Question

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A profit-maximizing firm in the short run has total fixed costs of $200. Its variable costs are as below.

Output             Total Variable Cost

            0                                  $0

                                                           

            1                                  $190

                                                                                               

            2                                  $360

                                                                                               

            3                                  $510

                                                                                   

            4                                  $650

                                                                                   

            5                                  $800

                                                                                   

            6                                  $990

                                                                                   

            7                                  $1,190

                                                                                   

            8                                  $1,420

            9                                  $1,770

            10                                $2,170

(A)       (3 pts.) Calculate average total cost when output is 5 units.

                                                                                    ANSWER: ________

(B)       (2 pts.)What is the marginal cost of the 9th unit of output?

                                                                                    ANSWER: ________

                                               

Answer C & D assuming that the firm can only produce integer amounts of output.

(C)       (3 pts) Suppose this firm can sell all the output it wants in the short run at a price of $220.

How much output should it produce and sell and what will its profits (or losses) be?

                        ANSWER:        Output will be             ________

                                              Profits or losses =          ________        

(D)       (2 pts.) Suppose instead this firm can sell all the output it wants in the short run at a price of $155. Again, how much output should it produce and sell and what will its profits (or losses) be?

                        ANSWER:        Output will be               ________

                                              Profits or losses =          ________

Answer 1

(A) Calculate average total cost when output is 5 units.

Total variable cost (at output=5)= TVC=$800

Fixed cost=TFC=$200

Total cost=TC=TFC+TVC=200+800=$1000

Average total cost=Total Cost/Output=1000/5=$200

B) What is the marginal cost of the 9th unit of output?

Total variable cost (at Q=8)=TVC(8)=$1420

Total variable cost (at Q=9)=TVC(9)=$1770

Marginal cost of 9th unit of output=[TVC(9)-TVC(8)]/(9-8)=(1770-1420)/(9-8)=$350

c) We can make following Marginal cost table for each level of output (as calculated in part b)

Output ,Q	Total Variable Cost, TVC	Marginal Cost=Change in TC/Change in Q
0	0
1	190	190
2	360	170
3	510	150
4	650	140
5	800	150
6	990	190
7	1190	200
8	1420	230
9	1770	350
10	2170	400

A profit maximizing firm continues to increase the output level as long as Marginal cost is less than or equal to market price. At a price of $220, we find that Marginal cost is less than 220 for Q=7. After that P is less than Marginal cost. So, optimal output will be 7 units.

Optimal output=7 units

Total Revenue=TR=Q*P=7*220 =$1540

Total Cost=TFC+TVC=200+1190=$1320

Total profit=TR-TC=1540-1320=$220

D)

A profit maximizing firm continues to increase the output level as long as Marginal cost is less than or equal to market price. At a price of $155, we find that Marginal cost is less than $155 for Q=5. After that P is less than Marginal cost. So, optimal output will be 5 units.

Optimal output=5 units

Total Revenue=TR=Q*P=5*155 =$775

Total Cost=TFC+TVC=200+800=$1000

Total profit=TR-TC=775-1000=-$225 (It is a loss of $225)