Question

1. Suppose the demand function facing a monopolist is given as p=50- and the cost function is given as C=109. Determine the total revenue function for the monopolist, and graph the relationship between total revenue, total cost and output. In your answer determine the profit maximizing level of output that would be chosen by the monopolist, and discuss mathematically how you know it is a profit maximum.

Answer 1

Ans. Demand function, p = 50 - q

Revenue/Cost 20 Quantity

=> Total Revenue, TR = p*q = 50q - q^2

=> Marginal revenue, MR = dTR/dq = 50 - 2q

Total cost, C = 10q

=> Marginal cost, MC = 10

Thus, profit, G = TR - TC

For profit maximization, first degree condition is,

dG/dq = dTR/dq - dTC/dq = 0

=> MR - MC = 0

=> MR = MC

=> 50 - 2q = 10

=> q = 20 units

Substituting this is demand function, p = 50 - 20 = $30

Second degree condition for maximisation,

d^2(G)/d(q)^2 = -2 < 0

Thus, profit is maximized at q = 20 units.

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