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 = 11 - 1.5Q.

If your cost of producing bran muffins is C(Q) = 3.5Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Instruction: Enter your response for the optimal package price rounded to two decimal places.

Optimal package size:  units

Optimal package price: $

Answer 1

The inverse demand function is given by P = 11 - 1.5Q. Marginal cost of each muffin is 3.5

For optimal size of the package use P = MC

11 - 1.5Q = 3.5

Q = 7.5 / 1.5

= 5 units

For optimal price of the package use Price = Consumer Surplus + cost of production

P = 0.5*(11 - 3.5)*5 + 3.5*5

= $36.25