Whats the amount the firm will decide to produce?

Question

Hey,

 

I got a economics test soon and was wondering if anyone could help me out with the following practice question: 

A firm called Mojo has a production technology to produce a good Y with the
following total costs: T C(Q) = 400 + 30Q + Q2
if Q > 0. If Q = 0, TC(0) = 0.
The market for the good Y is a perfectly competitive market. The market price
is 40. How much will Mojo decide to produce?
A: Two or less units
B: I do not know
C: More than two units

I dont have the answers. I personally thought it was A, because at any quantity the firm will lose money. And because the question says: Q = 0, TC(0) = 0. Which means for 0 production, there are no costs. Am I correct?

Answer 1

For this question you have to first find the MC function in terms of Q. This could be done by taking the first derivative of the TC function. 

 

MC(Q) = 30+2Q 

A firm maximizes its profit at a point where MC = MR = P (due to the market being a competitive market. So we equate the MC function to MR:

MC = MR =P

30+2Q = 40

Q=5

 

Also if the TC function is as stated, when Q=0 the firm still bears some fixed cost that would be equal to 400. (TC = 400+30(0)+0^2 = 400)