# 5 Taxes

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## 5.1 Taxes on consumption, asset income and labor income

Given the presence of asset income tax, consumption tax and labor income tax present (with tax rates $$\tau_{a},\tau_{c},\tau_{L}$$),

1. Write down the household budget constraint.

2. Write down the government budget constraint.

## 5.2 Goods Market.

Most of the time tax rate changes need the approval of the Congress, which is costly for society. Therefore, any tax change is reasonable to be assumed persistent or permanent. We consider the Y{d}-Y{s} analysis for goods market, where vertical axis is the before-tax interest rate.

1. What kind of tax rate change can affect today’s consumption demand? and how?

2. What kind of tax rate change can affect today’s labor employment? How does it affect the output supply curve $$Y^{s}$$?

3. What kind of tax rate change can affect today’s capital employment? How does it affect the output supply curve $$Y^{s}$$?

4. Investment today is determined by its future net-off-depreciation marginal capital productivity (benefit of investment) and its interest rate cost (cost of investment). Without tax, in equilibrium $$MPK-\delta=i$$. With tax, both terms need to be after-taxed. Write down the equilibrium conditions under the following scenarios.

1. A tax rate $$\tau$$ on interest income, but not on capital rental income.

2. A tax rate $$\tau$$ on capital rental income, but not on interest income.

3. A tax rate $$\tau$$ on both capital rental income and interest income.

4. Which of the above three scenarios can a tax rate change affect investment decision directly?

## 5.3 Income tax.

Suppose there is only income tax in the economy. The tax rate is $$\tau$$ for all sources of income. In addition, capital depreciation cost ($$P\delta K$$) and government transfer ($$PV$$) are tax deductible.

1. Write down the household budget constraint.

2. Write down the government budget constraint.

3. Discuss the trade-off for the substitution and the intertemporal substitution under this income tax system.

Consider a permanent increase in the income tax rate. To meet the government budget constraint, we assume that there is an equivalent amount of government transfer increase. Therefore, tax change does not directly provide a wealth effect. Use the $$Y^{d}-Y^{s}$$ tool to analysis its effect.

1. What happens to consumption?

2. What happens to investment?

3. What happens to output supply?

4. Since the change is permanent, the change in output supply is permanent. Such a permanent change implies a permanent wealth effect feedback on consumption. What does that mean on consumption?

5. What is the equilibrium outcome?

## 5.4 Permanent tax rate changes

Analysis the effect of a permanent increase of

1. Consumption tax rate.

2. Labor income tax rate.

3. Asset income tax rate.