Question

A consumer is making saving plans for this year and next. She knows her real income after taxes will be $50,000 in both years. Any part of her income saved this year will earn a real interest rate of 10% between this year and next year. Currently, the consumer has no wealth (no money in the bank or other financial assets, and no debts). There is no uncertainty about the future.

Formally derive the consumer’s intertemporal budget constraint.

Answer 1

The consumer's intertemporal budget constraint is derived by considering the savings and future consumption options available. The constraint is based on the consumer's real income after taxes and the real interest rate earned on savings.

Step-by-step explanation:

The consumer's intertemporal budget constraint can be derived by considering the savings and future consumption options available. The consumer's real income after taxes is $50,000 in both years. If she saves a portion of her income this year, it will earn a real interest rate of 10% between this year and next year. The consumer currently has no wealth. Therefore, her intertemporal budget constraint can be represented as:

Current Consumption + Future Consumption = Real Income + Real Interest from Savings

Let's assume the consumer saves an amount x this year. The real interest earned on this savings will be 10% of x, which is 0.10x. Therefore, the intertemporal budget constraint can be written as:

Current Consumption + Future Consumption = $50,000 + 0.10x