Question

Assume TR(Q) = 150 + 500-50° and TC(Q) = 100 + 6Q Create a table in Excel showing TR(Q), MR (0), TC(Q), MC (Q), π (Q), and marginal profit, as O goes from 0 to 10 in increments of 1 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

Marginal revenue function = d(TR)/dQ

MR = d(150+50Q-5Q2)/dQ = 50-10Q

MC = d(TC)/dQ

MC = d(100+6Q)/dQ = 6

Q	TR=150+50Q - 5Q2	TC =100+6Q	MC	MR	Marginal Profit= MR - MC
0	150	100	-	-	-
1	195	106	6	45	39
2	230	112	6	35	29
3	255	118	6	25	19
4	270	124	6	15	9
5	275	130	6	5	-1
6	270	136	6	-5	-11
7	255	142	6	-15	-21
8	230	148	6	-25	-31
9	195	154	6	-35	-41
10	150	160	6	-45	-51

Profit (TR-TC)
50
89
118
137
146
145
134
113
82
41
-10

B) At Q = 4 the profit is maximum

C) At the level of Q = 4 the marginal revenue is decreasing and the marginal cost is constant.

D) At Q = 4 the marginal profit is 9

E) When MR = MC we get the maximum quantity which maximize profit

MR = MC

50-10Q = 6

44 = 10Q

Q = 4.4

So the value is approximately equal to 4