Question

Every year, Heather hosts a holiday party for her friends. Her party budget is \(\$ 200 .\) Heather spends her budget on food platters that cost \(\$ 25\) each and on entertainment, which costs \(\$ 50\) per hour. [LO 7.4] a. Graph Heather's budget constraint for food and entertainment. b. To reward her loyal business, the entertainment company Heather hires has offered her a 50 percent discount on entertainment purchases for this year's party. On your graph, illustrate Heather's new budget constraint for food and entertainment. c. Assuming that food platters and entertainment are normal goods, what can you say about the quantity of each good that Heather will purchase after the discount? Will the quantity of entertainment increase or decrease, or is the change uncertain? Will the quantity of food increase or decrease, or is the change uncertain?

Short answer

After the discount, Heather will likely purchase more entertainment and food.

Step-by-step solution

Define the Budget Equation

Heather's budget equation before the discount is given by the equation \( 25F + 50E = 200 \), where \( F \) is the number of food platters, and \( E \) is the number of hours of entertainment. This equation represents all the possible combinations of food and entertainment that Heather can afford.

Plot the Initial Budget Constraint

To graph the budget constraint, solve the equation for the intercepts. For no entertainment, \( E=0 \), we find \( F = \frac{200}{25} = 8 \). For no food, \( F=0 \), we find \( E = \frac{200}{50} = 4 \). Plot these intercepts on a graph (\( F \)-axis and \( E \)-axis) and connect them with a straight line. This line represents Heather's initial budget constraint.

Adjust for the Entertainment Discount

With a 50% discount on entertainment, the new cost per hour becomes \( 25 \). The new budget equation is \( 25F + 25E = 200 \).

Plot the New Budget Constraint

Solve the new equation for intercepts. With no entertainment, \( E=0 \), we have \( F = \frac{200}{25} = 8 \). With no food, \( F=0 \), \( E = \frac{200}{25} = 8 \). Plot these points and connect them with a straight line. The new line lies to the right of the original, indicating more resources are available for both goods.

Analyze the Effect of the Discount on Purchases

With food and entertainment as normal goods, as the price of entertainment decreases, Heather can afford more of it. The quantity of entertainment will likely increase. Since the budget constraint level increases the overall purchasing power, the quantity of food is also likely to increase, due to the increase in income effect for normal goods.

Key concepts

Normal Goods

Normal goods are items that people buy more of when their income rises. These goods are essential because as people's purchasing power increases, they tend to buy more of these items. In Heather's case, food platters and entertainment serve as normal goods. This means that when Heather finds her budget stretches further due to a discount or increased satisfaction, she will likely purchase more of these goods.
Understanding normal goods can help you predict consumer behavior. Here are a few key points about normal goods:

• As income increases, demand for normal goods typically rises.
• These goods are considered to be positively correlated with income.

So, when Heather receives a discount on entertainment, it's equivalent to a rise in income. This can result in a higher quantity of both food platters and entertainment being purchased.

Income Effect

The income effect shows how a change in the consumer's purchasing power affects their consumption choices. In Heather’s situation, a discount on entertainment changes her budget constraint, effectively increasing her purchasing power.
Here's what you need to know about the income effect:

• It describes how changes in purchasing power influence the quantity demanded of normal goods.
• When goods become cheaper, the consumer feels richer, even if their actual income hasn't changed.

For Heather, the discount on entertainment acts similarly to a direct increase in her budget. Even though her budget of $200 hasn't changed, she can now buy more because entertainment is cheaper. Thus, both her consumption of entertainment and food plies end up increasing due to the income effect of the discount.

Graphing Budget Constraint

Graphing a budget constraint helps visualize the trade-offs between different goods that a consumer can afford. Heather's party planning situation is an excellent example of how to use a budget constraint graph. By placing food platters on the horizontal axis and entertainment on the vertical axis, Heather's choices can be more clearly understood.
Initially, Heather could afford a mix of food and entertainment that lay along the line formed by her budget constraint of $200. Her budget constraint can be represented as:

• Original equation: \( 25F + 50E = 200 \)
• New equation with discount: \( 25F + 25E = 200 \)

Plotting these on an axis, the original line pairs indicated she could spend on up to 8 food platters or up to 4 hours of entertainment. With the discount, she could now afford either 8 platters of food or 8 hours of entertainment. Her new budget line stretches further, reflecting the increased purchasing options.

Price Effect

The price effect combines the income and substitution effects—an essential part of understanding consumer behavior. In Heather's case, the entertainment discount directly reduces the per-hour cost she pays, which is a classic example of a price effect.
Important points to understand about the price effect include:

• As the price of a good falls, consumers can substitute away from higher-priced alternatives (substitution effect).
• The decreased price increases "real income," allowing consumers to purchase more (income effect).

For Heather, the reduction in cost of entertainment increases her effective income (due to the income effect) and makes entertainment relatively more attractive compared to food platters, potentially shifting her preference towards entertainment (substitution effect). Together, the reduced price encourages Heather to spend more overall and revamp her party with perhaps a bit more flair.