Question

An individual consumes two goods, clothing and food. Given the information below, illustrate both the income-consumption curve and the Engel curve for clothing and food. $$\begin{array}{|ccccc|} \hline \begin{array}{c} \text { PRICE } \\ \text { CLOTHING } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { F00D } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { CLOTHING } \end{array} & \begin{array}{c} \text { QUANTIT } \\ \text { F00D } \end{array} & \text { INCOME } \\ \hline \$ 10 & \$ 2 & 6 & 20 & \$ 100 \\ \hline \$ 10 & \$ 2 & 8 & 35 & \$ 150 \\ \hline \$ 10 & \$ 2 & 11 & 45 & \$ 200 \\ \hline \$ 10 & \$ 2 & 15 & 50 & \$ 250 \\ \hline \end{array}$$

Short answer

The Engel curve helps in understanding the relationship between a consumer's income and the demand for a good. On the other hand, the income-consumption curve helps visualize the changes in a consumer's optimal consumption combination with changes in income. Although tedious, this process is straightforward and merely involves plotting the appropriate curves with the given data.

Step-by-step solution

Calculate total spending for each good at each income level

Multiply the quantity of each good by its price. This will give us the total spending on each good at different income levels. For example, at an income of $100, the total spending on clothing is $10 * 6 = $60, and the total spending on food is $2 * 20 = $40.

Plot the Income-Consumption curve

On the x-axis, we plot the quantities of clothing and on the y-axis, we plot the quantities of food. At each income level, we mark a point representing the bundle of goods the consumer consumes. So at an income level of $100, mark the point (6,20), at an income of $150, mark (8,35), and so on. Connect these points to illustrate the income-consumption curve.

Plot the Engel Curve

To plot the Engel curve, we need to show the relationship between the income and the quantity of goods consumed. On the x-axis, plot income, and on the y-axis, plot total spending on each good. For clothing at income level of $100, mark the point (100, 60), at income $150, mark the point (150, 80), and so on. Do the same for food. Connect these points to illustrate the Engel curve.

Key concepts

Engel Curve

The Engel Curve is a graphical representation that displays the relationship between a consumer's income and the amount of a good that the consumer purchases. It's named after the statistician Ernst Engel, who discovered that the proportion of income spent on food decreases, even if actual expenditure on food rises, as income grows. Let's break this down:

In our exercise example, you'll notice that as the individual's income increases from \(100 to \)250, the quantity of clothing and food they consume also increases. This relationship can be visualized by plotting income on the x-axis and the total spending on each good on the y-axis. For clothing and food, the points (100, 60), (150, 80), (200, 110), and (250, 150) would be marked, respectively, and similarly, the points for food spending against income. By connecting these points, the Engel Curve for each good emerges.

An Engel Curve can either be linear or nonlinear, depending on the type of good; for necessities, it tends to be linear, showing a less than proportional increase in demand, while for luxuries, it might be more curved, indicating a greater proportion of income is spent as wealth grows.

Consumer Behavior in Microeconomics

In microeconomics, understanding how a consumer behaves is crucial. Consumer behavior examines the decision-making processes of individuals and households regarding their expenditure on goods and services. This involves looking into how consumers allocate their available budget on various goods while maximizing their utility, which is a measure of satisfaction.

The data in our exercise highlight various points that represent choices made by the consumer at different income levels. As the consumer's income increases, they choose to purchase larger quantities of both clothing and food. This reflects the consumer's response to a change in income, with the preferred combination of goods shifting, illustrating that as income grows, so does consumption - a fundamental observation in consumer behavior. Such analysis is pivotal as it allows economists to predict how changes in incomes and prices can affect demand for goods.

Budget Constraint Analysis

A budget constraint in microeconomics represents all the combinations of goods and services that a consumer can purchase given their income and the prices of the goods. The constraint is the boundary that consumer choice must operate within, as no one can spend more than their income. Analysis of budget constraints deals with the trade-offs a consumer makes when deciding how much to purchase of each good.

The step-by-step solution to the exercise involved calculating the total spending on each good at different income levels, effectively showing how the budget is allocated. When we graph these allocations, the line that connects all possible combinations – where the entire budget is spent – is the budget constraint. In our example, the quantity of clothing and food that can be purchased for each level of income can be plotted, generating distinct points that display the shift in the budget constraint as income varies. By analyzing shifts in the budget line, we can infer key insights into consumer preferences, potential trade-offs between goods, and the impact of income changes on consumption patterns.