Betty and Wilma wish to buy blouses and jeans. Betty has a...

Betty and Wilma wish to buy blouses and jeans. Betty has a budget of $$\$ 600$$, while Wilma has a budget of $$\$ 1,200$$. Using the indifference curve analyses given in the following table, determine prices for the blouses and jeans. For which commodity can you derive a demand curve? Derive this curve for Betty and Wilma. Finally, derive the market demand curve, assuming that they are the only consumers. $$ \begin{array}{|c|c|c|c|c|c|} \hline & & \begin{array}{c} \text { Quantity of } \\ \text { Blouses } \end{array} & \begin{array}{c} \text { Pairs of } \\ \text { Jeans } \end{array} & \begin{array}{l} \text { Price of } \\ \text { Blouses } \end{array} & \begin{array}{c} \text { Price of } \\ \text { Jeans } \end{array} \\ \hline {\text { Betty }} & \text { A } & \text { | } & & & x^2 \\ \hline & \text { B } & & & & \\ \hline {\text { Wilma }} & \text { A } & & & & \\ \hline & \text { B } & & & & \\ \hline \end{array} $$ FIGURE CANT COPY

Betty and Wilma wish to buy blouses and jeans. Betty has a budget of $$\$ 600$$, while Wilma has a budget of $$\$ 1,200$$. Using the indifference curve analyses given in the following table, determine prices for the blouses and jeans. For which commodity can you derive a demand curve? Derive this curve for Betty and Wilma. Finally, derive the market demand curve, assuming that they are the only consumers.
$$
\begin{array}{|c|c|c|c|c|c|}
\hline & & \begin{array}{c}
\text { Quantity of } \\
\text { Blouses }
\end{array} & \begin{array}{c}
\text { Pairs of } \\
\text { Jeans }
\end{array} & \begin{array}{l}
\text { Price of } \\
\text { Blouses }
\end{array} & \begin{array}{c}
\text { Price of } \\
\text { Jeans }
\end{array} \\
\hline {\text { Betty }} & \text { A } & \text { | } & & & x^2 \\
\hline & \text { B } & & & & \\
\hline {\text { Wilma }} & \text { A } & & & & \\
\hline & \text { B } & & & & \\
\hline
\end{array}
$$
FIGURE CANT COPY

Key Concepts

Market Demand Curve

The market demand curve represents the total quantity demanded for a good by all consumers in the market at various prices. It is obtained by horizontally summing the individual demand curves of all consumers. This aggregated demand curve is crucial in understanding market behavior, setting equilibrium prices, and analyzing the impact of policies or external shocks on the overall demand in the economy.

Demand Curve

A demand curve illustrates the relationship between the price of a good and the quantity demanded by an individual. It is typically derived by observing how the consumer’s optimal choice changes as the price of the good varies, holding other factors constant. This curve is predominantly downward sloping, reflecting that consumers purchase less of a good as its price increases. In theoretical analysis, one uses the conditions from budget constraints and indifference curve analysis to derive this relationship.

Indifference Curves

Indifference curves represent combinations of two goods that yield the same level of satisfaction or utility to the consumer. They help illustrate consumer preferences and are used to analyze how consumers might trade off one good for another while maintaining the same utility level. In theory, each curve corresponds to a different utility level, and the convexity of these curves reflects the assumption of diminishing marginal rates of substitution.

Budget Constraint

A budget constraint describes all the combinations of goods that a consumer can purchase given their income and the prices of the goods. It is represented as a straight line in a two-good model, where the intercepts correspond to the maximum quantities of each good that can be bought if all income were allocated to that good. The slope of this line is determined by the ratio of the goods’ prices, and it plays a crucial role in consumer choice theory as it limits the feasible consumption bundles.

Marginal Rate of Substitution (MRS)

The marginal rate of substitution is the rate at which a consumer is willing to give up one good in exchange for an additional unit of another good while keeping their overall utility constant. At the point of utility maximization, the MRS between two goods is equal to the ratio of their prices. This condition, derived from the tangency between an indifference curve and the budget line, is fundamental in deriving demand functions under the framework of consumer optimization.

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