Question

Suppose the demand for a certain item is given by D(p)=-4p^2+8p+8, where p represents the price of the item in dollars. Currently the price of the item is $19. Use marginal demand to estimate the change in demand when the price is increased by one dollar

Answer 1

To find the marginal demand, we need to find the derivative of the demand function with respect to price (p):

D'(p) = -8p + 8

To estimate the change in demand when the price is increased by one dollar, we plug in the current price into the derivative:

D'(19) = -8(19) + 8
= -152 + 8
= -144

Therefore, the marginal demand when the price is $19 is -144. This means that for every one dollar increase in price, the demand for the item is expected to decrease by approximately 144 units.