Question

Your business has estimated its total cost to be TC = 3800 + 0.25Q + 0.0018Q2; its marginal cost is thus MC = 0.25 + 0.0036Q, where Q is the amount of pieces provided and TC is in dollars. Because your market is moderately competitive, your business is capable of selling its output for $12.85 each (which therefore produces MR = 12.85 and TR = 12.85Q).

a. Make a table in Excel showing TC and TR with Q on the horizontal axis. Have Q go from 0 to 10,000 units (each row of your Q column can grow by a relatively large number so that your table isn’t large). Create a second table displaying MC and MR with Q again on the horizontal axis.

b. What is the optimal level of output for your business to produce/sell? What is the marginal revenue of the final unit sold?

c. What are the total revenue, total cost, and profit (net benefit/net revenue/etc.) of selling the optimal amount of units?

d. An eager worker at your business hints that, because the business makes $12.85 revenue for each unit sold, then the company could make still more profit by selling more than the level chosen in part b; why would your business not want to make and sell more output than the level you picked in part b?

Answer 1

(a)

(i) TR & TC

Q	TR	TC
0	0	3,800
1,000	12,850	5,850
2,000	25,700	11,500
3,000	38,550	20,750
4,000	51,400	33,600
5,000	64,250	50,050
6,000	77,100	70,100
7,000	89,950	93,750
8,000	1,02,800	1,21,000
9,000	1,15,650	1,51,850
10,000	1,28,500	1,86,300

(ii) MR & MC

Q	MR	MC
0	12.85	0.25
1,000	12.85	3.85
2,000	12.85	7.45
3,000	12.85	11.05
4,000	12.85	14.65
5,000	12.85	18.25
6,000	12.85	21.85
7,000	12.85	25.45
8,000	12.85	29.05
9,000	12.85	32.65
10,000	12.85	36.25

(b)

Setting MR = MC,

0.25 + 0.0036Q = 12.85

0.0036Q = 12.6

Q = 3,500

MR = 12.85 (since in perfect competition, MR = P)

(c)

When Q = 3,500,

TR = 12.85 x 3,500 = 44,975

TC = 3,800 + (0.25 x 3,500) + (0.0018 x 3,500 x 3,500) = 3,800 + 875 + 22,050 = 26,725

Profit = TR - TC = 44,975 - 26,725 = - 18,250

(d)

If an output higher than 3,500 units is sold, MC will increase, while MR (= P) will remain unchanged. So the firm will incur a marginal loss (= MC - P). The firm will optimize its profit by producing at the point where price equals MC.