Let Q(L) = 12L² – (L³)/4 with costs = 1000 + 50L. Let the price of output be P = $1.

A. Complete the table.

	Q(L)=12L2–(L3)/4	P= 1	C=1000+50L
L	Q	REV	COST	PROFIT	Profits if P=0.5
0
5
10
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

B. Graph revenues and costs as a function of Q: Can you explain why revenue is linear in output (a straight line) but costs are not linear.

C. Identify the profit maximizing level of L (and hence Q) in your figure.

D. Show the break-even level of Labour and Output. That is, what is the minimum level of L and Q that ensure positive profits given P = $1. Why do we need to raise output high enough to break even?

E. Why is it true that, at the optimal output, marginal cost = $1. Give the intuition.

F. Suppose P falls to $0.50. Will the firm choose Q = 0 (eg shut-down). Explain.