[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!]

Question:

In his book, Basic Economics, Thomas Sowell (2015) writes, “the price which one producer is willing to pay for any given ingredient becomes the price that other producers are forced to pay for that same ingredient” (p. 20). With that quote in mind, consider the following scenario: 

The demand to drink milk rises while the demand for milk in the form of cheese, ice cream, and yogurt remains the same. Assume that the supply of milk is perfectly inelastic. Explain why the elasticities of demand for milk in these other uses determine how much milk will be reallocated from these uses for direct consumption.

 

Answer:

One of the reasons I like this quote from Sowell’s book is that it gets us to consider the role that market prices play in allocating a resource across its various uses. In this case, the milk price allocates a fixed amount between those who want to drink it and those who demand milk to produce cheese, ice cream, and yogurt. 

Figure 1 illustrates this idea. The market demand for milk consists of the various demands for milk. The interaction of the market demand for milk and the fixed supply determines the market price, which, in turn, determines how much milk demanders will purchase for each use. Thus, the buyer with the highest willingness to pay for milk determines the price all buyers must pay.

As the question indicates, the demand for drinking milk rises. Figure 1 illustrates the increase in demand as the rightward shift of the demand for drinking milk. Since the market demand consists, in part, of the demand for drinking milk, it also shifts rightward, and so the price of milk rises to clear the market.

 

Figure 1: Individual and Market Demand for Milk

The question assumes that the market supply of milk is perfectly inelastic (reflected by the vertical market supply of milk in Figure 1). Hence, suppliers do not produce any more milk despite the higher price. So, the amount of milk allocated to the production of cheese, ice cream, and yogurt must fall to meet the increased demand for drinking milk.

What role do the price elasticities of demand for milk in these other uses play in determining the amount of milk reallocated from these uses to drinking?

The price elasticity of demand tells us how responsive quantity demanded is to price changes. It is the ratio of the percent change in quantity brought about by a percent change in price. The higher the absolute value of this ratio, the more responsive the quantity demanded to price changes.

Let’s suppose that at the initial market price of milk, the price elasticity of demand for cheese is less than ice cream, which is less than yogurt. The slopes of the demand curves for milk in these various uses in Figure 1 reflect these different elasticities.

Note that at the higher market price of milk, the change in quantity demanded for milk differs across the different uses of milk. For instance, the quantity of milk demanded for yogurt falls the most while the quantity of milk demanded for cheese falls 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 this result is not surprising is that, intuitively, demanders most sensitive to price changes will have the largest response to price changes. For example, suppose there were many substitutes for milk in the production of yogurt but few substitutes for milk in the production of cheese. In this case, the percent change in the milk demanded for yogurt would be larger than that demanded for cheese since yogurt producers have more options than cheese producers.

We could take this analysis further to uncover the effects on cheese, ice cream, and yogurt prices. We could also trace how an increase in demand for milk to drink 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. Incorporating the concept of elasticity allows us to go deeper in 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 elasticity, see this lecture on the supply and demand perspective by Kevin Murphy.

 

Bryan Cutsinger is an assistant professor of economics in the College of Business at Florida Atlantic University and a Phil Smith Fellow at the Phil Smith Center for Free Enterprise. He is also a fellow with the Sound Money Project at the American Institute for Economic Research, and a member of the editorial board for the journal Public Choice.