Question

Suppose Consumer \(\mathrm{X}\) has \(\$ 6\) to spend on food and clothing, where food costs \(\$ 1.50\) a unit and clothing costs \(\$ 1.00 \mathrm{a}\) unit. Draw his consumption-possibility line.

Short answer

The consumption-possibility line for Consumer X is a straight line connecting the points (4, 0) and (0, 6), representing all the combinations of food and clothing that can be bought with their $6 budget given the prices of food and clothing.

Step-by-step solution

Set up the budget constraint equation

First, we need to write the budget constraint equation for Consumer X. Let F represent units of food and C represent units of clothing. The equation will be: 1.50F + 1.00C = 6

Find the intercepts for food and clothing axes

To determine the points where the consumption-possibility line intersects the F (Food) and C (Clothing) axes, we will consider two cases: 1. The case when Consumer X spends the entire budget on food, which means they buy 0 units of clothing (C = 0). 2. The case when Consumer X spends the entire budget on clothing, which means they buy 0 units of food (F = 0). Case 1: C = 0 1.50F + 1.00(0) = 6 1.50F = 6 F = \( \frac{6}{1.50} = 4 \) Case 2: F = 0 1.50(0) + 1.00C = 6 1.00C = 6 C = \(\frac{6}{1} = 6 \) So, the consumption-possibility line intersects the F axis at the point (4, 0) and the C axis at the point (0, 6).

Draw the consumption-possibility line

Connect the points (4, 0) and (0, 6) to form the consumption-possibility line. This represents all possible combinations of food and clothing that Consumer X can purchase given their budget and the costs of food and clothing. The consumption-possibility line can be seen as a straight line connecting the points (4, 0) and (0, 6). This line represents all the combinations of food and clothing that Consumer X can buy with their budget of $6 given the prices of food and clothing.

Key concepts

Budget Constraint

A budget constraint represents the combinations of goods and services a consumer can purchase with a limited amount of income. In the case of Consumer X, who has $6 to spend on food and clothing, the budget constraint equation is given as 1.50F + 1.00C = 6, where F is the quantity of food and C is the quantity of clothing.

When constructing the budget constraint, it's crucial to identify the maximum amounts of each good that can be bought if all the budget is spent on either one. Solving the equation for each axis gives us intercepts on the graph, showing the maximum possible units of food (4 units) and clothing (6 units) that can be purchased with the budget. These specific points are the extremes of the budget constraint line, illustrating the trade-off between the two goods.

Economic Choice

Economic choice revolves around deciding which combination of goods and services to purchase with a given budget. In microeconomics, consumers make these choices by maximizing their satisfaction within the limits of their budget constraint.

For Consumer X, with limited resources, every purchase decision involves a trade-off. They might choose a point on their consumption-possibility line that provides the best mix of food and clothing based on personal preference, nutritional needs, or social requirements. The choice is not just about the quantity but also the combination of goods that will maximize their overall utility.

Opportunity Cost

Opportunity cost is a fundamental concept in economic theory that refers to the benefit a person misses out on when choosing one alternative over another. It's defined as the value of the next best alternative foregone.

In the context of Consumer X's decision, if they choose to spend more on food, the opportunity cost is the amount of clothing they have to give up, and vice versa. For instance, if Consumer X moves from a point with 3 units of food and 3 units of clothing to one with 4 units of food and only 2 units of clothing, the opportunity cost of the additional unit of food is the loss of one unit of clothing. Understanding this cost helps individuals make more informed decisions about their consumption.

Microeconomics

Microeconomics is the branch of economics that studies the behavior of individuals and firms in making decisions regarding the allocation of limited resources. It deals with issues like the budget constraint, economic choice, and opportunity cost, which are all critical in understanding how markets function.

In essence, microeconomics looks at the 'small picture' and focuses on the way consumers and producers interact in individual markets for goods and services. The consumption-possibility line, as seen in Consumer X's exercise, is a perfect example of a microeconomic model. It illustrates how consumers face trade-offs and must make choices that best suit their preferences and budgets.