Answer to Question #195342 in Microeconomics for Abrham

Question

3. Suppose a firm operating in a perfectly competitive market has a cost structure given by TC = 

10 q – 4q2 + 4 q3

and further assume the market demand curve is given by Qd = 2000-25P and 

if there are 500 firms in the market supplying similar product with individual supply curve of 

Qs= 3 +0.05P, then

A. The equilibrium price in the market

B. Determine the profit maximizing output 

C. Determine the break-even price

D. What minimum market price the firm needs to continue production?

Answer 1

(A)

$Qd=Qs\\2000-25P=3+0.05P\\2000-3=0.05P+25P\\1997=25.05P\\P=79.72055888\\Qs=3+0.05(P)=6.986027944\\Qd=2000-25(P)=6.986027944$

Therefore equilibrium price is $79.7205588 and equilibrium quantity is approximately 7

(B)

Profit is maximized at a point MR=MC

$TR=P\times Q\\=79.72055888Q\\MR=79.72055888\\MR=MC\\79.72055888=10-8Q+12Q^2\\79.72055888-10=-8Q+12Q^2\\69.72055888=-8Q+12Q^2\\12Q^2-8Q-69.72055888\\Q=2.76668378$

Therefore, the profit maximizing output is approximately 3

(C)

$TC=10Q-4Q^2+4Q^3\\MC=10-8Q+12Q^2\\MC=ATC\\10-8Q+12Q^2=10-4Q+4Q^2\\-8Q+12Q^2=-4Q+4Q^2\\12Q^2-4Q^2=-4Q+8Q\\8Q^2=4Q\\8Q=4\\Q=0.5\\P=MC=ATC=10-4Q+4Q^2\\=10-4(0.5)+4(0.5^2)\\=9$

Therefore the break even price is $9

(D)

shut down price

AVC minimized at Q=0

$P=MC=AVC\\AVC=\frac{VC}{Q}=10-4Q+4Q^2\\=10$

Therefore, 10 is the minimum market price the firm needs to continue production