Question

Suppose a consumer has an income of $20 that is spent on two goods: X and Y. The price of good X is $1.00 and the price of good Y is $3.00. Which of the following combinations (or bundles) of X and Y lie on the individual's budget constraint?

1) 5X + 5Y
2) 10X + 2Y
3) 8X + 4Y
4) 3X + 7Y

Answer 1

To find the combinations that lie on the individual's budget constraint, we can substitute the given options into the budget constraint equation. Options 1 and 3 are the combinations that satisfy the equation.

Step-by-step explanation:

The budget constraint equation can be represented as follows:

Budget = Price of X * Quantity of X + Price of Y * Quantity of Y

In this case, the consumer has an income of $20, the price of X is $1.00, and the price of Y is $3.00. So, the budget constraint equation becomes:

20 = 1 * Quantity of X + 3 * Quantity of Y

To find the combinations that lie on the individual's budget constraint, we can substitute the given options into the equation and check if they satisfy the equation. The combinations that satisfy the equation are the ones that lie on the budget constraint.

Let's substitute each option into the equation:

1. 5(1) + 5(3) = 20, so option 1 lies on the budget constraint.
2. 10(1) + 2(3) = 16, so option 2 does not lie on the budget constraint.
3. 8(1) + 4(3) = 20, so option 3 lies on the budget constraint.
4. 3(1) + 7(3) = 24, so option 4 does not lie on the budget constraint.

Based on this analysis, options 1 and 3 are the combinations that lie on the individual's budget constraint.