Consumption and Savings Decisions: A Fun Economic Puzzle

(a) How much will people consume in each period if their initial incomes are m1=1 and m2=0?

If your math is rusty, substitute the expressions in the utility function and solve for the savings in the first period.

(b) How would you forecast consumption tomorrow based on consumption today if you observe many individuals with the initial income setup?

Explain your prediction relationship.

(c) If m2 suddenly increases to 1 as well, how would the consumption in each period change compared to the initial setup?

Would your forecast based on today's consumption still be accurate? Explain why or why not.

(d) How does this situation relate to the Lucas Critique and the challenges it poses to economic forecasting?

(a) Answer:

In the given scenario with m1=1 and m2=0, consumption in each period can be calculated as follows: c1 = 0.5 and c2 = 0.5 as well. Therefore, people will consume 0.5 in each period.

(b) Answer:

If you were to forecast consumption based on today's consumption, it might show a stable relationship under unchanged conditions. However, unexpected changes in income or preferences may lead to deviations from this prediction.

(c) Answer:

If m2 increases to 1, consumption habits could change with the additional income in the second period. The initial forecast may still be accurate depending on how individuals adjust their consumption behavior with the higher income.

(d) Answer:

This situation showcases the relevance of the Lucas Critique, highlighting the need to consider individual responses to changing conditions in economic models and forecasts. The model in (b) may not accurately predict consumption changes in real-world scenarios due to unforeseen adjustments in income or policies.

The question addresses consumption and savings decisions under specific income periods. When income changes across periods, consumption habits may also change. The Lucas Critique underlines why some models and forecasts may fail under real-world conditions due to variable human behavior.

Explanation:

This question covers the concepts of consumption decisions, saving decisions and the Lucas Critique in economics.

(a) With m1=1 and m2=0, and using the defined utility structure and budget restrictions, you would solve for s1. Since income in the second period is 0, to get any utility in the second period, the individual will need to save some income in the first period. One way is to set s1 = 0.5; implying that c1 = 0.5 and c2 = s1 = 0.5 as well.

(b) If you were to forecast tomorrow's consumption based on today's consumption, you might predict a stable relationship, assuming no changes to income or preferences. However, this may not always hold true due to unpredictable changes in income or changes in the individual's time preferences or other factors that affect consumption decisions.

(c) If m2 increases to 1, the person would now have income in the second period. Depending on their saving decisions, consumption in both periods could increase. Your previous forecast could still be accurate, but it would depend on how the individual reacts to the increase in income.

(d) This situation relates to the Lucas Critique in that the Lucas Critique states that individuals adjust their expectations based on changes in policy, and therefore, forecast models should take these changes into account. The model established in (b) may not correctly predict consumption in the 'real' situations of (a) and (c) if policy changes or other unanticipated events occur.

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