Chapter 3: Problems 3, 4, and 7
3. The Olde Yogurt Factory has reduced the price of its popular Mmmm Sundae from $2.25 to $1.75. As a result, the firm’s daily sales of these sundaes have increased from 1,500/day to 1,800/day. Compute the arc price elasticity of demand over this price and consumption quantity range.
ED = [(1800 1500)/(1800+1500)]/[(1.75 2.25)/(1.75 + 2.25)], so ED = 0.727 for Mmmm Sundaes. This is inelastic in this price range. It suggests the Olde Yoguart Factory should consider a price increase, as this will increase revenues and reduce costs.
4. The subway fare in your town has just been increased from a current level of 50 cents to $1.00 per ride. As a result, the transit authority notes a decline in rider-ship of 30 percent.
a. Compute the price elasticity of demand for subway rides.
b. If the transit authority reduces the fare back to 50 cents, what impact would you expect on the ridership? Why?
a. ED = 30%/+100% = 0.3 is the price elasticity for subway rides. This is inelastic.
b. Ridership probably would not return to the original level because some people may have invested in alternatives (cars, etc.) or found other transit options that they are reluctant to give up.
7. In an attempt to increase revenues and profits, a firm is considering a 4 percent increase in price and an 11 percent increase in advertising. If the price elasticity of demand is −1.5 and the advertising elasticity of demand is +0.6, would you expect an increase or decrease in total revenues?
Any demand function can be decomposed into percentage changes and elasticities of the component parts. If Q = f(P, A), where P is price, A is advertising, ED and EA are price and advertising elasticities, then: %Q = %P(ED) + %A(EA) = (+4%)(-1.5) + (+11%)(.6) = +.6%. We expect a small increase in quantity of .6%. Total revenue will increase since both price and quantity increase. With 6% higher prices and .6% higher quantity,...