Question

[Uses the Indifference Curve Approach] a. Draw a budget line for Rafaella, who has a weekly income of \(\$ 30 .\) Assume that she buys chicken and eggs, and that chicken costs \(\$ 5\) per pound while eggs cost \(\$ 1\) each. Add an indifference curve for Rafaella that is tangent to her budget line at the combination of 4 pounds of chicken and 10 eggs. b. Draw a new budget line for Rafaella, if the price of chicken falls to \(\$ 3\) per pound. Assume that Rafaella views chicken and eggs as substitutes. What will happen to her chicken consumption? What will happen to her egg consumption?

Short answer

After drawing Rafaella's initial budget line and indifference curve, we found that she would buy 4 pounds of chicken and 10 eggs to maximize her utility. Once the price of chicken drops to \$3 per pound, we draw a new budget line, which intersects the y-axis at 30 and x-axis at 10. Considering chicken and eggs as substitutes, Rafaella is now likely to increase her consumption of chicken due to the lower relative price in comparison to eggs and, conversely, reduce her egg consumption.

Step-by-step solution

Drawing the Initial Budget Line

On a graph where the x-axis is chicken and the y-axis is eggs, the initial budget line can be drawn by determining the maximum affordance for each good. The maximum amount of chicken Rafaella can buy is equal to her income divided by the price of chicken, which is \( \frac{30}{5}=6 \) pounds. The maximum amount of eggs is \( \frac{30}{1} = 30 \) eggs. Hence, the budget line will intersect the y-axis at 30 and the x-axis at 6.

Adding an Indifference Curve

An indifference curve shows all combinations of chicken and eggs that provide Rafaella with the same level of satisfaction. The curve is composed of points (combinations of goods) which Rafaella values equally. Rafaella's indifference curve in this case should be tangential to her budget line at the combination of 4 pounds of chicken and 10 eggs. This is an optimal consumption point where she maximizes her utility given her budget constraints.

Drawing the New Budget Line

The price of chicken falls to \$3 per pound. This changes Rafaella's budget line because she can now afford more chicken with the same income. The maximum amount of chicken she can buy now is \( \frac{30}{3}=10 \) pounds. Therefore, the new budget line will intersect the y-axis at 30 (as price of eggs has not changed) and the x-axis at 10.

Predicting Changes in Consumption

As Rafaella sees chicken and eggs as substitutes, a drop in the price of chicken encourages her to consume more chicken and less eggs. Her chicken consumption will increase and her egg consumption will decrease.

Key concepts

Budget Constraint

When dealing with consumer choices, the budget constraint is a vital concept. It represents the combinations of goods a consumer can purchase given their income and the prices of those goods. For Rafaella, who has a weekly income of $30, her budget constraint originally consisted of two goods: chicken and eggs, priced at $5 per pound and $1 each, respectively. This restricts her to either 6 pounds of chicken or 30 eggs if she spent all her money on one item.

The budget constraint is depicted as a line on a graph, where the x-axis shows chicken, and the y-axis shows eggs. The endpoints represent maximum potential consumption of each good, forming a line that indicates all possible combinations Rafaella can afford if she spends her entire budget. This visual tool helps in understanding how changes in income or prices can shift the consumer’s purchasing power.

Whenever there's a price change, as in the case where the chicken's price dropped to $3, the budget line rotates accordingly. This new line allows Rafaella to purchase up to 10 pounds of chicken or keep buying 30 eggs, thereby affecting available choices.

Consumer Choice Theory

Consumer choice theory revolves around how consumers make decisions to maximize their satisfaction or utility, given their budget constraints. Rafaella's decision-making can be visualized using an indifference curve, which represents all combinations of chicken and eggs that provide her with equal satisfaction.

The point where her indifference curve touches (or is tangent to) her budget line signifies her optimal choice. In the exercise, Rafaella's optimal consumption was 4 pounds of chicken and 10 eggs, where she received the maximum utility possible with her $30 budget at the original prices.

• Indifference Curve: Reflects constant satisfaction across different combinations of goods.
• Tangency Point: Indicates the most preferred combination of goods under budget constraints.

Changes in prices or income might alter this optimal decision. This theory helps to highlight how and why specific combinations of goods are chosen by consumers, reflecting personal preferences and trade-offs.

Substitute Goods

Substitute goods come into play when a consumer can replace one good with another due to similar utility. In Rafaella's case, chicken and eggs are considered substitutes. This means if the price of chicken decreases, as it did from $5 to $3 per pound, she is more likely to purchase more chicken since it becomes a better deal than eggs.

Understanding substitute goods involves recognizing the partial interchangeability between two items in fulfilling a consumer’s wants. When the price of one falls, demand shifts towards the cheaper alternative, underlining the economic principle of substitution.

• Price-Effect: A decrease in the price of chicken causes an increase in its demand.
• Substitution-Effect: A choice shift from eggs to chicken as the preferred good due to cost advantage.

This behavior showcases how relative price changes can impact consumption patterns and overall demand in a market, central to predicting consumer reactions to price fluctuations.