Suppose Mona runs a small cake business from her kitchen (using a small electric

Question

Suppose Mona runs a small cake business from her kitchen (using a small electric oven). She faces an inverse demand of P = 100 Q/2 for her cakes. Her cost of baking Q cakes is C(Q) = 1/2Q^2. Suppose Mona decorates her cakes so uniquely that she practically becomes a monopolist. what price should she set for her cakes? How many does she sell? What is her profit? Edward, Mona's friend, offers her two new ovens at a price of dollar 200 each. If she accepts Edward's offer, how many cakes will she produce in each oven? What will her profits be ? Should she accept Edward's offer?

Explanation / Answer

(a)

P = 100-Q/2

TR = 100Q - Q^2/2

MR = dTR/dQ = 100 - 4Q

C = 1/2Q^2

MC = dC/dQ = Q

Profit max output at MR=MC will be

100 - 4Q = Q

5Q = 100

Q = 20

At Q = 20, P = 100 - 20/2 = 90

TR = 90*20 = 1800

TC = 1/2*400 = 200

Profits = 1800-200 = 1600

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