Using the table below, what is the firm's optimal output level?

Question

Output     Price     Total Cost

0             1750     $1000

1             1700     2,000

2             1650     2,800

3             1600     3,500

4             1550     4,000

5             1500     4,500

6             1450     5,200

7             1400     6,000

8             1350     7,000

9             1300     9,000

 

 

a) 6.


b) 7.


c) 8.


d) 9.


e) cannot be determined from the information given.

Answer 1

This is a profit maximization equation, firms always product where marginal revenue is equal to marginal cost. Marginal revenue is defined as the change in total revenue given a one unit change in total cost. For the table above the change in Q for every level of production is 1 unit so the marginal revenue for each level of price is:

 Q      MR

0        ---

1        50

2        50

3        50

4        50

5        50

6        50

7        50

8        50

9        50

 

Now we need to look at the marginal cost, which is defined as the change in total cost given a one unit change in quantity, the table below list the marginal cost for each level of output.

Q       MC

0       ----

1       1000

2       800

3       700

4       500

5       500

6       700

7       800

8       1000

9       2000

 

Now looking at the table with marginal revenue and marginal cost combined we have:

Q       MC       MR
0       ----       ---
1       1000     50
2       800       50
3       700       50
4       500       50
5       500       50
6       700       50
7       800       50
8       1000     50
9       2000     50

 

There is not a point where marginal revenue is equal to marginal cost on this table so the correct answer would be e) we cannot tell from the information given.