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 = 9 - 0.5Q. If your cost of producing bran muffins is C(Q) = 4.5Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Answer 1

The optimal production quantity is 9

Step-by-step explanation:

• The consumer's inverse demand is:

P = 9 - 0.5Q

• The cost of producing bran muffin is given by:

C(Q)=4.5Q

Under perfect competition, the equilibrium is given by:

P = marginal cost

9 - 0.5 Q= 4.5

4.5 = 0.5Q

Q = 9

P= 4,5

Hence, the optimal production quantity is 9