Consider a competitive industry with large number of firms, all of which have id

Question

Consider a competitive industry with large number of firms, all of which have identical cost functions c(y) = y^2 + 1, y>0 and c(0) = 0. Marginal cost is M C(y) = 2y. Suppose the market demand curve is given by D(p) = 52 - P 1. What is the supply curve of individual firm? Denote by S_i(p) 2. What is the smallest price at which the product can be sold 3. In the long run what will be the equilibrium number of firms in the market 4. What is the equilibrium price and quantity produced by each firm.

Explanation / Answer

1.Here we know that,Total Cost=TC=y2+1,

MC(y)=Derivative of C(y) with respect to y .MC(y)=2y=Marginal Cosy.

Si(p)which is P=MC(y)=2y This implies supply curve of individual firm is S(p)=2y.

2.Long Run Average Total Cost=TC/Q=y2+1/y=y+y-1

Taking derivative of average total cost,

dATCdy=1-1y-2=0

1y2=1,y=1.

That means minimum price at which product will be sold is=P=2*1=2.

3.From the explanation we know that the market demand curve is-D(p)=52-p,

where we know the value of p=2,then,D(2)=52-2=50.

So the long run euilibrium number of firm is=50/2=25.

4.At Equilibrium,

D(p)=S(p)

52-p=2y

As y=1,

p=52-2=50.

The equilibrium price is 50 and quantity 1.

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