Question

You are the manager of a monopoly. A typical consumer's inverse demand function for your firm's product is P = 250- 4Q, and your cost function is TC = 10Q. A. MC is fixed and is equal to $10 (MC=AC=S). MR=250-8Q.

(P=price, Q=quantity of output, TC=total cost, MC=marginal cost, MR=marginal revenue, S=supply)

1)What price the company should choose to get maximum profit if the company will use ordinary pricing strategy?
2)Now suppose the company is thinking about using price discrimination for lower income group of customers. If the company will offer discount of $30 in price to the lower income groups how much additional profit will the company earn? Illustrate graphically.
3)Explain the conditions needed to apply the price discrimination strategy?

Answer 1

$$TR=\int MR=250Q-4Q^2$$

$$Pr=TR-TC=250Q-4Q^2-10Q=240Q-4Q^2$$

1)

$$Pr^/=240-8Q$$

$$240-8Q=0$$

$$Q=30$$

$$p=250-4\times30=130$$

2)

$$p=100$$

$$100=250-4Q$$

$$Q=37.5$$

$$Pr=240\times37.5-4\times37.5^2=3375$$

$$\varDelta Pr=3600-3375=225$$

3) For the implementation of price discrimination by a monopolist, it is necessary that the direct elasticity of demand for a product at a price from different buyers be significantly different;

so that these customers are easily identifiable;

so that further resale of goods by buyers is not possible.