Question

Hideki attends baseball games and goes to movie theaters. Baseball tickets cost \(\$ 15,\) and movie tickets cost \(\$ 10 .\) His entertainment budget is \(\$ 180\). \(\left[\mathrm{LO}_{7.4}\right]\) a. Graph Hideki's budget constraint for baseball and movie tickets. b. Suppose the home team is having a good season, and the price of baseball tickets goes up to \(\$ 20\) per game. Graph the new budget constraint. c. Assuming that baseball and movie tickets are normal goods, what can you say about the quantity of each good that Hideki will consume after the price of baseball tickets goes up? Will the quantity of baseball games he attends increase or decrease, or is the change uncertain? Will the quantity of movies he watches increase or decrease, or is the change uncertain?

Short answer

Baseball games attendance will decrease, movie watching may increase.

Step-by-step solution

Understanding the Budget Constraint

Hideki has a budget of $180. Let's denote the number of baseball games he attends as \( B \) and the number of movies he attends as \( M \). The cost for baseball games is \( 15B \) and for movies is \( 10M \). The budget constraint equation is, therefore, \( 15B + 10M = 180 \).

Graphing Initial Budget Line

To graph the initial budget line, find the intercepts: when \( B = 0 \), \( 10M = 180 \) gives \( M = 18 \). When \( M = 0 \), \( 15B = 180 \) gives \( B = 12 \). Thus, plot a line from \((B, M) = (0, 18)\) to \((12, 0)\).

Graphing the New Budget Line

With the increased ticket price, the cost for baseball games changes to \( 20B \). The new budget constraint is \( 20B + 10M = 180 \). For this line, intercepts are when \( B = 0 \), \( M = 18 \) and when \( M = 0 \), \( 20B = 180 \) results in \( B = 9 \). Plot this new line from \((B, M)=(0, 18)\) to \((9, 0)\).

Analyzing Changes in Consumption

Since the price of baseball games increases and both are normal goods, Hideki will likely decrease his consumption of baseball games due to higher costs, shifting to more movies. This is due to the substitution effect (choosing more of the relatively cheaper good, movies) and an income effect (both goods are normal, overall consumption might decrease but incline towards movies).

Key concepts

Normal Goods

Normal goods are those types of goods for which the demand increases as the consumer's income rises, and decreases when the consumer's income falls. In Hideki's case, both baseball tickets and movie tickets are considered normal goods.
When his budget or income allows, Hideki enjoys indulging in both activities more. However, if his budget tightens due to price increases, such as with the baseball tickets, the desire to spend as much on these goods may decrease.
This behavior is common as we tend to prioritize our spending on goods that offer us better satisfaction or utility when our financial situation changes.

Substitution Effect

When the prices of goods change, consumers often shift their consumption based on relative prices—a phenomenon known as the substitution effect. With the increase in the price of baseball tickets, Hideki might reconsider attending as many games.
Instead, he could substitute some of his baseball game outings with movie nights, as long as movies still offer a favorable price point compared to baseball games.

• This results from the increased cost associated with baseball games making movies relatively cheaper and more attractive economically.
• The substitution effect drives consumers to optimize their satisfaction by choosing cheaper alternatives when prices shift.

Thus, in response to baseball ticket price hikes, we can expect Hideki to buy more movie tickets, assuming his preferences for both activities remain constant.

Income Effect

The income effect occurs due to changes in purchasing power—or how much a consumer's budget effectively allows them to purchase. This effect can influence consumption patterns along with the substitution effect.
When the price of baseball tickets rises, Hideki's budget buys less than before. This is akin to a reduction in his disposable income, affecting his ability to purchase both goods, even though they are normal goods.

• Since both goods are desirable (normal), Hideki might still want to attend both, but with less effective income, he will possibly choose fewer baseball games.
• The income effect can lead him to adjust overall consumption downward, yet favor movies due to their unchanged pricing.

These changes highlight how a price increase in one good permeates through one's entire budget, altering consumption behavior for multiple goods.

Consumption Changes

Changes in prices and budget constraints directly impact consumption choices. For Hideki, the price increase of baseball tickets alters his feasible consumption possibilities. We foresee the following consumption changes:

• A decrease in the number of baseball games Hideki attends, due to their increased cost making them less affordable within the same budget.
• An increase in movie attendance, or at the very least a relative preference shift towards movies, triggered by both substitution and income effects.

Overall, the budget constraints dictate Hideki's decisions, leading him to adjust his entertainment activities to maintain a semblance of satisfaction without exceeding his budget.