Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words.
Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure.
1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points.
2. What are the person’s
3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words.
4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α.
5. How does L ∗ change as you increase wage w and non-labor income V ?
6. How does C ∗ change as you increase wage w and non-labor income V ?
7. Are leisure and consumption normal goods? Explain.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
