Suppose that the supply of x units of a product at price p dollars per unit is given by the following. p = 50 + 60 ln(4x + 2)

Question

Suppose that the supply of x units of a product at price p dollars per unit is given by the following.

p = 50 + 60 ln(4x + 2)

Approximate the price increase associated with the number of units supplied changing from 37 to 38.

Answer 1

This question is asking us to calculate the marginal cost at x = 37, which just means p^'(37).

p^'(x) = 240/(4x + 2)

p^'(37) = 240 / 150 = $1.60 / unit / unit.

The price per unit would increase by ~ $1.60.