Answer to Question #96934 in Macroeconomics for Gurpreet Kaur

Question

You have to determine the optimal number of trucks that the company should buy in order to use them in their projects. Let denote "Y" as the number of trucks. The Marignal Benefit to the company is given by the expression: MB = 80,000 - Y.
The Marginal Cost given by the expression: MC = 10,000 + (1/2,000)Y2

a. Please calculate the optimal amount of trucks that this company should buy and include a diagram.

b. Provide some reasons that might explain the slopes of the marginal benefit and marginal cost curves.

c. Assume that marginal cost is LOWER than marginal benefit, should more trucks be bought? Illustrate.

Answer 1

a. The optimal amount of trucks that this company should buy is at which MB = MC.

80,000 - Y = 10,000 + (1/2,000)Y^2,

(1/2,000)Y^2 + Y - 70,000 = 0,

Y^2 + 2,000Y - 140,000,000 = 0,

D = 2,000^2 + 4×1×140,000,000 = 564,000,000.

Y = (-2,000 + 23,748.68)/2 = 10,874 units.

b. The slopes of the marginal benefit and marginal cost curves are the result of diminishing marginal returns.

c. If marginal cost is LOWER than marginal benefit, then more trucks should be bought.