Question

A consumer lives for two periods and earns an income of $100 and $120 in the first and second periods respectively. They can borrow and lend money between periods at an interest rate of 5%. They can spend their income on a consumption good x in each period, that cost $1 per unit. Draw this consumer's budget constraint for consumption x₁ and x₂ in periods 1 and 2 respectively.

Answer 1

To draw a consumer's budget constraint for two-period consumption of good x, one must consider incomes of $100 and $120 for the first and second periods respectively, and an interest rate of 5% for borrowing and lending. The intercepts on the axes represent the maximum consumption in each period without saving or borrowing, and the slope represents the tradeoff between present and future consumption, including the impact of the interest rate.

Step-by-step explanation:

Drawing a Budget Constraint for a Two-Period Consumption Model

To represent the consumer's budget constraint for consumption x1 and x2 in periods 1 and 2, we must consider the income levels and the interest rate that affects borrowing and lending between the periods. The consumer has an income of $100 in the first period and $120 in the second period, with a borrowing and lending interest rate of 5%. Since the consumer can either save or borrow between periods, the budget constraint will be a line showing the maximum consumption possibilities in both periods.

Without borrowing or lending, the consumer could consume up to 100 units of good x in the first period, and 120 units in the second period, corresponding to their incomes. However, if the consumer saves $1 in the first period, that dollar would grow to $1.05 in the second period due to interest. Conversely, if the consumer borrows $1 in the first period, they would have to repay $1.05 in the second period.

To construct the budget constraint, you would draw a line where the x-intercept on period 1 (horizontal axis) would be at 100 units of good x (if the consumer spends all income in period 1 and saves nothing for period 2), and the y-intercept on period 2 (vertical axis) would be at the amount of good x that could be purchased with $120 plus any savings from period 1 multiplied by 1.05. Similarly, if the consumer borrows, the y-intercept would be less than the 120 units of good x since they need to repay the borrowed amount with interest. Therefore, the line would slope downward from the x-intercept to the y-intercept, representing all combinations of consumption between both periods that are within the consumer's budget.