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The American Baker’s Association reports that annual sales of bakery goods last year rose 15 percent,...

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: $

Solutions

Expert Solution

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

Rahul Sunny answered 2 years ago
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