what is the market supply curve? Qs = -44 + 20P - 4(10) -2(8)

= -100 + 20P, thus Inverse supply becomes

P = 5 + .05Q Plotting in a table Q P 5 5.25 10 5.5 15 5.75 20 6 25 6.25

Now, suppose that M increases to 18, then what happens to supply, or to quantity supplied?

Qs = -44 + 20P - 4(10) -2(18)

= -120 + 20P, thus There is a change in supply P = 6 + .05Q Q P 5 6.25 10 6.5 15 6.75 20 7

(42)

25 7.25

Alternatively, suppose that P increases from 6.5 to 17what happens to Q? There is a change of quantity supplied from 10 to 20.

5 5.5 6 6.5 7 7.5 8 8.5 0 10 20 30 40 50 S1 S2 Graphically Q P1 P2 0 10 15 2 9 14 4 8 13 6 7 12 8 6 11

1. Definition. Equilibrium : A price quantity combination where Qs = Qd, and where Ps =

Pd.

Analytically. Suppose Qd = 100 - 4P +10I, and

Qs = 10 + 6P -3W

If W = 30, I =10, what are equilibrium values? Qd = 100 - 4P +10(10), and

Qs = 10 + 6P -3(30)

Qd = 200-4P

(43)

Setting Qd = Qs implies that P Qd Qs 15 140 170 14 144 164 13 148 158 12 152 152 11 156 146 10 160 140 9 164 134

Observe at a price of 15 dollars, there is a surplus, Qs = 170 > Qd = 140. Conversely, at a

price of $9, there is a shortage, Qd = 164 > Qs = 134.

2. The stability and desirability of equilibrium. Absent a tendency for markets to

equilibrate (or given regulations which prevent such convergence), the surplus or shortages just discussed would be permanent. However, markets do equilibrate. Given excess supply the sellers have an incentive to reduce prices. This price reduction

prompts changes in quantity supplied and quantity demanded. Similarly, given an excess demand, buyers have an incentive to bid prices up, again causing a change in quantity supplied and quantity demanded.

Importantly, if the assumption of ‘pure privacy’ is satisfied, the equilibrium outcome is also socially desirable. Given an absence of externalities, the TC curve equals TSC and the TB curve equals TSB. Thus, D=MSB and S=MSC. At the equilibrium, where S=D, the net difference between TSB and TSC are maximized.

3. Binding the market. Permanent shortages and surpluses can be caused by regulation.

A price floor: A regulated minimum price, below which the market price cannot

fall. If the floor is below the equilibrium, the regulation exerts no effect. If the floor is above the equilibrium, there is a permanent shortage that the market cannot eliminate.

a. Example. A price floor: Suppose the government refuses to let cheese be sold for less than $3.00 per pound. Result: A permanent surplus, and one that cannot be resolved by the market

A price ceiling: A regulated maximum price, above which the market price

cannot rise. If the floor is above the equilibrium, the regulation exerts not effect. If the floor is below the equilibrium, there is a permanent shortage that the market cannot eliminate.

b. Example: A Rent control. Result: A shortage of housing, and one that cannot be resolved by the market.

(44)

Complications: One solution by sellers is to force multiple purchases (e.g., Impose a price ceiling on rents, but then make people agree to unusual lease terms, or to purchase other high cost items along with the lease). In fact, it is possible that given rent controls, the non-monetary components associated with increasing the price of a good may generate a full price for each consumer that equals the total market consumer surplus.

Notice that when a ceiling binds the market, the full economic price is the sum of the pecuniary plus the non-pecuniary price (e.g., the price of waiting, purchasing undesired packages of goods, etc.) In general, with a price ceiling, buyers who purchase a good will pay the demand price, at the restricted quantity. For example

P Pf Pc S D Qc Q

Given a Price ceiling Pc, Qc units will be sold. The full economic price paid by buyers

will equal Pf.

There are parallel examples in input markets (where the government acts more aggressively).

Usury laws (a market for loanable funds) Minimum wage legislation.

The point: Equilibrium is a socially desirable outcome. We interfere with the workings of a competitive market at our peril!

Lecture 11

REVIEW___________________________________________________:

II. Chapter Market Forces: Demand and Supply

D. Equilibrium. Putting Supply and Demand Together 1. Definition.

2. The Stability and desirability of equilibrium 3. Binding the market.

(45)

Price ceilings

Point: Binding the market imposes high social costs

Preview__________________________________________________________ E. Comparative Statics.

1. Single market changes. 2. Multiple Market Changes III. Quantitative Demand Analysis

A. Price Elasticity of Demand 1. Motivation

LECTURE______________________________________________

E. Comparative Statics. Given the tendency of markets to converge to competitive

predictions in an unfettered and competitive market, we can use this model to predict the effects of changes in the world.

1. Single market changes.

Strategy: To find the new equilibrium, consider the old equilibrium price, and the new equilibrium supply and demand curves. Then shortages or surpluses will motivate an adjustment.

a. Change in demand, supply stable.

Example, suppose the price of coffee falls by half. What should this do to the market for pastries?

Example: What should the current economic recession do to the price and quantity of automobiles sold?

b. Change in supply, demand stable

Example: Suppose a new process for manufacturing computers is developed that cuts production costs by 50%. What is the predicted effect on the number of computers sold, and the price of computers?

c. Change in supply and demand… (and ambiguous effects).

