Question

You are the manager of Colgate, and the demand and cost functions for Colgate enamel toothpaste are given by Q = 24-3P and C(Q) = 10 – 4Q + Q².

1. 1. Find the inverse demand function for Colgate toothpaste.
2. 2. Find the price and output that maximize profits.
3. 3. Compute Colgate profits.
4. 4. Explain the difference between the pricing strategy of the monopolistic competitive firm and the pricing strategy of the perfect competitive firm. Explain which firm benefits society more.

Answer 1

Q = 24-3P , this can be rewritten as 3P = 24 - Q or P = 8 - Q/3 (this is known as the inverse demand function)

Total Revenue = Price*Quantity = 8Q - (Q^2)/3

MR = dTR/dQ = 8 - 2Q/3 (the first order derivative of the total revenue function)

C(Q) = 10 – 4Q + Q²

MC = dTC/dQ = -4 + 2Q (the first order derivative of the total cost function)

MR=MC for equilibrium

8 - 2Q/3=-4 + 2Q

2Q + 2Q/3 = 12

8Q/3 = 12

8Q = 36 or Q = 4.5

P = 8 - Q/3 = 8 - 4.5/3 = 6.5

Profits = TR-TC = (8Q - (Q^2)/3) - (10 – 4Q + Q²)

= (8*4.5 - ((4.5)^(2))/3) - (10 - 4*4.5 + (4.5)^(2))

Profits =17

The monopolistically competitive firm has some control over price due to the product differentiation. The firm has some control over price. If differentiation is successful, the firm charges a premium for brand, size shape etc. The perfectly competitive market on the other hand charges a single price. The firms are merely price taker as the industry decides the price on the basis of demand and supply. The competitive firm charges a price lower than monopolistically competitive firm and produces an output more than the monopolistically competitive firm. The competitive firm does not create any deadweight loss unlike monopolistically competitive firm. The perfectly competitive firm thus creates more welfare for the society.