A. Orange juice and apple juice are known to be perfect...

a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate priceconsumption curve (for a variable price of orange juice) and income-consumption curve. b. Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-consumption curves $$\begin{array}{|lccccc|} \hline & X_{1} & X_{2} & P_{1} & P_{2} & 1 \\ \hline \text { Week 1 } & 10 & 20 & 2 & 1 & 40 \\ \hline \text { Week 2 } & 7 & 19 & 3 & 1 & 40 \\ \hline \text { Week 3 } & 8 & 31 & 3 & 1 & 55 \\ \hline \end{array}$$ Did Bill's utility increase or decrease between week 1 and week 2? Between week 1 and week 3? Explain using a graph to support your answer. b. Now consider the following information about the choices that Mary makes: $$\begin{array}{|lccccc|} \hline & X_{1} & X_{2} & P_{1} & P_{2} & I \\ \hline \text { Week 1 } & 10 & 20 & 2 & 1 & 40 \\ \hline \text { Week 2 } & 6 & 14 & 2 & 2 & 40 \\ \hline \text { Week 3 } & 20 & 10 & 2 & 2 & 60 \\ \hline \end{array}$$ Did Mary's utility increase or decrease between week 1 and week 3 ? Does Mary consider both goods to be normal goods? Explain. c. Finally, examine the following information about Jane's choices: Draw a budget line-indifference curve graph that illustrates Jane's three chosen bundles. What can you say about Jane's preferences in this case? Identify the income and substitution effects that result from a change in the price of good $x$.

a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate priceconsumption curve (for a variable price of orange juice) and income-consumption curve.
b. Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-consumption curves
$$\begin{array}{|lccccc|}
\hline & X_{1} & X_{2} & P_{1} & P_{2} & 1 \\
\hline \text { Week 1 } & 10 & 20 & 2 & 1 & 40 \\
\hline \text { Week 2 } & 7 & 19 & 3 & 1 & 40 \\
\hline \text { Week 3 } & 8 & 31 & 3 & 1 & 55 \\
\hline
\end{array}$$
Did Bill's utility increase or decrease between week 1 and week 2? Between week 1 and week 3? Explain using a graph to support your answer.
b. Now consider the following information about the choices that Mary makes:
$$\begin{array}{|lccccc|}
\hline & X_{1} & X_{2} & P_{1} & P_{2} & I \\
\hline \text { Week 1 } & 10 & 20 & 2 & 1 & 40 \\
\hline \text { Week 2 } & 6 & 14 & 2 & 2 & 40 \\
\hline \text { Week 3 } & 20 & 10 & 2 & 2 & 60 \\
\hline
\end{array}$$
Did Mary's utility increase or decrease between week 1 and week 3 ? Does Mary consider both goods to be normal goods? Explain.
c. Finally, examine the following information about Jane's choices:
Draw a budget line-indifference curve graph that illustrates Jane's three chosen bundles. What can you say about Jane's preferences in this case? Identify the income and substitution effects that result from a change in the price of good $x$.

Key Concepts

Price-Consumption Curve

The price?consumption curve is a graphical representation that shows how the optimal consumption bundle changes as the price of one good varies, holding the consumer’s income and the other good’s price constant. It traces the locus of points of tangency between the budget line and the highest attainable indifference curves, mapping out how the consumer's choice shifts with price changes.

Income-Consumption Curve

The income?consumption curve illustrates the change in optimal consumption bundles as the consumer’s income alters, with prices held constant. It shows how increases or decreases in income affect the consumer's purchasing decisions and can indicate whether a good is normal or inferior by the direction in which consumption shifts.

Perfect Substitutes

Perfect substitutes are goods that a consumer views as equivalent in terms of utility, so that they can replace one another at a constant rate. When goods are perfect substitutes, the indifference curves are straight lines, and the consumer’s choice is based solely on the relative prices, often leading to a corner solution where only the cheaper option is consumed.

Perfect Complements

Perfect complements are goods that are consumed in fixed proportions, such that gaining additional units of one good without the other does not increase overall utility. Their indifference curves are L-shaped, reflecting the fact that the consumer’s satisfaction depends on consuming the goods together in a specific ratio.

Utility and Indifference Curves

Utility is a measure of a consumer’s satisfaction or happiness from consuming goods, and indifference curves represent different combinations of goods that provide the consumer with the same level of utility. These curves are used to analyze consumer preferences and the trade-offs that occur when choosing between different bundles of goods.

Budget Constraint

A budget constraint represents the combinations of goods a consumer can afford given their income and the prices of those goods. It is depicted as a straight line on a graph, with its slope determined by the price ratio, and is a fundamental component in understanding how consumers maximize utility subject to financial limits.

Income Effect and Substitution Effect

The income effect and substitution effect are components of the total change in quantity demanded resulting from a price change. The substitution effect reflects changes in consumption as a consumer replaces more expensive goods with cheaper ones, keeping utility constant, while the income effect captures changes due to the alteration in real purchasing power. Decomposing these effects helps in understanding consumer behavior in response to price movements.

Normal Goods

Normal goods are those for which demand increases as the consumer's income rises. Analyzing consumption changes in response to income variations helps determine whether a good is normal, as normal goods show an upward-sloping relationship on the income-consumption curve, indicating that higher income leads to greater consumption of the good.

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