SHORT-RUN PRODUCTION
TRUE OR FALSE STATEMENTS
1. According to the law of diminishing returns, additional units of the labour input increase the total output at a constantly slower rate.
2. In the short-run all inputs are fixed.
3. If the marginal product is at its maximum, the output of the firm will be zero.
4. If we increase the labour input in the short-run, the output of the firm will increase as well.
5. If the output is decreasing, both the average product and the marginal product will be negative.
PROBLEMS
1. A certain product’s short-run production function is the following: Q=60L+12L2-L3.
a) Which levels of employment does ensure the maximal output, the maximal marginal product and the maximal average product?
b) Calculate the labour elasticity of production at L=8!
2. Hard Adam associate professor prepares microeconomic exercises. The only input of his work is time. The production function is Q=4L0,5, where Q is the number of exercises and L is the time of work.
a) Illustrate the production function of the exercises’ preparing!
b) Give the formulas of the average and marginal products!
c) Does the average product have an increasing part?
3. The following table contains the results of an agricultural process. Apart from the labour input, all inputs are fixed.
a) Calculate the marginal product and the average product of the labour input at any level of output!
b) At which level of labour employment do the diminishing returns occur?
c) At which level of input will the average product and the marginal product equal?
L Q APL MPL
2 100
3 160
4 224
5 280
6 330
7 370
8 400
9 425
4. Fill in the following table! Give the optimal level of input employment and the level of output at that case!
Labour Total Product (Q) Marginal Product (MP) Average Product (AP)
3 - 75
4 80
5
6 20 60
7 40
5. Let suppose a firm with the following production function: Q=2L0,75K0,25. a) Calculate the marginal products of both inputs!
b) Calculate the elasticity of production!
6. The following table contains numerical information about a firm’s short-run production.
Calculate the marginal and average products!
L Q APL MPL
0 0
2 25
3 45
5 70
7 84
9 90
10 91
7. Calculate the missing data of the following table!
L Q APL MPL
0
2 12,5
3
5 14 12,5
7
9 90 3
10
11 91 0
SOLUTIONS
1. Outputmax: 10. MPmax: L=4, APmax: L=6. At L=8 ε=0,652.
2. APL=4/20,5; MPL=2/L0,5.. The AP curve doesn’t contain upward sloping part.
3.
L Q APL MPL
2 100 50 -
3 160 53,3 60
4 224 56 64
5 280 56 56
6 330 55 50
7 370 52,86 40
8 400 50 30
9 425 47,22 25
4.
Labour Total Product (Q) Marginal Product (MP) Average Product (AP)
3 225 - 75
4 305 80 76,25
5 340 35 68
6 360 20 60
7 280 -80 40
Optimal labour employment: APL max (76,25). L=4.
5. MPL=1,5x(K/L)0,25; MPK=0,5x(L/K)0,75; εL=0,75; εK=0,25.
6.
L Q APL MPL
0 0 - -
2 25 12,5 12,5
3 45 15 20
5 70 14 12,5
7 84 12 7
9 90 10 3
10 91 9,1 1
7.
L Q APL MPL
0 0 - -
2 25 12,5 12,5
3 45 15 20
5 70 14 12,5
7 84 12 7
9 90 10 3
10 91 9,1 1
11 91 8,27 0
LONG-RUN PRODUCTION
TRUE OR FALSE STATEMENTS
1. It will be worth to increase the labour input at the expense of capital, if the marginal product of the labour is larger than the marginal product of capital.
2. Isoquant curve shows all the combinations of capital and labour that can be used to produce with a given total cost.
3. If the marginal product of a dollar’s worth of labour equals that of a dollar’s worth of capital, allocation of inputs will be optimal.
4. The increase of an input’s price doesn’t change the slope of the isocost curve.
PROBLEMS
1) A firm’s long-run production function is Q=3LK+300. The firm spends 3000 euro on the inputs. From this sum of money, it can apply maximum 10 workers (L). The price ratio of the inputs is PL/PK=1.
a) Calculate the optimal input allocation!
b) How will the combination of the two inputs change, if the budget of the firm increases by 20 percent?
c) Calculate the output of both cases!
d) Illustrate the isocost and isoquant curves and the optimal choices of the firm!
