Unit 3: Production and Cost – Problems
3.1: Production
CORE PROBLEMS
Problem 1
The following table shows total output (tax returns completed per day) for an accounting firm, as it depends on the number of accountants who are hired.
Accountants Returns
0 0
1 5
2 12
3 17
4 20
5 22
a. Calculate the marginal product of each accountant.
b. Over what range of employment are there increasing marginal returns to labor? c. Over what range of employment are there diminishing marginal returns to labor?
3.2: Short-run costs
CORE PROBLEMS
Problem 1
A firm can hire capital for $4 per unit and can hire labor for $3 per unit. Its production function is shown. Fill out the table below with the corresponding short-run cost functions for the firm.
K L Q TFC TVC TC AFC AVC ATC MC
16 1 6 --
16 4 8
16 9 10
16 16 12
16 25 14
Problem 2
Reconstruct the rest of this firm’s short-run cost functions based on the information given in the table below.
Q TFC TVC TC AFC AVC ATC MC
0 100 0 -- -- -- --
1 150
2 280
3 380
4 500
5 630
Problem 3
The questions in this problem refer to the diagram below, which shows the cost functions for a designer named Leo who produces toy trains.
a. At an output of three trains per week, what are average total cost and average variable cost? b. As output rises from four to seven trains, is marginal cost rising or falling?
c. At an output of four trains, is marginal cost higher or lower than average total cost? Is average total cost increasing or decreasing at this output level?
d. What is the minimum value of average total cost? At what output level is it achieved? e. At what level of output are marginal cost and average total cost equal?
f. How many trains should Leo produce if he wants his average total cost to be $50? g. How many trains should Leo produce if he wants his marginal cost to be $55? h. Average fixed cost is the vertical distance between which curves?
i. At an output of 3 trains per week, what is average fixed cost? j. At an output of 3 trains per week, what is total fixed cost?
k. Over what range of output are there diminishing marginal returns?
Problem 4
The cost of a license paid by a business to operate inside of a county increases from $400 per year to $500 per year.
a. What effect will this increase have on the firm’s marginal cost?
SUPPLEMENTARY PROBLEMS
Problem 5
Find four things wrong with the diagram below.
Problem 6
You are an auditor and a firm reports to you the cost data given below. Explain why these data must be incorrectly reported.
Q AVC ATC
1 10 44
2 12 28
4 16 26
6 24 31
Problem 7
You already sold 200 doses of a new medicine you developed. Here is your average total cost schedule.
Q ATC
199 $199
200 $200
201 $201
Problem 8
A producer of ink bottles spills ink all over his cost data! Help him by reconstructing the rest of the table below.
Q TFC TVC TC AFC AVC ATC MC
0 -- -- -- --
10 20
20
30 390 11
40 420
50 2 14
Problem 9
A cake manufacturer is currently making 10 cakes every day. The marginal cost of the 10th cake is $24 and the average total cost of producing 10 cakes is $6. What is the average total cost of producing 9 cakes?
Problem 10
3.3: Long-run costs
CORE PROBLEMS
Problem 1
The questions in this problem refer to the diagram below, which shows the long-run average total cost curve, along with several short-run average total cost curves for a firm that produces pretzels. The owner currently is producing 10 pretzels per day, but the manager suggests increasing production to 20 pretzels per day immediately.
a. In the short-run, what point will represent the firm’s cost situation if the owner follows the manager’s advice?
b. If the owner continues to produce 20 pretzels per day, what point will represent the firm’s cost situation over the long-run? How can it get there?
c. Eventually the company does very well and expands its output to 70 pretzels per day. But the company then wants to scale back to 20 pretzels per day again. The owner wants to scale back production by laying off workers and renting less space. But the manager suggests reducing output just by cutting back on raw materials and laying off workers. Who’s right? Discuss with reference to the curves shown here.
Problem 2
A firm can choose between two different methods of production.
METHOD 1: Fixed cost of $10 and marginal cost of $3 per unit METHOD 2: Fixed cost of $20 and marginal cost of $1 per unit.
a. Calculate the firm’s total cost and average total cost if it produces using method 1.
Q TC ATC
1 2 3 4 5 6 7 8
b. Calculate the firm’s total cost and average total cost if it produces using method 2.
Q TC ATC
1 2 3 4 5 6 7 8
c. Show the firm’s long-run average total cost curve.
Q LRATC
