Question

15. Assume TRO) 150+50Q 502 and TC(Q) 100 6Q Create a table in Excel showing TR(Q), MR(Q) , TC(Q), MC(Q), π(Q), and marginal profit, as Q goes from 0 to 10 in increments of1 b. Identify the level of Q that maximizes profit. c. At the level of Q that maximizes profit, what is the relation between MR and MC? d. At the level of Q that maximizes profit, what is marginal profit? e. Check your answer in part b using calculus

Answer 1

a)

Q	TR	TC	MR = ∆TR/∆Q	MC= ∆TC/∆Q	Profit = TR - TC	Marginal Profit = ∆Profit/∆Q
0	150	100	-	-	50	-
1	195	106	45	6	89	39
2	230	112	35	6	118	29
3	255	118	25	6	137	19
4	270	124	15	6	146	9
5	275	130	5	6	145	-1
6	270	136	-5	6	134	-11
7	255	142	-15	6	113	-21
8	230	148	-25	6	82	-31
9	195	154	-35	6	41	-41
10	150	160	-45	6	-10	-51

b) Profit is maximized at the output level of 4.

c) At the profit maximizing level of output, MR > MC.

d) At the profit maximizing level of output, Marginal Profit is $9.

e) Profit = TR - TC = (150 + 50Q - 5Q²) - (100 + 6Q) = = 150 + 50Q - 5Q² - 100 - 6Q = 50 + 44Q - 5Q²

Marginal Profit = 44 - 10Q

Profit is maximized When Marginal Profit i > or = 0

44 - 10Q > or = 0

44 > or = 10Q

44 / 10 > or = Q

4.4 > = Q

Thus, if we round it, we can find Q = 4.