Question

3. A firm, Gargantua, has the following demand and cost functions: Demand p(x) = 18 ?1 2 ? x Cost c(x) = x2 (a) What is Gargantua’s profit function? (b) What is Gargantua’s profit-maximizing o 416 BOWLES, FOLEY & HALLIDAY - DRAFT (c) What is the price at Gargantua’s profit-maxiziming output? (d) What is Gargantua’s total profit at its profit-maximizing output? (e) Sketch Gargantua’s marginal cost, average cost, marginal revenue and average revenue curves on one set of axes and show what its profit and costs would be (shade the relevant areas).

Answer 1

(a) Profit Function = Total Revenue - Total Cost

Total Revenue = Price * Quantity =

Total Cost = x²

Profit Function =

(b) Profit Maximizing Output: Marginal Revenue = Marginal Cost

Marginal Revenue = 18 - x

Marginal Cost = 2x

Therefore, profit maximizing output: 18 - x = 2x

That implies to 3x = 18. hence x =6

The profit-maximizing output = 6

(c) Given Demand function =

Now x = 6. Substituting x value in demand function we get P = 15

(d) Total Profit Function = 18x - (3/2)x²

Now at profit maximizing x = 6.

Substituting x value in total profit equation we get = 18 * 6 - (3/2) (36) = 108 - 54 = 54

Total Profit at profit maximizing output = 54

(e)