Consider a perfectly competitive industry in which the inver

Consider a perfectly competitive industry in which the inverse demand is given by p(y)=2001-2y and each firm has the following cost function: c(y)= In the long-run equilibrium, what price will be charged for the product? What total quantity will be sold? How many firms will operate in this market? A tax of 6 dollars per unit sold is now imposed on each firm operating in this market. In the long-run equilibrium, what price will be charged for the product? What total quantity will be sold? How many firms will operate in this market? Suppose instead that a monopolist operates in this market. There is no tax imposed on the monopolist, and he can produce the product at a constant marginal cost of c. What price will the monopolist charge (as function of c)? Can this price be below the price you found in part a?

Solution

In perfect competition market, long run equilibrium would be where AC(average cost) is minimum.

TC = Y³/3 + 18

AC = TC/Y = Y²/3 + 18/Y

To find the minimum of AC, we need to differentiate it & put it equal to zero.

dAC/dY = 2/3*Y + 18*(-1)Y^-2 = 0

Solving this will give us Y = 3 (Quantity for single firm).

Minimum AC = 3²/3 + 18/3 = 9 (price)

Putting this P in the demand equation will give the market demand

so P = 2001 - 2Y

Y = 996(market demand)

No of firms = 996/3 = 332

(b) if $6 tax is on the seller,

In the short run, both consumers and producers will suffer from the tax imposed.In the long run, since the supply curve is completely elastic, the new tax will reduce only consumer surplus. Producer surplus will remain equal to zero, since there are no profits to be made. all the burden wpould be on the buyer so price will increase to 9+6= 15

now the market demand would be 15 = 2001 - 2Y, demand = 993.

(c) a monopolist will maximize his proft at a point where MC =MR

2001 - 4Y = c

4Y = 2001 - c

Y =(2001 - c)/4

so P = 2001 - 2Y

P = 2001 - (2001 -c)/2

P = 2001 - 1000.5 - 0.5c = 1000.5 - 0.5c