The relationship between Price elasticity of demand and Marginal Revenue can be shown to be:

MR = P 1 ?1/|e|

There are two types of customers that come to the Barnegat Fish Company to have their signature crab cakes: An affluent group with a price elasticity of demand for crabcakes of e = ?2; and a less wealthy type with a price elasticity of demand for crab cakes of e = ?5. The restaurant wants to introduce a coupon to encourage more people to visit their restaurant.

Thus every buyer pays the posted price of $P per crab cake but those who tender the coupon get a discount of $X off the posted price. If the Marginal Cost of a crab cake is $2.00, what is the price of the crab cake and what is the value of the coupon?(Set MR=MC).