Question

Your company has estimated its total cost to be TC = 54,000 + 2Q + 0.012Q²; its marginal cost is thus MC = 2 + 0.024Q, where Q is the quantity of units produced and TC is in dollars. Since your market is relatively competitive, your company is able to sell its output for $122.00 each (which thus yields MR = 122 and TR = 122Q).

a.   Produce a chart 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 increase by a relatively large number so that your table isn’t huge). Produce a second chart showing MC and MR with Q again on the horizontal axis.

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

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

d.   An eager intern at your company suggests that, since the company earns $122 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 company not want to produce and sell more output than the level you chose in part b?

Answer 1

TC = 54,000 + 2Q + 0.012Q²

MC = 2 + 0.024Q

Price = 122

TR = 122Q

a)

Output	Total Cost	Total Revenue	Marginal Cost	Marginal Revenue
0	54000	0
1000	68000	122000	14000	122000
2000	106000	244000	38000	122000
3000	168000	366000	62000	122000
4000	254000	488000	86000	122000
5000	364000	610000	110000	122000
6000	498000	732000	134000	122000
7000	656000	854000	158000	122000
8000	838000	976000	182000	122000
9000	1044000	1098000	206000	122000
10000	1274000	1220000	230000	122000

b) 2 + 0.024Q = 122

Q = 5,000

Optimal level of company occurs when marginal cost = marginal revenue which occurs at output level 5,000. Marginal revenue from last unit sold is 122.

c) Total Cost at Q = 5,000 is 364,000 while total revenue from selling 5,000 units is 610,000. Total Profit at 5,000 units produced is 610,000 - 364,000 = 246,000

d)

Output	Total Cost	Total Revenue	Marginal Cost	Marginal Revenue	Profit
0	54000	0			-54000
1000	68000	122000	14000	122000	54000
2000	106000	244000	38000	122000	138000
3000	168000	366000	62000	122000	198000
4000	254000	488000	86000	122000	234000
5000	364000	610000	110000	122000	246000
6000	498000	732000	134000	122000	234000
7000	656000	854000	158000	122000	198000
8000	838000	976000	182000	122000	138000
9000	1044000	1098000	206000	122000	54000
10000	1274000	1220000	230000	122000	-54000

Profit level is maximum by selling 5,000 units which can be seen in the above table. As per Intern, if we produce more of the good to earn more revenue, it will actually raise marginal cost more than marginal revenue which will start reducing total profit level.