Question

Paula is a Uber driver and must decide how many hours she would like to work in a week in which she is available 90 hours at most. She makes 30 USD per hour worked. Paula enjoys two things: aggregate consumption of goods, c, and hours of leisure, ℓ. Her utility is given by

U(c,l)=(c−60)¹/² ℓ ¹/²

The price of consumption goods is normalized to P = 1.
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(a) What is Paula's budget constraint?
(b) What is Paula's optimal choice of aggregate consumption, c, and hours of leisure, ℓ ?

Answer 1

Paula's budget constraint, given her availability of 90 hours and wage of $30 per hour, is C + L = $2700, where C is consumption and L is leisure. Her optimal choice will balance the utility from consumption and leisure and can be found by maximizing the utility function U(c,l) = (c-60) ½ ℓ ½, constrained by her budget.

Step-by-step explanation:

Understanding Labor-Leisure Choices in Economics

When analyzing Paula's decision as an Uber driver, we consider her budget constraint and preferences for consumption and leisure to determine her optimal choice. With a maximum of 90 hours available for work or leisure each week and a wage of $30 per hour, her budget constraint represents the trade-off between earning money and enjoying leisure time. The price of consumption goods (P) is normalized to 1.

(a) Paula's Budget Constraint: The budget constraint is given by the equation C + P ∙ L = W ∙ H, where C is the aggregate consumption, L is hours of leisure, W is the wage rate, and H is the total hours available. For Paula, since P = 1 and W = $30/hour, and she has 90 hours at her disposal, the equation simplifies to C + L = 90 ∙ 30, which means C + L = $2700. This equation indicates that the total value of her consumption and leisure cannot exceed $2700 per week.

(b) Optimal Choice of Aggregate Consumption, c, and Hours of Leisure, ℓ: To maximize her utility given by U(c,l) = (c-60) ½ ℓ ½, Paula must consider her preferences outlined by her utility function. She'll aim for the point where her budget constraint touches the highest possible indifference curve on a graph illustrating her utility. To find the exact optimal values for c and ℓ, calculus would be used to maximize the utility function subject to the budget constraint, generally resulting in a solution that equals the marginal rate of substitution to the wage rate.

The decisions made by Paula mirror those outlined in provided examples with other individuals such as Vivian and Petunia who similarly balance work and leisure, adjusting to changes in wages and hours available. This analysis is a fundamental concept in labor economics and helps in understanding individual decision-making in response to economic incentives.