Question

Suppose that the (inverse) demand curve for Cranberries is given by P = 40 − 6Q and TC = $4Q + $3Q²

1. What are four conditions required for a competitive market?
2. What is equilibrium Price and Quantity and Profit if the market is competitive?
3. What is equilibrium Price and Quantity and Profit if there are two firms in the market (note Q = q₁ + q₂)?
4. What is equilibrium Price and Quantity and Profit if there are monopoly in the market (note Q = Q)?
5. If there were 3 firms, where do you estimate the output and the price would be—this does not require a mathematical calculation—it is based on the expectations created by the prior three answers (1-b, 1-c, and 1-d).

Answer 1

ANSWER:

a) The conditions required for a competitive market:

i) Number of buyers and sellers in the market is very large.

ii) None of the buyer or the seller has influence on market price. So, they behave like price takers in the market.

ii) Products of the firms are identical to each other.

iii) No barriers of entry and exit for firms in the market. So, in Long run, no firm will earn supernormal profit.

b) Inverse demand curve, P = 40 - 6Q

Total Cost, TC = 4Q + 3Q² ; Marginal Cost, MC = dTC/dQ = 4 + 6Q

If the market is competitive, the equilibrium will be attained at the point where,

P = MC

or, 40 - 6Q = 4 + 6Q

or, 12Q = 36

or, Q = 3

Hence, P = 40 - 6Q = 40 - 6*3 = 40 - 18 = 22

So, in competitive market, Q* = 3, P* = 22

c) In duopoly, we assume that both firm has same cost structure.

TC₁ = 4q₁ + 3q₁²

TC₂ = 4q₂ + 3q₂²

Each firm will maximise their own profit.

Firm 1's profit, ₁ = P .q₁ - TC₁ = [40 - 6(q₁ + q₂)]*q₁ - (4q₁ + 3q₁²)

For profit maximisation, d₁ / dq₁ = 0

so, 40 - 12q₁ - 6q₂ - 4 - 6q₁= 0

or, 18q₁ = 36- 6q₂

or, 3q₁ = 6 - q₂  ... this is the best response function of firm 1

Again differentiating firm 2's profit function with respect to q₂ and setting it equal to zero, we will get the best response function of firm 2. As both the firm have same cost structure, we can say the best response function of firm 2 will be,

3q₂ = 6 - q₁

Now solving these two best response equation, we will get the equilibrium quantity of each firm.

Hence, 3q₂ = 6 - 2 + q₂/3

or, (9q₂ - q₂)/3 = 4

or, 8q₂ = 12

or, q₂ = 3/2 = 1.5

q₁ = 2 - q₂/3 = 2 - 1.5/3 = 2 - .5 = 1.5

Hence, Q= 3, P = 40 - 18 = 22

d. Monopoly equilibrium can be attained at a point, where, MR = MC

revenue, R = P .Q = (40 - 6Q) * Q

Marginal Revenue = MR = dR/dQ = 40 - 12Q

Marginal Cost, MC = dC/dQ = 4 + 6Q

At equilibrium, 40 - 12Q = 4 + 6Q

or, 18Q = 36

or, Q = 2

and P = 40 - 6* 2 = 40 - 12 = 28

At monopoly, Q* = 2, P* = 28