Question

(3)The demand (P) and total cost ( TC) functions for commodity Z can be represented by the following equations:

P = 1400 – 7.5Q

TC= Q^3-6Q^2+140Q+750

(a)Graph the marginal revenue and marginal cost for Q = 0, 5, 10, 15, 20 and 25

(b)What is the profit maximizing output for this firm?

(c)Find the price the firm will sell its output.

(d)If the market clears, find the profit the firm could earn.

Answer 1

A. P=1400-7.5Q

MR=1400-15Q

MC= 3Q^2-12Q+140

Q	MC	MR
0	140	1400
5	155	1325
10	320	1250
15	635	1175
20	1100	1100
25	1715	1025

B.

Profit maximising output is where MC =MR.

So MC= MR at Q=20

C. When Q=20,

P=1400-7.5*20= $1250

D. Profit=TR-TC= P*Q-(Q^3-6Q^2+140Q+750)= (20*1250)-((20)^3-(6(20)^2)+140*20+750))

=$15850

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