Some notes on horizontal supply curves

This post is mostly for my students.

In a competitive market, a firm's supply curve is dictated by its marginal costs - the cost of producing an additional unit of output. If a firm can't get enough from selling its product to cover the marginal cost of production, it won't bother producing in the first place. If the price a firm gets for its widgets covers the marginal production costs, making them is worthwhile, so the firm will increase production - and continue doing so until price and marginal cost are equal.

Firms have to think about their average costs, as well as their marginal costs. If the price is above average cost, they make a super-normal profit. In a competitive market, over the long-run, any profits attract new firms into the industry, bidding down the price. If the market price dips below average costs, firms go out of business, and the price rises again over the longer-run. In the long-run, a competitive market is made up of firms producing where price equals marginal cost, and making - other than a normal rate of return on their capital investments - zero profits.

The firm-level and long-run industry level considerations together generate a market supply curve. These supply curves can be upwards sloping, but they don't have to be. Suppose, with the most efficient possible t-shirt production technology,* a typical firm has marginal costs of $10 per t-shirt, and is just breaking even. The market supply curve is made up of dozens, hundreds, or thousands of identical firms, all producing where price=marginal cost=$10. This is shown in the diagram below: at a quantity of 1, price and marginal costs are $10. At a quantity of 10, price and marginal costs are $10. At a quantity of 100, price and marginal costs are $10.

The beauty of these constant marginal cost, horizontal supply curve examples is that they are so easy to analyze. Price is equal to $10. Put that into an equation and work with it.

Seriously. Suppose that demand for t-shirts is, say, Q=9543-27P, and t-shirts are supplied in a competitive market at a price (or at a constant marginal cost) of $10. Then P=10, and the equilibrium quantity is Q=9543-27*P or Q=9543-27*10 or 9273. That's it. Two steps: (1) to find the price, write down p=whatever the marginal cost is (2) substitute for price in the demand curve. That's the equilibrium quantity. 

It seems strange to people who are used to seeing questions of the form

Demand: Q^d=100-10P^d, Supply: Q^s=10P^s and then solving by as:

Q^d=Q^s  and so 100-10P=10P, 100=20P, P=5, substituting back, Q=10*5=50. 

But in fact, all that's happened with the horizontal supply curve that the first step, where the quantities were equated to solve for price, has been cut out - because the supply curve nails down the price.

Why use horizontal supply curves - or, more generally, why assume constant marginal costs?

Public economics is about taking the competitive market equilibrium and making things messy - adding social costs to private costs, considering the impact of taxes, sometimes looking at imperfectly competitive markets, collective consumption problems such as public goods. If things are going to get messy, it's best to start out as simple as possible.

* that is, its producing at the minimum point on its average cost curve.

Comments

[LS]

For supply curves that do slope up, it would be helpful to expand on the concept of producer surplus and economic rent in relation to short run, long run, marginal cost and average cost for the firm and industry.

Specifically, when is everything to the left of an upwards sloping supply curve considered producer surplus, economic rent or both?

[PeterN]

Isn't there a bit of a problem with defining non-monopoly profit at equilibrium to be zero? In that case either most products are rarely at equilibrium, or almost all producers have a monopoly.

I think it's closer to say that marginal return in the long run approaches the point where its NPV falls below the expected NPV of a redeployment of the resources made available from ceasing production (discounted for risk and uncertainty).

Either you make a higher margin new version of the product, make a new product and/or sell the old product to someone with lower costs or cheat on costs (The price of a Hershey bar doesn't change, just the amount of chocolate in it. Banks start adding fees for formerly free services...).

[Frances Woolley]

PeterN "Isn't there a bit of a problem with defining non-monopoly profit at equilibrium to be zero?"

I'm not sure I understand your point. Remember that "zero profits" includes normal rate of return on capital. Accounting profits can be positive even when econ profits are zero. "Positive profits" would mean an super-normal rate of return on capital.

[Peter N]

I think this article (link courtesy of Tyler Cowen) will explain things better than I could.

http://crookedtimber.org/2007/06/07/profits-and-loss/#more-5955

In the MR comments I found this gem from Tom Kelly:

"In the long run, there are no profits. Truly profitable companies make their profits by refusing to operate in the long run."

[Frances Woolley]

Peter - Context. it's all context.

The question the students have to analyze in this case is whether or not the Ontario government's policy of requiring direct wired in smoke alarms in all new buildings is a good one. In this case, the assumption that installing smoke alarms has a constant marginal cost is really not a bad one from the point of view of a simple calculation of the costs and benefits of smoke alarms.

Now one could argue that the cost of installing a smoke alarm costs isn't *really* a cost because of x/y/z - e.g. that the charge for the smoke alarm is, in part, economic rents enjoyed by the supplier of smoke alarms, and thus, from a social point of view, it's a transfer not a cost. That might make an interesting exam/assignment question.

But just calculating the total costs of installing smoke alarms, and doing a simple benefit cost calculation, is a good place to begin. Not all complications can be dealt with simultaneously, and the question given the students (not shown here) focuses more on demand than supply side market failures.