Question

Suppose that there are 10,000 DVR firms all making exactly the same DVR and producing at a total cost of 300Q + 50Q²where Q equals the number of DVRs produced per month. All firms are price takers and the monthly market level demand for DVRs is represented by

Q = 45,000 – 50P.

a) What is the firm supply curve?

b) What is the market supply curve?

c) What price and quantity correspond to the market equilibrium? How much does each individual firm produce in this equilibrium?

Answer 1

Total cost of each firm ;

TC = 300Q + 50Q²

where, Q equals the number of DVRs produced per month

Monthly market level demand for DVRs is represented by;

Qd = 45000 - 50P

a) The firms supply function is the marginal cost function which is calculated as;

MC = d/dQ (300Q + 50Q²)
MC = 300 + 100Q

Therefore, firm's supply function will be;

P = 300 + 100Q
100Q = P - 300
Qs = P/100 - 3

b) The supply function for 10,000 DVR firms will be;

Qs_m = 10000Qs
= 10000(P/100 - 3)
Qs_m =100P - 30000

c) The equilibrium level will be achieved when;

MR = MC

Total revenue will be;

TR = P*Q

Qd = 45000 - 50P
50P = 45000 - Q
P = 900 - Q/50

TR = (900 - Q/50)Q
TR = 900Q - Q²/50

MR = d/dQ (900Q - Q²/50)
MR = 900 - Q/25

The equilibrium level will be ;

MR = MC
900 - Q/25 = 300 + 100Q
900 - 300 = 100Q + Q/25
600 = 2500Q+Q / 25
15000 = 2501Q
Q = 6

P = 900 - 6/50
P = $899.8