A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government gives a subsidy of rate s of her income (i.e. her income is (1+s) times what it would be without the subsidy). The worker cannot save, and initially faces no tax. She consumes a single consumption good, c. 1. Write a budget constraint for this individual and plot it. 2. Suppose that the worker has well-behaved preferences, i.e. she likes more consumption and leisure rather than less, she dislikes working, and she has decreasing marginal utility in consumption and leisure. a. Display graphically what the optimal consumption-leisure choice for this worker (no need for exact numbers as we don’t know the utility function; give intuition) 3. Imagine that instead of a subsidy rate, s, the government imposes income tax at rate t. What is the new budget constraint? Display on the same picture. In the new optimum, is the consumption higher? Explain the answer in terms of wealth and substitution effects.

A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government gives a subsidy of rate s of her income (i.e. her income is (1+s) times what it would be without the subsidy). The worker cannot save, and initially faces no tax. She consumes a single consumption good, c. 1. Write a budget constraint for this individual and plot it. 2. Suppose that the worker has well-behaved preferences, i.e. she likes more consumption and leisure rather than less, she dislikes working, and she has decreasing marginal utility in consumption and leisure. a. Display graphically what the optimal consumption-leisure choice for this worker (no need for exact numbers as we don’t know the utility function; give intuition) 3. Imagine that instead of a subsidy rate, s, the government imposes income tax at rate t. What is the new budget constraint? Display on the same picture. In the new optimum, is the consumption higher? Explain the answer in terms of wealth and substitution effects.

Economics Today and Tomorrow, Student Edition

1st Edition

ISBN:9780078747663

Author:McGraw-Hill

Publisher:McGraw-Hill

Chapter1: What Is Economics

Section1.3: What Do Economists Do?

Problem 5R

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