Question

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

For perfectly competitive markets,

the enterprises are price takers

$P= 60-2Q$

$TC= 100+3Q^2$

For price takers

$P = MC =MRC$

$MC= \frac{\Delta TC}{\Delta Q}$

$MC = 6Q$

In equilibrium,

MC= P

$6Q= 60-2Q$

$Q=7.5$

While P is,

$P= 60- 2(7.5)$

$P= 60-15$

$P= 45$

For a monopoly equilibrium is the same as in perfectly competitive markets;

$MC = MR$

Total revenue

$P×Q = 60Q-2Q^2$

$MR = 60- 4Q$

In equilibrium,

$60-4Q = 6Q$

$Q = 6$

Price,

$P= 60 - 2(6)$

$P = 48$