Answer to Question #312904 in Economics of Enterprise for felix

Question

1.Given the following demand equation P = 60- 2Q and the cost equation TC(q) = 100+3Q2

For the market of shoes

a.If the enterprises in this market take advantages of perfectly competitive market, find the equilibrium outputs and price.

b.If the seller in this market takes the advantages of pure monopoly, find the equilibrium outputs and price.

c.If the seller in this market takes the advantages of oligopolistic market, find the equilibrium outputs and price.

Answer 1

a) in perfectly competitive market,equilibrium prices and quantity are set by free market forces and hence, MR=MC

P=60-2q

TR=P$\times$ Q

=(60-2q)$\times$ q

=60q-$2q^2$

MR=$\frac{d(tr)}{dq}$ 60q-$2q^2$

MR=60-4q

TC_(q)=100+$3q^2$

MC=$\frac{d(tc)}{dq}$ 100+$3q^2$

MC=6q

therefore at equilibrium

MR=MC

60-4q=6q

10q=60

Q=6

p=60-2q,where q=6

p=60-(2$\times6)$

p=60-12

p=48

therefore at equilibrium ,p=48,q=6

B).in pure monopoly,eventhough the seller is the market controller and the buyer the price and output taker,in short run and normal optimal operation the equilibrium prices and output is the set when

MC=MR,

and abnormal profits of price discrimination when AR>AC ,so since this a normal case in short run:

MR=MC

P=60-2q

TR=P$\times$ Q

=(60-2q)$\times$ q

=60q-$2q^2$

MR=$\frac{d(tr)}{dq}$ 60q-$2q^2$

MR=60-4q

TC_(q)=100+$3q^2$

MC=$\frac{d(tc)}{dq}$ 100+$3q^2$

MC=6q

therefore at equilibrium

MR=MC

60-4q=6q

10q=60

Q=6

p=60-2q,where q=6

p=60-(2$\times6)$

p=60-12

p=48

therefore at equilibrium ,p=48,q=6

and p>48,q>6 for abnormal profits

C).In oligopolistic market structure,there is interdependence among firms and hence a firm cannot make independent price and output decision due to rivaly behavior.they have a kinked demand curve

and so in short run

MR=MC

P=60-2q

TR=P$\times$ Q

=(60-2q)$\times$ q

=60q-$2q^2$

MR=$\frac{d(tr)}{dq}$60q-$2q^2$

MR=60-4q

TC_(q)=100+$3q^2$

MC=$\frac{d(tc)}{dq}$ 100+$3q^2$

MC=6q

therefore at equilibrium

MR=MC

60-4q=6q

10q=60

Q=6

p=60-2q,where q=6

p=60-(2$\times6)$

p=60-12

p=48

therefore at equilibrium ,p=48,q=6