In a competitive industry, why are economic profits normal (zero) in the long run? What about if firms are not identical, and have different costs?

Profits are zero in the long run because entry and exit are free in competitive markets. Any firms earning positive (supernormal) profits in an industry will attract entrants, who want profits of their own. This will increase the supply and will continue until all profits are squeezed to zero (and then no more firms enter). Conversely, firms earning negative profits (loses) will exit the industry over the long run, decreasing the supply, and firms will continue to do this until losses fall back to zero. Thus, the stable equilibrium condition is that an industry tends to earn profits of zero, as any deviation would cause entry and exit until profits/losses get competed back to zero.

Firms that have rent-generating inputs see lower costs, and therefore higher profits. The problem is, these rent-generating inputs can be “poached” and enticed to work for other firms. This competition between firms pushes up prices for those rent-generating inputs. This raises the costs for those firms employing those inputs, in the form of higher salaries, higher lease prices, etc., whatever it takes to keep the input working for the firm and not a different firm. In equilibrium, rents rise until they push costs to equal revenues, and hence, profits to equal 0.

Assume that consumers view tax preparation services as undifferentiated among producers, and that there are hundreds of companies offering tax preparation. The current market equilibrium price is $120. Amy’s Audits is a local tax preparation firm that has a daily short-run cost structure given by:

\[\begin{align*} C(q)&=100+4q^2\\ MC(q)&=8q\\ \end{align*}\]

How many tax returns should Amy prepare each day if her goal is to maximize profits?

Amy is in a perfectly competitive market, so she will prepare up to the quantity where \(p=MR(q)=MC(q)\).

\[\begin{aligned} p&=MC(q)\\ 120&=8q\\ 15&=q^*\\ \end{aligned}\]

She will prepare 15 tax returns per day to maximize profits.

The following graph will help visualize all the parts of this question:

How much profit will she earn each day?

Profit is total revenues minus total costs:

\[\begin{aligned} \pi &= pq-C(q)\\ \pi &=(120)(15)-(100+4q^2)\\ \pi &= 1800-(100+4(15)^2)\\ \pi &= 1800-1000\\ \pi &= \$800\\ \end{aligned}\]

Her profits are $800 (per day).

Alternatively, we could calculate profits as price minus average costs times quantity. First we would need to find average costs at \(q^*=15\):

\[\begin{aligned} AC(q)&=\frac{100}{q}+4q\\ AC(15)&=\frac{100}{15}+4(15)\\ AC(15)&\approx 6.67+60\\ AC(15)&\approx 66.67\\ \end{aligned}\]

Knowing this, we plug it into the formula for profits using price and average costs:

\[\begin{aligned} \pi &=(p-AC(q^*))q^*\\ \pi &\approx(120-66.67)15\\ \pi &\approx(53.33)15\\ \pi &\approx \$800\\ \end{aligned}\]

At what market price would she break even?

A firm breaks even where its Average cost equals its marginal cost. We aren’t given average cost, so we first need to find it by taking total cost and dividing by quantity:

\[\begin{aligned} AC(q)&=\frac{C(q)}{q}\\ AC(q)&=\frac{100+4q^2}{q}\\ AC(q)&=\frac{100}{q}+4q\\ \end{aligned}\]

Now we know that average cost is minimized where:

\[\begin{aligned} AC(q)&=MC(q)\\ \frac{100}{q}+4q&=8q \\ \frac{100}{q}&=4q\\ 100&=4q^2 \\ 25&=q^2 \\ 5&=q^*\\ \end{aligned}\]

We know the quantity but we need to find the *price* where the
firm breaks even, so plugging this back into average cost:

\[\begin{aligned} AC(q)&=\frac{100}{q}+4q\\ AC(5)&=\frac{100}{(5)}+4(5)\\ AC(5)&=20+20\\ AC(5)&=40\\ \end{aligned}\]

Amy will break even, and earn normal profits of 0 if the market price were $40 per tax return.

