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).
Bryan Cutsinger
Jan 8 2025 at 4:13pm
John,
I’m not following why the supply curve for wool would shift.
Bryan
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.
Bryan Cutsinger
Jan 8 2025 at 4:14pm
David,
When you say the supply of wool is reduced, do you mean quantity supplied or the entire supply schedule? I think I understand what you’re saying, but wanted to confirm.
Bryan
Manfred
Jan 10 2025 at 4:12pm
I agree with David as long as he meant quantity supplied (of wool).
The supply curve of wool is perfectly elastic, which means that (I think) does not move.
But the demand for wool with go down because a substitute is now cheaper.
Bryan Cutsinger
Jan 11 2025 at 3:15pm
In that case, I agree. I wasn’t sure if David meant a change in supply or a change in quantity supplied.
-Bryan
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.
Bryan Cutsinger
Jan 8 2025 at 4:16pm
Monte,
I’m not sure why we move leftward along the wool demand curve. Has there been a change in wool supply? If so, why?
Bryan
Monte
Jan 9 2025 at 9:48pm
My thinking was that we would see a leftward movement along the wool demand curve because, with cotton cheaper due to the increased supply of cotton, the price of wool remaining unchanged would cause consumers to buy less wool. The quantity demanded for wool decreases at its current price, reflecting a typical response to a price change for a substitute good.
Bryan Cutsinger
Jan 11 2025 at 3:17pm
I think we may be saying the same thing but using different words. I agree there would be a leftward shift of the wool demand curve. Unless wool supply changes, there would not be a leftward movement along a given wool demand curve.
-Bryan
Thomas L Hutcheson
Jan 4 2025 at 10:20am
There will be a change in the supply of cotton and a fall in its price. Although the demand for cotton will not increase the “amount demanded” will. Wool is the exact opposite. The supply of wool will be unchanged but the amount supplied will fall as the demand for wool falls.
Bryan Cutsinger
Jan 8 2025 at 4:15pm
Nice!
Knut P. Heen
Jan 7 2025 at 8:25am
The statement is not precise enough. If demand is a function of both the price of cotton and the price of wool, that function does not change due to a change in supply of cotton. If demand is a function of only the price of cotton as in econ101 (the curve given by the cross-section of the former surface holding the price of wool constant), that function may change if the price of wool changes.
Notice that the only reason your question is “interesting” is that econ101 does not give a proper mathematical description of the problem (the price of wool is left out in the demand function).
Now, suppose the new production technology increases the income of some agents in the economy such that their demand for cotton increases. Oops, the income is assumed constant even though the purpose of adopting the new technology is to increase income.
Bryan Cutsinger
Jan 8 2025 at 4:21pm
Knut,
I agree that the statement is ambiguous. We can evaluate it under different assumptions.
If wool and cotton are substitutes, then the demand functions for both include the prices of the other. While we all teach econ 101 differently, I do include the prices of substitute and complimentary goods in demand functions.
Bryan