Question

The demand for potato chips in a comptitive market is P=100-2Q and supply is P=Q.

- What is the equilibrium price and quantity?

- What is the value of the area of consumer and producer surplus?

- What are the gains to trade in the market?

Suppose the potato chip market is monopolized by one firm. Assume the suupply function now represents the monopolist's marginal cost schedule. The demand schedule is unchanged.

- What is the monopolist's marginal revenue mathematically?

- With a monopoly, what is the equilibrum price and quantity?

- What is the value of the area of consumer and producer surplus?

- What are the gains to trade in the market?

- What is the value of the dead weight loss?

Answer 1

Solution: Since the market is competitive, equilibrium will occur at a point where Market demand = Market supply. So let us equate these two:

100- 2Q= Q

100/3 = Q

Q=33.33.

So price is also EQUAL TO 33.33

Consumer surplus : The area above the price line and below the demand curve is known as consumer surplus.So

When Q is 0 Price is 100.

In order to find consumer surplus we have o find the area of the triangle PPcE. So let us apply the formula of area of triangle :

Area of a triangle = 1/2 * base * height.

=1/2 * (33.33) * (100 -33.33)= 1111.055

HENCE CONSUMER SURPLUS = 1111.055.

PRODUCER SURPLUS= PRODUCER SURPLUS IS THE AREA ABOVE THE SUPPLY CURVE AND BELOW THE PRICE LINE. BUT HERE THERE IS AREA BETWEEN THESE TWO LINE.BECAUSE THE PRICE LINE AND THE SUPPLY CURVE BOTH ARE SAME.SO THERE IS NO PRODUCER SURPLUS UNDER THIS.

GAINS TO TRADE = PRODUCER SURPLUS + CONSUMER SURPLUS = 0 + 1111.055 =1111.055.

PART 2.

If the firm is monopoly firm :

Then the Total reveune = price * quantity = (100-2Q) *Q = 100Q -2Q^2

AND MARGINAL REVENUE = = 100-4Q

AND MARGINAL COST = Q.

In case of monopoly the profits are maximized at a point where MR =MC so let us equate these two :

100-4Q =Q

100/5 =Q

20=Q. WHILE P = 100- 2*20 = 100-40 =60

Consumer surplus

THE area PPmEm is the consumer surplus in case of monopoly and that is equal to =

Consumer surplus = 1/2 * (100-60) * 20 = 1/2 * 40 * 20 = 400

While producer surplus is the area EmKPcPm = 20*26.67=533.4.

Total gains from trade = 533.4 + 400 = 933.4