Suppose you are the manager of Alpha Enterprises - a firm that holds a patent th

Question

Suppose you are the manager of Alpha Enterprises - a firm that holds a patent that makes it the exclusive manufacturer of bubble memory chips. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for bubble memory chips are

Q=25-.5p,

C=50+2Q

a. What is the firm's inverse demand function?

b. What is the firm's marginal revenue when producing 4 units of output?

c. What are the levels of output and price when you are maximizing profits?

d. What will be the level of your profits?

Explanation / Answer

a. Inverse demand function: p(Q) = 50 - 2*Q
b. Marginal Revenue is given by the derivative of the Revenue with respect to the quantity. The Revenue is given by R(Q) = P(Q)*Q = 50*Q - 2*Q^2. So the Marginal Revenue is MR(Q) = 50 - 4*Q.

Then MR(4) = 50-4*4 = 34.

c. The profit maximizing level given by the following problem:

max R(Q) - C(Q) with respect to Q.

So by the First-Order Condition:

50 - 4*Q - 2 = 0. Solving for Q, we got: Q = 12. So the Price is P(12) = 26.

d. The profit is given by R(12) - C(12) = 26*12 - 50 - 2*12 = 238.

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