Question

Consider the following weekly cost function:

TC = 200 + 120Q - 6Q^2 + 0.2Q^3

a. What are the total fixed costs per week associated with this technology?
a.) 60
b.)120
c.)200
d.) Zero. This is a long-run function

b. What is the number of units of output per week (Qs) that occurs at the end of Stage I
a.) 6
2.) 15
3.) 9
4.) 12

Answer 1

(a)

Fixed cost is that portion of total cost which is independent of Quantity(Q) and hence is constant.

Here Total Cost(TC) = 200 + 120Q - 6Q² + 0.2Q³

We can see from above that portion of TC which is independent of Q or hence is constant is 200

So ,Total Fixed Cost = 200

Hence, the correct answer is (c) 200

(b)

In Stage , Total cost is increasing at a diminishing rate. This means that Marginal Cost(MC) is decreasing. After than Production exhibits diminishing returns and because of which Marginal Product decreases and Marginal Cost(which moves in opposite direction to production) increases. Thus, Stage 1 ends till the quantity where Marginal Cost(MC) is decreasing.

Here Total Cost(TC) = 200 + 120Q - 6Q² + 0.2Q³

Marginal Cost(MC) = d(TC)/dQ = 120 - 12Q + 0.6Q²

MC is decreasing means d(MC)/dQ < 0 => d(MC)/dQ < 0 => -12 + 1.2Q < 0 => Q < 10

Last quantity which is lesser than 10 is Q = 9(considering only integers).

Hence, the correct answer is (c) 9