Question

Consider the following national income model:

? − ? − ?< − ?< = 0

? − ? − ?(? − ?) = 0

? − ? − ?? = 0

where Y= income, C=consumption, I= investment, G= government spending, T= taxes

?, ?, ?, and ? are parameters: ? is positive because consumption is positive even if disposable income (? − ?) is zero; ? is a positive fraction because it represents the marginal propensity to consume; ? is positive because even if ? is zero the government swill still have a positive tax revenue; ? is a positive fraction because it an income tax rate that is less than 100 percent.

?, ?, and ? are endogenous variables whereas ?, ?, ?, ?, ?, and ? are exogenous variable.

Part I. Using the implicit function rule, find the income-tax multiplier that explains how the income tax rate ? causes the (equilibrium) income to change. Does the result make economic sense? Explain its sign and economic implication.

Part II. In the same way, find how the government spending affects the (equilibrium) consumption. Does the result make economic sense? Explain its sign and economic implication.

Answer 1

This is equilibrium level of income

Part I

we have to find income tax multipier

increase in income tax reduces the disposable income. Consumption depends on disposable income.Lesser disposable income leads to lesser consumption and thereby lesser aggregate spending. Thus an increase in income tax leads to decline in income.

Part II

how government spending affects consumption at equilibrium level

According to macroeconomics, there are 2 types of thoughts on effect of increased government spending on consumption.

The standard RBC model generally predicts a decline in consumption in response to a rise in government spending.In a nutshell, an increase in (nonproductive) government purchases (financed by current or future lump-sum taxes) has a negative wealth effect which induces a rise in the quantity of labor supplied at any given wage. That effect leads, in equilibrium, to a lower real wage, higher employment and higher output.

IS-LM model predicts the opposite effect, an increase in consumption as a result of an increase in government spending. The rise in consumption is caused by the higher disposable income generated from the direct effect of government spending on the level of economic activity, combined with the assumed dependence of consumption on current disposable income.

In the above question, IS-LM effect seems to be in place