The American Baker’s Association reports that annual sales of bakery goods last

Question

The American Baker’s Association reports that annual sales of bakery goods last year rose 15 percent, driven by a 50 percent increase in the demand for bran muffins. Most of the increase was attributed to a report that diets rich in bran help prevent certain types of cancer. You are the manager of a bakery that produces and packages gourmet bran muffins, and you currently sell bran muffins in packages of three. However, as a result of this new report, a typical consumer’s inverse demand for your bran muffins is now P = 7 - 1.5Q. If your cost of producing bran muffins is C(Q) = 1.0Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Explanation / Answer

Demand function: P=7-1.5Q

Cost function: 1Q

In order to maximize profits, the seller must sell bran till the point MR=MC

From the demand function, MR=7-3Q

From cost function, MC=1

Thus, at the optimal point, 7-3Q=1

Or, 6=3Q

Or, Q=2 and P=$4

Thus, the baker must sell 2 bran muffins in a single package and sell them at a price of $4 each

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