Sarah has been selling 5000 baseball caps per month at 850 e

Sarah has been selling 5,000 baseball caps per month at $8.50 each. When she decreased the price to $6.50 she sold 6,000 baseball hats.

a.What is the demand elasticity?

b.If Sarah\'s marginal cost is $7 per cap, what is her desired markup and what is her initial actual markup?

c.Was raising the price profitable?

Solution

(a) Using mid-point method,

Demand elasticity (Ed) = (Change in quantity / Averge quantity) / (Change in price / Average price)

= [(6,000 - 5,000) / (6,000 + 5,000)] / [$(6.5 - 8.5) / $(6.5 + 8.5)]

= (1,000 / 11,000) / (- 2.5 / 15)

= - 0.54

(b) Mark-up = (Price - MC) / MC

Desired mark-up = $(6.5 - 7) / $7 = - $0.5 / $7 = - 0.0714

Initial mark-up = $(8.5 - 7) / $7 = $1.5 / $7 = 0.2143

(c) Since absolute value of Ep is less than 1, demand is inelastic. With inelastic demand, an increase in price will increase total revenue and profits ceteris paribus. Therefore increasing price will be profitable.