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 = 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: 5

Optimal Package Price: ________

Answer 1

Firstly we find the cross price elasticity of demand (E).
E = Percentage change in demand/Percentage change in sale of bakery goods = 50%/15% = 3.33

Now, produces maximizes profit according to the rule MR = MC

Total Revenue, TR = P*Q = (11 - 1.5Q)*Q = 11Q - 1.5Q²
Marginal Revenue, MR = d(TR)/DdQ = 11 - 2(1.5Q) = 11 - 3Q
Marginal Cost, MC = dC/dQ = 3.5

Now, MR = MC gives,
11 - 3Q = 3.5
So, 3Q = 11 - 3.5 = 7.5
So, Q = 7.5/3
So, Q = 2.5

P = 11 - 1.5Q = 11 - 1.5(2.5) = 11 - 3.75 = 7.25

Optimal package size = 7.25/3.33 = 2 muffins per package
And P = 7.25