The American Baker’s Association reports that annual sales of bakery goods last

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 = 6 - 0.5Q.

If your cost of producing bran muffins is C(Q) = .5Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Instruction: Round your answer for the optimal package price to two decimal places.

Optimal package size:  units
Optimal package price: $

Explanation / Answer

P = 6 - 0.5Q.

TR = P xQ = 6Q - 0.5Q2

MR = d(TR)/dQ = 6 - Q

TC = 0.5Q and MC =0.5

The firm will be in equilibrium when MR = MC

6 - Q= 0.5

So, Q =5.5

Then, P = 6 - 0.5Q = 6 - 0.5 x 5.5 =$3.25

Optimal package size: 5.5 units
Optimal package price: $3.25

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