Question

Let P₁ and P₂ denote the prices of consumption in the two periods, and let W denote the value of the individual's lifetime income; thus the budget constraint is P₁ C₁ +P₂ C₂ =W (a) What are the individual's utility-maximising choices of C₁ and C₂ , given P₁ ,P₂ , and W ?

Answer 1

The utility-maximizing consumption of C₁ and C₂ for given prices P₁, P₂, and lifetime income W is determined by the budget constraint equation, where the consumer equates the ratio of marginal utility to price for both periods of consumption.

Step-by-step explanation:

The individual's utility-maximizing choices of C₁ and C₂ given P₁, P₂, and W (lifetime income) can be found by applying the budget constraint equation. To maximize utility, the consumer will equate the ratio of the marginal utility of each good to its price. This condition is known as the equal marginal principle and can be represented by the equation:

MU₁/P₁ = MU₂/P₂

Where MU is the marginal utility of consumption in each period, and P is the price of consumption in each period. The highest total utility is achieved when these ratios are equal, implying the consumer is making an optimum trade-off between the two periods' consumption, considering their budget. This is under the assumption that the goods in question are normal goods. If one good is an inferior good, the consumer may consume more of it as their income decreases.