### Graph the two-period budget constraint for consumption

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Suppose that the government taxed consumption.
To be specific, suppose we have a two-period model. An individual earns labor income Y0 =\$100k at time zero, and earns no labor income at time 1. The individual may consume or save that income. Savings grow at rate r=.03. For every dollar of consumption, the individual pays the tax rate τ=.30 to the government.

a. Graph the two-period budget constraint for consumption. What is the slope? Is this tax distortionary?
b. The government modifies the consumption tax somewhat so that the first \$20k of consumption in each period is tax free. Now graph the budget constraint.

2. Claim: "The Mortgage Interest Tax Deduction is a regressive policy. A simpler, better policy that could achieve the same goals would be a home ownership tax credit that applies equally to all homeowners regardless of income or the value of the home." In a mini-essay (300 words) state whether you agree or disagree with that claim and explain your reasoning.

3. A corporation produces output with a market price of \$200 per unit. The marginal product of capital is 1/(2K), where K is units of capital, with each unit assumed to cost \$1. (So when we talk about capital in this problem, units and \$ value are equivalent.) The life span of the capital is 5 years, implying the straight line depreciation rate δ=.2. The financing cost of capital is ρ=.05.

a. If depreciation and financing costs are not included in accounting costs, what is the optimal level of capital for the firm?
b. If the corporate tax is 35%, what is the optimal level of capital?
c. If depreciation at a rate δ=.2 is included in accounting costs, what is the optimal level of capital? [Hint: remember to calculate the present value of the deduction. Use .05 for the discount rate.]
d. For c., what is the effective corporate tax rate?
e. The firm is going to borrow the money for its capital purchases. The interest paid on the debt can be added to accounting costs. Suppose it turns out that the present value of this expense is .10 for every dollar of capital purchased. What is the optimal level of capital now?
f. For e., what is the effective corporate tax rate?

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