You are the manager of a firm that sells its product in a competitive market at a price of $50. Your firm's cost function is c=40+5q2(squared). Your firm's maximum profits are?
Answer:
profit = revenue - cost
revenue = price x quantity = 50 x quantity
cost = 40 + 5 x quantity x quantity
So you have:
P = 50 x Q - 40 - 5 x Q x Q
To get the maximum value for P with respect to Q, differentiate and set to 0.
That is, set dP/dQ = 0 and solve for Q.
Since P(Q) is a quadratic, dP/dQ is linear, so solving dP/dQ = 0 is easy and there is one solution.
If you don't know calculus, then you can plot the P as a function of Q and get the answer. (Trying to learn economics without having taken calculus is a mistake.)
Or, you can take advantage of the fact that this is a multiple choice question and compute P(Q) for the 4 choices.
But it is obvious that D loses money big time:
revenue(45) = 45 x 50 = 2,250
cost(45) = 40 + 5 x 45 x 45 = 40 + 5 x 2,025 = 10,165
profit(45) = 2,250 - 10,165 = -7,915
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