Econ:214 Intermediate Macroeconomics Homework 2

发布时间：2024-06-05

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Econ:214 Intermediate Macroeconomics

Homework 2

Due Date: Jan 24, 2024

Problem 1. Suppose that the government imposes a proportional income tax on the rep-resentative consumer’s wage income. That is, the consumer’s wage income changes from w (h − l) to w (1 − t)(h − l) where t is the tax rate. What effect does the income tax have on consumption and labor supply? Determine the utility maximizing condition. Explain your results in terms of income and substitution effects.

Problem 2. Suppose that the representative consumer’s dividend income increases, and his or her wage rate falls at the same time. Determine the effects on consumption and labor supply and explain your results in terms of income and substitution effects. Notice that there are three difference cases you need to consider:

(a) The magnitude of an increase in dividend income is greater than the magnitude of a decrease in wage rates.

(b) The magnitude of an increase in dividend income is less than the magnitude of a decrease in wage rates.

Problem 3. Suppose, as in the federal income tax code for Canada, that the representative consumer faces a wage income tax with a standard deduction. That is, the representative consumer pays no tax on wage income for the first x units of real wage income, and then pays a proportional tax t on each unit of real wage income greater than x. Therefore, the consumer’s budget constraint is given by

Now, suppose that the government reduces the tax deduction x. Using diagrams, determine the effects of this tax change on the consumer, and explain your results in terms of income and substitution effects. Make sure that you consider two cases: consumers do not pay any tax before x is reduced, and consumers pay income taxes before x is reduced.

Problem 4. Suppose that the government imposes a producer tax. That is, the firm pays t units of consumption goods to the government for each unit of output it produces. De- termine the effect of this tax on the firm’s demand for labor. (Hint: the profit is now π = (1 − t)zF (K, Nd) − wNd.)