Below what hypothetical price would she shut down in the short run?

A firm shuts down in the short run when it can no longer cover its average variable costs. We know the minimum average variable cost happens when it is equal to marginal cost. Since we are not given it, we first need to find average variable costs.

\[\begin{aligned} AVC(q)&=\frac{VC(q)}{q}\\ AVC(q)&=\frac{4q^2}{q}\\ AVC(q)&=4q\\ \end{aligned}\]

Now we know \(AVC\) is minimized where:

\[\begin{aligned} AVC(q) &= MC(q)\\ 4q &= 8q \\ q&=0 \\ \end{aligned}\]

Average variable cost is minimized when Amy produces no output.

Let’s check and see what price has an output of 0, by using either the \(AVC(q)\) or \(MC(q)\) curves:

\[\begin{aligned} AVC(q)&=4q\\ AVC(0)&=4(0)\\ AVC(0)&=\$0\\ \end{aligned}\]

So she would shut down only when the price is less than $0 (which can’t happen). This happens when the AVC function is not a curve, but a straight line starting at the origin.

Sketch a graph and be sure to label everything you found in parts A-D.

See graph above.

What is Amy’s supply curve in the *short run*? Write a
function or describe it via the graph in E.

Her short run supply curve is her marginal cost curve above her shut down price (minimum of AVC, or $0).

What is Amy’s supply curve in the *long run*? Write a function
or describe it via the graph in E.

Her long run supply curve is her marginal cost curve above her break even price (minimum of AC, or $40)

What is the difference between allocative (in)efficiency, productive (in)efficiency, rent-seeking, and X-inefficiency?

*Allocative efficiency* describes the efficiency of how
resources are allocated: resources should be allocated to their
highest-valued uses. The practical way to measure this is economic
surplus, consumer surplus [The difference between the maximum prices
buyers are willing to pay, and the market price they actually pay,
i.e. the triangular area between the Demand curve and the market price
to the left of equilibrium quantity.] plus producer surplus [The
difference between the minimum prices sellers are willing to accept, and
the market price they actually receive, i.e. the triangular area between
the Supply curve and the market price to the left of equilibrium
quantity.] In equilibrium in competitive markets, firms are all charging
\(p=MC\), goods are being produced to
the point where the marginal benefit to society (Demand) is equal to the
marginal cost to society. At this point, total economic surplus is
maximized.

A monopolist, which produces less output at a higher price reduces consumer surplus (it transfers some of it into profit) and creates deadweight loss.

*Productive efficiency* is maximized when a firm is producing
at the least-cost technology. In graphical terms, firms are producing at
the minimum of their average cost curves (minimum efficient scale). In
competitive markets, this is achieved in long run equilibrium, since
competitive firms always charge \(p=MC\), and long run equilibrium requires
firms to earn no profits (so no entry or exit occurs), which implies
\(p=AC\). Since \(MC=p=AC\), by the mathematical relationship
between marginal cost and average cost, average cost must be at its
minimum where it is equal to marginal cost.

*Rent-seeking* is all the costly investments that firms will
make to attain economic rents — returns above opportunity cost. In a
market power context, this often refers to investing resources into
creating barriers to entry, often by appealing to political authorities
to eliminate competition.

*X-efficiency*, or more to the point, X-inefficiency occurs
where firms with market power get complacent or lazy, from lack of
competition. This raises the firm’s costs compared to what they
otherwise would be where everyone is working at full capacity. As a
monopoly, this will *further* decrease output and raise the price
(reducing consumer surplus and creating deadweight loss), reducing
allocative efficiency.

Sketch a graph of a monopoly with no fixed costs, and constant equivalent average & marginal costs. Label all of the following:

- The equilibrium quantity and price if the market were competitive
- The profit-maximizing quantity and price for the monopoly
- The consumer surplus, profit, and deadweight loss under monopoly