Questions: Household Optimization and Consumption-Savings Decisions

Question 1

A household has a very low elasticity of intertemporal substitution (EIS ≈ 0). If the central bank raises interest rates substantially, what happens to this household's consumption allocation across periods?

• A. Current consumption falls sharply as the household saves much more to take advantage of higher returns
• B. Consumption stays roughly equal across periods — the household strongly prefers smooth consumption and responds little to interest rate incentives
• C. Future consumption falls because higher interest rates reduce the present value of future income
• D. Current consumption rises because the household becomes wealthier through higher interest payments on existing savings

Answer: (B)

The elasticity of intertemporal substitution (EIS) measures how responsive the consumption ratio (c₂/c₁) is to changes in the interest rate. An EIS near zero means the household strongly resists shifting consumption across time regardless of the incentive — whether the interest rate is 1% or 20%, they prefer roughly equal consumption in both periods. This is the preference analogue of perfectly inelastic demand. A high-EIS household would behave as in option A; this question tests whether the student understands that EIS is what governs the size of the response.

Question 2

In the two-period household optimization model, the 'price' of one unit of future consumption in terms of foregone present consumption is:

• A. Exactly 1 — present and future consumption are equivalent goods
• B. β (the discount factor) — reflecting the household's pure impatience
• C. 1/(1+r) — saving one unit today yields (1+r) units tomorrow, so one future unit costs 1/(1+r) present units
• D. (1+r) — higher interest rates make future consumption more expensive

Answer: (C)

The intertemporal budget constraint is c₁ + c₂/(1+r) = y₁ + y₂/(1+r). The coefficient on c₂ is 1/(1+r), which is the relative price of future consumption: to obtain one unit tomorrow, you sacrifice 1/(1+r) units today (by saving it at rate r, it grows to exactly 1 by next period). When r rises, 1/(1+r) falls — future consumption becomes cheaper relative to present consumption, creating a substitution incentive to save more. This mirrors a standard relative price change in consumer theory.

Question 3

According to the household consumption Euler equation, when interest rates rise, households unambiguously reduce current consumption and increase future consumption.

• T. True
• F. False

Answer: False

The substitution effect of a higher interest rate does push toward more saving (less current consumption), because the return to saving increases. However, for households that are net savers, higher interest rates also generate a positive income effect — they earn more on existing savings, making them wealthier and inclined to consume more in both periods. These effects work in opposite directions, and the net impact on current consumption is theoretically ambiguous, depending on the EIS and the household's net financial position. The Euler equation characterizes the optimality condition but does not by itself resolve which effect dominates.

Question 4

The consumption Euler equation requires that the marginal utility of current consumption equals the discounted, interest-adjusted marginal utility of future consumption at the optimum.

• T. True
• F. False

Answer: True

The Euler equation U'(c₁) = β(1+r)U'(c₂) is exactly this condition: at the optimum, the household is indifferent at the margin between consuming one unit today (gaining U'(c₁)) and saving it (gaining β(1+r)U'(c₂) next period). If this condition were violated — say, if saving one unit gave more discounted marginal utility than spending it — the household could improve by saving more, contradicting optimality. This first-order condition is the fundamental tool for analyzing how consumption responds to interest rates, income shocks, and preference changes.

Question 5

Why does the elasticity of intertemporal substitution (EIS) determine whether monetary policy (interest rate changes) is effective at shifting household consumption behavior?

Model answer: The Euler equation shows that the interest rate is the 'price' incentive for shifting consumption between periods. How strongly a household responds to this price incentive is exactly what the EIS measures. A high EIS means even a small change in interest rates produces a large reallocation of consumption from present to future — monetary policy is powerful. A low EIS means households stubbornly prefer smooth consumption regardless of the interest rate incentive — monetary policy has little effect on the consumption-savings margin. Since aggregate consumption is the sum of household decisions, the economy-wide EIS determines whether central bank interest rate policy can meaningfully shift spending timing.

This is why the EIS is one of the most important and contested parameters in macroeconomics. Estimates range from about 0.1 to over 1.0, with the value driving model predictions about business cycles, the effectiveness of quantitative easing, and optimal fiscal policy design.