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 = 4 - 0.5Q.

If your cost of producing bran muffins is C(Q) = 1.5Q, 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

Ans.

given to us -

P = 4 - 0.5 Q

TC or C(Q) = 1.5Q

so, Marginal Cost = dTC / dQ

                                   = 1.5

Equilibrium is achieved where P = MC, so

4 -0.5Q = 1.5

0.5Q = 2.5

Q = 2.5 / 0.5 = 5

So the optimal package size is 5.

Optimal Package Price = 0.5 ( 4 - 1.5 ) ( 5 ) + 1.5 (5)

                                      = 0.5 ( 2.5 ) ( 5 ) + 1.5 (5)

                                      = 6.25 + 7.5

                                      = 13.75

Hence Optimal package price will be 13.75.

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