A firm sells two products which are partial substitutes for each other. If the price of one product increases then the demand for the other substitute product rises. The prices of the products (in £) are p1 and p2 and their respective demand functions are
q1 = 517 − 3.5p1 + 0.8p2 q2 = 770 − 4.4p2 + 1.4p1
What price should the firm charge for each product to maximize its total sales revenue?
QNO2 A firm produces two products which are sold in two separate markets with the demand schedules
p1 = 600 − 0.3q1 p2 = 500 − 0.2q2
Production costs are related and the firm faces the total cost function TC = 16 + 1.2q1 + 1.5q2 + 0.2q1q2 If the firm wishes to maximize total profits, how much of each product should it sell? What will the maximum profit level be?
QNO3 A multi plant monopoly operates two plants whose total cost schedules are TC1 = 8.5 + 0.03q21
TC2 = 5.2 + 0.04q22 If it faces the demand schedule p = 60 − 0.04q where q = q1 + q2, how much should it produce in each plant to maximize profits?
QNO4 A firm produces two products which are sold in separate markets with the demand schedules
p1 = 210 − 0.4q12 p2 = 491 − 6q2
Production costs are related and the firm’s total cost schedule is
TC = 32 + 0.8q21 + 0.7q22 + 0.1q1q2
How much should the firm sell in each market to maximize total profits?
QNO5 A firm sells its output in a perfectly competitive market at a fixed price of £200 per unit. It buys the two inputs K and L at prices of £42 per unit and £5 per unit, respectively, and faces the production function q = 3.1K0.3 L0.25 What combination of K and L should it use to maximize profit?
QNO6 A multiplant monopoly operates two plants whose total cost schedules are TC1 = 36 + 0.003q31 TC2 = 45 + 0.005q32 If its total output is sold in a market where the demand schedule is p = 320 − 0.lq where q = q1 + q2, how much should it produce in each plant to maximize total profits?