Question

An individual sets aside a certain amount of his income per month to spend on his two hobbies, collecting wine and collecting books. Given the information below, illustrate both the price-consumption curve associated with changes in the price of wine and the demand curve for wine. $$\begin{array}{|ccccc|} \hline \begin{array}{c} \text { PRICE } \\ \text { WINE } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { B00K } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { WINE } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { BOOK } \end{array} & \text { BUDGET } \\ \hline \$ 10 & \$ 10 & 7 & 8 & \$ 150 \\ \hline \$ 12 & \$ 10 & 5 & 9 & \$ 150 \\ \hline \$ 15 & \$ 10 & 4 & 9 & \$ 150 \\ \hline \$ 20 & \$ 10 & 2 & 11 & \$ 150 \\ \hline \end{array}$$

Short answer

The individual spends less on wine and more on books as the price of wine increases, as reflected by the downward sloping Price-Consumption Curve (PCC). The demand curve for wine, plotted using the price and quantity of wine, also slopes downward, adhering to the law of demand that as prices rise, quantity demanded falls.

Step-by-step solution

Understand and interpret data

The table provided gives us the information about the prices of wine and book, the quantities of wine and books consumed, and the budget which is constant. So we will use this data to construct the price consumption curve and demand curve for wine.

Plotting the Price-Consumption Curve (PCC)

On a graph, let's put the quantity of wine on the vertical axis and quantity of book on the horizontal axis. Plot different points using the quantities of wine and book from the table for different prices of wine. Connect all these points to draw the PCC. It is observed that as the price of wine increases, the quantity of wine consumed decreases, meaning the individual pivots to buying more books instead, hence the PCC slopes downward.

Drawing the Demand Curve

On a different graph, plot the price of wine on the vertical axis and the quantity of wine on the horizontal axis. Use the price and quantity of wine data from the table to plot different points on this graph. Connect these points to get the demand curve. Like most goods, the wine also has a downward sloping demand curve reflecting the law of demand, that is, as the price of wine increases, quantity demanded decreases.

Key concepts

Understanding the Demand Curve

The demand curve is a graphical representation used to illustrate how much of a good or service consumers are willing and able to purchase at different prices. It is an essential tool in understanding consumer behavior in response to price changes. In the context of the given exercise, the demand curve for wine is plotted on a graph where:

• The vertical axis represents the price of wine.
• The horizontal axis shows the quantity of wine.

By plotting the price of wine against the quantity consumed, you can observe a downward slope in the demand curve. This slope indicates that as the price of wine rises, consumers tend to purchase less wine. This negative relationship between price and quantity demanded exemplifies the classic law of demand. The slope of the curve can provide valuable insights:

• A steeper curve suggests less sensitivity to price changes, meaning even significant changes in price result in relatively smaller changes in quantity demanded.
• A flatter curve indicates high sensitivity, where small price changes could lead to large changes in quantity purchased.

Explaining the Law of Demand

The law of demand states that, all else being equal, as the price of a good rises, the quantity demanded of the good falls. Conversely, as the price of a good drops, the quantity demanded increases. This fundamental principle of economics helps explain consumer purchasing behavior. In the exercise, as the price of wine increases from $10 to $20, the quantity of wine purchased falls from 7 to 2 units. This direct observation demonstrates the law of demand: higher prices lead to lower demand. The reasons behind such behavior include:

• Substitution Effect: Consumers substitute a more costly good with a cheaper alternative, in this case, likely buying more books as the price of wine increases.
• Income Effect: As wine becomes more expensive, consumers feel poorer, thereby reducing their quantity demanded.

Overall, the exercise showcases how the law of demand is consistently observed in consumer actions across varying price levels. The key takeaway is the inherent, inverse relationship between price and quantity demanded, crucial for making effective business and economic decisions.

Investigating the Budget Constraint

A budget constraint illustrates the combinations of goods and services a consumer can purchase with a given income. It is represented graphically as a line depicting all possible allocations of two goods, given the prices and the consumer's budget. In the exercise, the budget is fixed at $150 per month. The individual divides this budget between two hobbies: collecting wine and books. With the price of books constant at $10, changes in the price of wine significantly affect quantities bought. The budget constraint can be understood by examining:

• The cost and quantity of wine and books that can be purchased within the $150 budget.
• How decisions change as the price of wine varies, keeping the total expenditure within the budget limit.
• The trade-offs between wine and books when reallocating spending in response to wine's price fluctuations.

For example, as the price of wine rises, fewer bottles can be purchased, even if the consumer chooses to purchase more books to optimize their spending. Using the budget constraint helps highlight the real-world limitations consumers face, forcing prioritization between competing needs and desires.