Question

Question 1:

Consider a perfectly competitive market in good x consisting of 250 consumers with utility function:

u(x,y) = xy

Denote Px to be the price for good x and suppose Py=1. Each consumer has income equal to 10. There are 100 forms producing good x according to the cost function c(x)=x^2 + 1.

a) Derive the demand curve for good x for a consumer in the market

b) Derive the market demand curve for good x

C) Derive the individual firm’s supply curve for good x.

D) Derive the market supply curve for good x  

e) Determine the equilibrium price and quantity in the market for good x.

F) is the market currently in long run equilibrium? Why or why not?

Answer 1

1) utility Maximizing condition:

MUx/px= MUy/py

Y/px=x/1

Y=px*x

Budget constraint,

M=py*y+px*x

M=1*(px*x)+px*x=2*px*x

X=M/(2*px)

M=10

X=5/px

2) Market demand is sum of individual demand

X=250*5/px=1250/px

3) individual firm supply function is nothing marginal cost function.

MC=2x

P=2x( inverse supply)

X=0.5p( supply function)

4) Market supply is sum of individual supply,

X=100*0.5p=50p

5) Equilibrium at market demand= market supply

1250/p=50p

P^2=25

P*=5

X*=50*5=250

The long run Equilibrium price is equal to Minimum average cost.

The average is Minimum at , where it is equal to marginal cost.

ATC=x+1/x

ATC= MC

X+1/x=2x

1/x=x

X^2=1

X=1

Min ATC=1+1/1=2

So price is not equal to Minimum average cost,so Equilibrium is not in long run.