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 = 8 - 1.5Q. If your cost of producing bran muffins is C(Q) = 2.0Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Answer 1

Answer:

Optimal package size = 4 units

Optimal package price = $20

Explanation:

P = 8 - 1.5Q and C(Q) = 2.0Q, MC = 2

To obtain optimal package size, we put

Price is equal to the marginal cost, P = MC

8 - 1.5Q = 2

     1.5Q = 6

          Q = 6 ÷ 1.5

              = 4

Therefore,

Optimal package size = 4 units

Hence,

Optimal package price:

= 0.5[8 - 2] × 4 + 2 × 4

= 12 + 8

= $20