Question

Currently, demand elasticity for the product you produce is ep= -2 and you sell Q1=10 at P1=8.

Your total cost is fixed at $4 per unit produced. A client would like to purchase Q2=15 at a lower price (P2).

Compute P2 and determine if it would be profitable to satisfy your client. What range of prices would generate profit for you?

Answer 1

Elasticity of Demand = % Change in qty demanded / % Change in Price

-2 = (Change in Qty demanded/Change in price)*(original price/original qty)

-2 = (5/change in price)*(8/10)

Change in Price = (5*8)/(10*-2) = -2

that means for the quantity to rise from 10 to 15 the price must fall from 8 to 6 (The minus sign indicates a fall in price). We can also assume the change as fall in price considering the law of demand. The law says the price and quantity demanded are inversely related. So for quantity demanded to rise price must have fallen. The quantum of fall in price in our case is 2.

The revenue before price fall = 10*8 = 80 and cost = 4*10=40, profits =revenue-cost = 80-40=50

revenue after price fall = 15*6 = 90, cost = 4*15 = 60, profits = 90-60 = 30

The profits have fallen so it is not a wise decision to reduce the price. However in our case the revenues have gone up.