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.
This, our first problem for 2025, is ready for you to solve! 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.
READER COMMENTS
John Hall
Jan 2 2025 at 11:54am
It helps to separate things out a little bit
Cotton supply curve shifts right, but wool supply curve shifts left/up. For cotton, assuming no change in demand (and a downward sloping demand curve), the quantity sold should increase and the price should decrease. For wool, assuming no change in demand (and a downward sloping demand curve), the quantity sold should decrease and the price should increase.
However, the price of wool is assumed to be unchanged. Why would this happen? It can’t happen due to a shift in the demand curve because the supply curve is perfectly elastic. There are two obvious reasons why the price of wool would remain unchanged: demand is perfectly elastic or there is a price ceiling.
That the demand for cotton is unchanged because the price of wool is unchanged is consistent with them being substitutes (and assuming no other change in demand for cotton).
David Seltzer
Jan 2 2025 at 12:30pm
Bryan: A bit of a brain teaser. My attempt at an answer: Given the supply of cotton increases, the supply curve shifts down and to the right. If demand for cotton remains the same, the equilibrium price of cotton will decline. If the price of cotton is lower in this case, the price of wool will remain constant if supply is reduced and demand for wool is reduced( shift down and to the left). Of course, I could be wrong.
Monte
Jan 2 2025 at 10:10pm
The only certainty in economics is uncertainty. But under the conditions stated, there will be a rightward shift of the supply curve for cotton and a movement along the demand curve (up and to the left) for wool. I’m tempted to agree with John Hall that the demand curve for cotton is perfectly elastic, but we’d then have to assume that cotton and wool are perfect substitutes, which technically they are not. So all that can be said is that an increase in the supply of cotton will lead to a decrease in the quantity demanded for wool.