Example: Suppose software costs fall, and that at the same time a new Pentium X chip is developed that can be installed to do twice as much at 1/2 the price. What is the net effect of these changes on the price and quantity of personal computers sold?

Example: Consider the market for cheese produced by U.S. farmers. Suppose that due to the flooding in Northern Europe, Farmers in the Netherlands lose half of

(46)

their dairy herd. Suppose also that new environmental deregulation cuts

production costs in half. What are the net effects of these changes on the market for cheese produced by U.S. Farmers?

A more complicated story variant: Consider the above problem, but suppose that at the outset the U.S. government imposed a price floor for cheese that at the initial equilibrium. How does the price ceiling affect results?

Lecture 12

REVIEW___________________________________________________:

II. Chapter Market Forces: Demand and Supply

D. Equilibrium. Putting Supply and Demand Together Equilibrium is

1. Stable

2. Socially desirable E. Comparative Statics.

1. Single market changes. 2. Multiple Market Changes

Preview__________________________________________________________ III. Quantitative Demand Analysis

A. Price Elasticity of Demand 1. Motivation

2. Calculation

a. Arc price elasticity of demand: b. Point price elasticity of demand c. Percentage Changes

Lecture ______________________________________________________

III. Chapter 3. Quantitative Demand Analysis

Introduction: In the preceding chapter we reviewed the basic supply and demand model

used to predict price and quantity outcomes. This model is an extremely useful device for making qualitative predictions. An important limitation of the model as it has been presented, however, is that it does not allow quantitative predictions. For quantitative predictions, it is necessary to more fully characterize the arguments in the demand and supply functions.

We start with demand in this chapter. The presentation is divided into two parts. The first will deal with the quantitative conclusions that may be fairly limited elasticity

(47)

information. In the second part, we turn more comprehensive analysis of demand estimation via the use of regression.

A. Price Elasticity of Demand

1. Motivation: Elasticity this is a tool for estimating responsiveness of some dependent variable to a change in a dependent variable, based on very little information.

Definition: Elasticity: The percentage change in an independent variable brought about by a 1% change in an independent variable.

Intuitively, elasticity may be regarded as a measure of sensitivity. If people are sensitive, we will say that they are elastic. If they are insensitive, we will regard them as

inelastic.

For concreteness, we will focus initially on price elasticity of demand (change definition accordingly)

Price Elasticity of Demand: The percentage change in Quantity Demanded brought about

by a 1% change in the price of a good, or

η = %∆Qd/%∆P = ∆ Q/Q = ∆ QP

∆P/P ∆PQ

2. Calculating Elasticity of Demand. There are three ways to calculate price elasticity of demand: arc price elasticity, point price elasticity, and direct percentage changes. The method that is appropriate in any particular context depends on the information provided.

a. Arc Price Elasticity. Applies to a discrete change. For example, consider the demand curve implied by the following table:

P Q 4 40 5 10 P 5 4 D 10 40 Q

(48)

Notice ∆Q may be calculated as Q1-Q0, and

∆P = P1-P0. Then η = (Q1-Q0)P/(P1-P0)Q

But it makes a big difference if you use (P0,Q0) as your divisor, or (P1,Q1).

For example:

(40-10) (4) = 30(4) = -3.00 (4-5) (40) -1(40)

(40-10) (5) = 30(5) = -15.00 (4-5) (10) -1(10)

Neither of these points is inherently more correct. As a convention, we calculate the arc price elasticity of demand using the average of the distance between the 2 points:

η = (Q1-Q0)(P1+P0)/2

(P1-P0)(Q1+Q0)/2.

In this case

= (40-10) (4+5)/2 = 30(4.5) = -5.4

(4-5) (40+10)/2 -1(25)

Arc Price elasticity is interpreted as follows: Over the range of prices between $4 and $5

on average, a 1% reduction in price increases quantity demanded by 5.4 %.

b. Point price elasticity: When you are given a slope, and a point. Insight η = (dQ/dP)(P/Q)

Example: Suppose a demand curve is Q = 30 - 10P

Then, if P = 2, then Q=10 and elasticity is -10 ( 2/10) = -2.

Uses: Mostly when given a demand function.

Point Price elasticity is interpreted as follows: At a price of $2 a 1% reduction in price

(49)

c. Percentage changes. For rough policy purposes. Insight η = (%∆Q)/(%∆P)

Example. Suppose that beer sales at Joe's Inn increased 20% in response to a “half price” (50% off night). What is the implied elasticity of demand?

-20/ 50 = -.4

Example: Suppose that Joe sells 400 beers per day. What would be the effect of a 10% increase in beer prices on his sales?

-.4 = %∆Q/10 implies 4 % decrease, or a decrease of .04(400) = 16 beers per day.

Lecture 13

REVIEW___________________________________________________:

II. Chapter Market Forces: Demand and Supply A. Price Elasticity of Demand

1. Motivation 2. Calculation

a. Arc price elasticity of demand:

Example: If Rick Redfern reduces the price of potato chips from $2 per bag to $1 per bag, and if daily sales increase from 10 to 15, what is the arc price elasticity of demand?

η = (10-15)(2+1) = -5(3) = -3/5 (2-1) (10+15) 1(25)

b. Point price elasticity of demand

Example: If demand is given by

Q = 100 – 10P and P = 6, what is price elasticity of demand?

η -10 (6)/40 = -1.5

(Notice: If P = 4, elasticity becomes

η -10 (4)/60 = -.67

A preview: Price elasticity changes with position on the demand curve.