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 - 0.5Q. If the cost of producing bran muffins is C(Q) = 2.5 Q determine the optimal number of bran muffins to sell in a single package and the optimal package price

Answer 1

The inverse demand function is P = 7 – 0.5Q. Marginal cost is MC = 2.5. The optimal number of muffins in a package are found at P = MC which gives 7 – 0.5Q = 2.5 or Q = 4.5/0.5 = 9 muffins

Price of the package = CS + revenue if price is equal to MC

= 0.5*(7 – 2.5)*9 + 9*2.5

= $42.75

Therefore, the optimal number of bran muffins to sell in a single package is 9 and the optimal package price is $42.75