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Homework answers / question archive / Theory of Firms The market price of a car is $7K
Theory of Firms The market price of a car is $7K. Each machine costs $100K, and each labor costs $100K. A car producer ABC's production schedule is as below. The Production Function (Output) Number of Machines Labor 1 3 4 5 0 0 0 0 0 1 0 30 51 67 80 92 2 0 51 71 87 101 113 3 0 67 87 103 117 128 4 0 80 101 117 130 142 5 0 92 113 128 142 154 ??? ?? aloOOOOO (a) Consider short run. ABC has 2 machines. Fill the table below and answer the following questions. Output TFC TVC MC Car Price Total Revenue TC Profit 0 51 71 87 101 113 (Remark: MC=AC/AQ. Assume the MC of in between each two output levels in the table to be the same Eg, the MC of the first car is the same as the MC of the 12 car.) 1). How many cars will ABC produce and sell to maximize its profit? ABC will produce cars. 11). How much profit will it make? The profit is (b). Consider the long run. 1). Fix the number of labor to be 3. What is the Marginal Product of Capital of the 3rd machine? MPKE
11). Fix the number of machines to be 4. What is the Marginal Product of Labor of the 3rd labor? MPLE 111). Suppose the firm decided to produce 100 cars. If the firm finds at its current labor-machine combination MPK/Pk
1.
Price of car= $7K
Machine cost= $100K
Labor cost= $100K
a)
ABC has 2 machines.
TFC= Number of machines x machine cost= 2 x 100K= $200K
TVC= Number of L x Cost of L
MC= Change in TVC/Change in output
Car price= $7K
Total revenue(TR)= Car price x output
TC= TVC+TFC
Profit= TR-TC
| L | Output | TFC | TVC | MC | Car price | Total revenue | TC | Profit |
| 0 | 0 | $200K | 0 | 0 | $7K | 0 | $200K | -$200K |
| 1 | 51 | $200K | $100K | $100K | $7K | $357K | $300K | $57K |
| 2 | 71 | $200K | $200K | $100K | $7K | $497K | $400K | $97K |
| 3 | 87 | $200K | $300K | $100K | $7K | $609K | $500K | $109K |
| 4 | 101 | $200K | $400K | $100K | $7K | $707K | $600K | $107K |
| 5 | 113 | $200K | $500K | $100K | $7K | $791K | $700K | $91K |
i) ABC will produce 87 cars to maximize profit
ii) The profit is $109K
b)
Consider the long run:
i) If number of L=3, the MPK= Change in output/Change in K
At L=3, K= 2, Output= 87
At L=3, K= 3, output= 103
MPK= (103-87)/(3-2)= 16 At 3rd machine
ii) MPL= Change in output/Change in L
At L= 2, K= 4, output= 101
At L=3, K= 4, output= 117
MPL= (117-101)/(3-2)= 16 At 3rd Labor
iii) If MPK/Pk < MPL/Pl it means that marginal productivity of K per unit cost of K is less than the marginal productivity of L per unit cost of L. It implies that it is more beneficial for the firm to hire more L and less of K.
The firm should increase Labor and decrease Capital.
iv) Firm produce where MPK/Pk = MPL/Pl, as Pk=Pl which means for profit maximization MPL=MPK:
When L=3, K= 2, output= 87
When L=3, K= 3, output= 103
MPK= 16
When L=2, K= 3, output= 87
When L=3, K= 3, output= 103
MPL= 16
Here MPL=MPK which impliesL
Firm will produce 103 cars