2) A company’s total cost is 2400 thousand Ft. Let suppose, that it can buy 4L or 8K inputs from this sum of money. The company’s production can be characterised with the following production function: Q=LK.
a) Determine the input allocation in this case!
b) How will the use of inputs change, if the price of the labour increases by one third?
c) Calculate the output in both cases!
d) Illustrate the isocost and isoquant curves and the optimal choices of the firm!
3) Let suppose, that only one combination (1:2) of L and K inputs can be used to produce a given product. The prices of the inputs are: PL=200, PK=100, the firm spends 10 000 euro on them.
a) Determine the input allocation in this case!
b) How does the resource allocation change after a 10 percent price rise of the L input?
c) Illustrate the isocost and isoquant curves and the optimal choices of the firm!
4) Let suppose, that only one combination (1:2) of L and K inputs can be used to produce a given product. The prices of the inputs are: PL=200, PK=100, the firm spends 10 000 euro on them.
a) Determine the input allocation in this case!
b) How will the resource allocation change, if the budget of the company decreases by 20 percent?
c) Illustrate the isocost and isoquant curves and the optimal choices of the firm!
SOLUTIONS
1. a) L0=5, K0=7,5. b) L1=6, K1=9. c) Q0=412,5, Q1=462.
2. a) L0=2, K0=4. b) L1=1,5, K1=4. c) Q0=8, Q1=10.
3. a) L0=25, K0=50. b) L1=23,8, K1=47,6.
4. L0=25, K0=50. b) L1=20, K1=40.
COSTS OF PRODUCTION
TRUE OR FALSE STATEMENTS
1. A company will achieve economic profit, if its accounting profit is larger than the accounting cost.
2. Depreciation is a non-accountable implicit cost.
3. Marginal profit curve will reach its maximum, if the marginal cost curve is at its minimum.
4. The average variable cost curve cannot intersect the average fixed cost curve.
5. The average total cost curve is located below the average fixed cost curve till a certain output level, after that point it is located above it.
6. The average variable costs curve intersects the marginal cost curve where it is located above the average fixed cost curve.
PROBLEMS
1. We know the annual data of a company:
Accounting profit 12800
non-accountable implicit cost 8400
Explicit costs 8600
Economic costs 17400
Calculate the accounting and implicit cost and the economic and normal profit of the company!
2. The economic cost of a company in the last year was 7500 thousand forints. The implicit cost was 1350 thousand forints, 350 thousand forints of the latter was accountable. Economic profit was 560 thousand forints.
Determine the accounting and explicit costs and the accounting and normal profits of the firm!
3. The mother of a business student quit her job that has been paying 50 thousand forints per month and starts her own business. She desires to start a book-keeping office. She hires two book-keepers with 50 thousand forints wages per person. The taxes on payments are 30 percent.
The rent of the office is 60 thousand forints per month. To furnish the office she borrows 1500 thousand forint from a bank. The duration of the loan is 5 years; expectedly the furniture wears out during that time. The interest rate on the loan is 20 per cent. According to her calculations the total revenue reaches 4000 thousand per year.
Determine the total, accounting and implicit cost and the profit of the enterprise!
4. Fill in the following table!
Q TC FC VC MC AC AFC AVC
0 60
1 80
2 115
3 155
4 210
5. Fill in the following table!
Production Variable cost Fixed cost Total cost Marginal cost Average cost
0 20 - -
1 45
2
3 10 22
4 17
SOLUTIONS
1) Accounting costs 9000; implicit costs 8800; economic profit 4400; normal profit 8400 thousand Ft.
2) Accounting costs 6500; explicit costs 6150; accounting profit 1560; normal profit 1000 thousand Ft.
3) Total costs 3480, accounting costs 2880; implicit costs 900; accounting profit 1120;
normal profit 600; economic profit 520 e Ft.
4)
Q TC FC VC MC AC AFC AVC
0 60 60 0 - - - -
1 80 60 20 20 80 60 20
2 115 60 55 35 57,5 30 27,5
3 155 60 95 40 51,6 20 31,6
4 210 60 150 55 52,5 15 37,5
5)
Production Variable cost Fixed cost Total cost Marginal cost Average cost
0 0 20 20 - -
1 25 20 45 25 45
2 36 20 56 11 28
3 46 20 66 10 22
4 48 20 68 2 17
