Question

1) Given a firm's revenue is defined as R(Q) = 160Q - 3Q^2. While the firm's cost is defined as C(Q) = 20 + 11Q. The firm's marginal profit of producing the 7th unit is ___?

2) For a downward-sloping linear demand curve, the associated marginal revenue curve:

		has twice the slope as the demand curve.
		is positive for all levels of sales.
		is parallel to the quantity axis.
		lies below and is parallel to the demand curve.
		coincides with the demand curve.

Answer 1

1) For a revenue function of R(Q) = 160Q - 3Q^2 and a cost function of C(Q) = 20 + 11Q.

Profit = R(Q) - C(Q) = 160Q - 3Q^2 - (20 + 11Q)

= 149Q - 3Q^2 - 20

Marginal profit = derivative of profit = 149 - 6Q.

The firm's marginal profit of producing the 7th unit is 149 - 7*6 = $107

2) MR always has twice the slope as the demand curve. This is because P > MR for every unit sold.