
[Editor’s note: We’re bringing back price theory with our series on Price Theory problems with Professor Bryan Cutsinger. You can view the previous problem and Cutsinger’s solution here and here. Share your proposed solutions in the Comments. Professor Cutsinger will be present in the comments for the next two weeks, and we’ll again post his proposed solution shortly thereafter. May the graphs be ever in your favor, and long live price theory!]
Question: Suppose that cotton and wool are substitutes. In addition, suppose that the supply of cotton is upward sloping while the supply of wool is perfectly elastic. Evaluate: A new production technique that increases the supply of cotton will reduce the quantity of wool supplied, but there will be no change in the price of wool and, thus, no change in the demand for cotton.
Solution: We can illustrate this solution graphically. The figure on the left hand side represents the market for wool, while the figure on the right hand side represents the market for cotton.
READER COMMENTS
Glen Whitman
Jan 23 2025 at 1:38pm
I’m curious about how you teach the topic of substitutes in a more typical case where both supply curves are upward-sloping. The simple version would be pretty close to what you have here, except that decrease in demand for wool (induced by the lower price of cotton) would result in a lower price of wool. And then you could stop the analysis there to avoid further complications.
But, as your last sentence implies, there could be a feedback effect. The lower price of wool would cause a decrease in demand for cotton. And that would result in an even lower price for cotton. And that would cause a further reduction in the demand in wool. And that would cause the price of wool to fall a bit more, resulting in a further reduction in demand for cotton. You could in principle go back and forth forever, but because the effects are getting smaller and smaller, you would “close in” on a final position; to say much more than that, I think you’d need a general equilibrium model.
But I never do this with my students, even at the intermediate level. I usually stop where you stopped in the simplified model in which wool supply is flat. If a smart student asks whether the lower price for wool would have an effect on the cotton market whose supply shift initiated all this, I’ll usually say something like, “Yes, but that’s a second-order effect and we usually don’t need to worry about it.”
Bryan Cutsinger
Jan 24 2025 at 3:05pm
Glen,
When I teach this type of problem using upward sloping supply curves, I use McCloskey’s approach from Applied Theory of Price (p. 123). Basically, I arbitrarily pick a point on both diagrams where the process you describe stops. As long as my students understand the direction of the feedback effects and that the process will eventually stop, I’m good.
I agree that if you wanted to say something more detailed than that, you’d need a more complicated model, so I don’t bother at the intermediate level.
-Bryan
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