Q1: (10 points) Let Q(L) = 6L2 – (L3)/6 with costs = 300 + 100L. Let the price of output be P = $4.
a) Complete the table on the next page. You can do this in excel or by hand.
b) Graph revenues and costs as a function of Q: Can you explain why is revenue 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. Why do we need to raise output high enough to
break even?
e) Why is it true that, at the optimal output, marginal cost = $4. Give the intuition.
f) Suppose P falls to $1.8. Confirm that the firm will choose Q = 0 (eg shut-down). Explain
what is happens.