Let Them Eat Steak: Cutsinger’s Solution

Understanding the Impact of Price Changes on Consumer Behavior

Question:

Russ buys 5 sirloins per week. True or false: If the price of sirloin rises by $5 apiece, and if Russ’ preferences and income remain constant, he will have $25 a week less to spend on other things.

Solution:

Consumer behavior is heavily influenced by prices, as observed in the real world. When prices fluctuate, so does consumer decision-making.

Consumer theory dictates that individuals maximize utility by consuming goods up to the point where the marginal value of one more unit equals its market price. In the case of a price increase, such as the rise in sirloin prices for Russ, the marginal value at the optimal consumption level must also increase by $5 to align with the new price.

As Russ consumes more sirloin, the marginal value decreases, leading him to adjust his consumption to maintain the equilibrium between marginal value and price. This adjustment may result in Russ buying fewer sirloins than before.

Applying Mathematical Analysis

We can further illustrate this concept by examining Russ’s budget constraint. If Russ allocates his income, M, towards purchasing sirloin, S, and other goods, Y, his budget constraint can be represented as:

M = P_SS + P_YY

With the price of sirloin increasing by $5, the revised budget constraint becomes:

M = (P_S + 5)S + P_YY

Although Russ’s income and the price of other goods remain constant, the maximum quantity of other goods he can purchase remains unchanged at M/P_Y. However, the change in relative prices alters the slope of his budget line, leading Russ to adjust his consumption pattern and optimize his spending between sirloin and other goods.

While Russ’s real income may decrease due to the price increase, he adapts his spending to reflect the new price dynamics. Therefore, it is not accurate to assume he will have $25 less to spend on other goods each week.