[Editor’s Note: Dear readers, you delighted us with all your responses to Professor Cutsinger’s inaugural EconLog Price Theory Problem. Thanks! We reprint that question below, followed by his suggested solution. Next week, we’ll post problem #2. Long live price theory!]
Ask:
In his book, Basic economicsThomas Sowell (2015) writes, “the price a producer is willing to pay for a given ingredient becomes the price other producers are forced to pay for that same ingredient” (p. 20). With that quote in mind, consider the following scenario:
The demand for drinking milk is increasing while the demand for milk in the form of cheese, ice cream and yoghurt remains the same. Assume that the supply of milk is completely inelastic. Explain why the elasticity of demand for milk from these other uses determines how much milk from these uses will be reallocated for direct consumption.
Answer:
One of the reasons I like this quote from Sowell’s book is that it prompts us to think about the role that market prices play in distributing a resource among its different uses. In this case, the price of milk divides a fixed amount between those who want to drink it and those who need milk to produce cheese, ice cream and yogurt.
Figure 1 illustrates this idea. The market demand for milk consists of the various milk demands. The interaction between market demand for milk and fixed supply determines the market price, which in turn determines how much milk demanders will buy for each use. The buyer with the highest willingness to pay for milk therefore determines the price that all buyers have to pay.
As the demand indicates, the demand for drinking milk is increasing. Figure 1 illustrates the increase in demand as the rightward shift in demand for drinking milk. Because market demand partly consists of the demand for drinking milk, it also shifts to the right, and so the milk price rises to clear the market.
Figure 1: Individual and market demand for milk
This question assumes that the market supply of milk is completely inelastic (reflected by the vertical market supply of milk in Figure 1). Suppliers therefore no longer produce milk despite the higher price. The amount of milk allocated to the production of cheese, ice cream and yoghurt must therefore decrease to meet the increased demand for drinking milk.
What role do the price elasticities of demand for milk for these other uses play in determining the amount of milk transferred from these uses to drinking water?
The price elasticity of demand tells us how sensitive the quantity demanded is to price changes. It is the ratio of the percentage change in quantity caused by a percentage change in price. The higher the absolute value of this ratio, the better the quantity demanded responds to price changes.
Let us assume that at the initial market price of milk, the price elasticity of demand for cheese is less than that of ice cream, which is less than that of yogurt. The slopes of the milk demand curves for these different uses in Figure 1 reflect these different elasticities.
Note that with a higher market price of milk, the change in the quantity of milk demanded differs per milk use. For example, the quantity of milk demanded for yoghurt decreases the most, while the quantity of milk demanded for cheese decreases the least. This result is not surprising given our assumption that the price elasticity of demand for yogurt was higher than that of cheese or ice cream.
Another reason why this result is not surprising is that, intuitively, the demanders who are most sensitive to price changes will have the greatest response to price changes. For example, suppose there are many milk substitutes in the production of yogurt, but few milk substitutes in the production of cheese. In this case, the percentage change in milk demanded for yogurt would be greater than that for cheese, since yogurt producers have more options than cheese producers.
We could carry out this analysis further to reveal the effects on the prices of cheese, ice cream and yoghurt. We could also consider how an increase in demand for drinking milk affects the prices of milk substitutes. Our answers to these questions would also depend on these price elasticities.
This question highlights the interconnected nature of markets. By integrating the concept of elasticity, we can go deeper into understanding the nature of these connections.
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For those interested in a formal discussion of the relationships between changes in supply, demand, prices, quantities, and elasticities, see this lecture on the supply and demand perspective by Kevin Murphy.
Bryan Cutsinger is an assistant professor of economics at Florida Atlantic University’s College of Business and a Phil Smith Fellow at the Phil Smith Center for Free Enterprise. He is also a fellow at the American Institute for Economic Research’s Sound Money Project and a member of the editorial board of Public Choice magazine.