Question

Monopolistic firm has the inverse demand function p = 250 – 5Q. Firm’s total cost of production is C = 1250 + 10Q + 8Q² :

1. Create a spreadsheet for Q = 1 to Q = 20 in increments of 1. Determine the profit-maximizing output and price for the firm and the consequent level of profit.

2. Will you continue the production at the profit-maximizing level of output? Show why or why not?

3. Calculate the Lerner Index of monopoly power for each output level and verify its relationship with the value of the price elasticity of demand at the profit-maximizing level of output.

4. Now suppose that a specific tax of 10 per unit is imposed on the monopoly. What is the effect on the monopoly’s profit-maximizing price?

Answer 1

Profit Maximisation is a concept in which a firm tries to maximise its profits in reference to the cost it incurrs this includes variable as well as fixed costs. As a formula this is achieved, when marginal cost is equal to marginal revenue (Marginal meaning the impact on addition of one additional unit).

Answer 1) If P=250-5Q and the firms total cost of production is C=1250+10Q+8Q2,

The bellow matrix describes the value of Price and Cost of Production at various levels of quanitity produced from 1 to 20 ie Q=1 till 20.

Answer 2) At present in this case since, the firm is coming closer to the levels wherein the Marginal Cost is equal to the Marginal revenue the most recommended case if it were to select from 1-20 would be 20 units of production.

Further, to achieve complete profit maximisation it should go on producing additional units of the product till, the Marginal cost is equal to the Marginal Revenue. In this case as the company goes on to increase the production it is coming closer to the levels of optimum production since marginal costs are declining steadily and coming closer to the Marginal Revenue.

Answer 4 ) Taxes increase the Total cost of the firm and thereby this would mean that in addition to the total cost occurred an additional 10 per unit will be incurred by the firm and the levels of optimum production would change accordingly.

The bellow mentioned Diagram highlights the same:-

The effect on the monopoly would be an increase in the Marginal and average cost meaning that it would now have to produce additional units to increase profits to reduce the price and thereby coming closer to achieving Profit maximisation wherein the Marginal Cost would equal Marginal Revenue.