Problem: General Cereals, Inc. (GCI) produces and markets Sweeties!, a popular ready to eat breakfast cereal. In an effort to expand sales in the Secaucus, New Jersey, market, the company is considering a 1 month promotion whereby GCI would distribute a coupon for a free daily pass to a local amusement park in exchange for three box tops, as sent in by retail customers. A 25% boost in demand is anticipated, even though only 15 percent of all eligible customers are expected to redeem their coupons. Each redeemed coupon costs GCI $6, so the expected cost of this promotion is .30$ (=0.15x$6/3) per unit sold. Other marginal costs for cereal production and distribution are constant at $1 per unit. Current demand and marginal revenue relations for Sweeties! are
Q=16,000 - 2,000P
MR=ATR/AQ=$8-$0.001Q (note...my font doesn't have the triangle symbol so I'm using A to represent it.)
Demand and marginal revenue relations that reflect the expected 25% boost in demand for Sweeties! are the following:
Q=20,000-2,500P
MR=ATR/AQ=$8-$0.0008Q
Q1. Calculate the profit-maximizing price/output and profit levels for Sweeties! prior to the coupon promotion.
Q2. Calculate these same values subsequent to the Sweeties! coupon promotion and following the expected 25% boost in demand.