Section;1. Use the Keynesian cross to predict the impact on equilibrium GDP of the following. In each case;state the direction of the change and give a formula for the size of the impact.;a. An increase in government purchases.;b. An increase in taxes.;c. Equal-sized increases in both government purchases and taxes.;2. In the Keynesian cross, assume that the consumption function is given by C = 200 + 0.75 (Y T);planned investment is 100, and government purchases and taxes are both 100.;a. Graph planned expenditure as a function of income.;b. What is the equilibrium level of income?;c. If government purchases increase to 125, what is the new equilibrium income?;d. What level of government purchases is needed to achieve an increase in income of 1,600?;3. In the development of the Keynesian cross in the textbook, we assumed that taxes are a fixed;amount. Most countries, however, levy some taxes that rise automatically with national income.;(Examples in the United States include the income tax and the payroll tax.) Lets represent the;tax system by writing tax revenues as;= +;where and t are parameters of the tax code. The parameter t is the marginal tax rate: if;income rises by $1, taxes rise by t $1.;a. How does this tax system change the way consumption responds to changes in GDP?;b. In the Keynesian cross, how does this tax system alter the government-purchases;multiplier?;c. In the IS LM model, how does this tax system alter the slope of the IS curve?;4. The following equations describe an economy.;= + +.;= 120 + 0.5().;= 100 10.;= 50.;= 40.;() = 20.;= 600.;= 2.;a. Identify each of the variables and briefly explain their meaning.;b. From the above list, use the relevant set of equations to derive the IS curve. Graph the IS curve;on an appropriately labeled graph.;c. From the above list, use the relevant set of equations to derive the LM curve. Graph the LM;curve on the same graph you used in part (b).;d. What are the equilibrium levels of income and interest rate?;5. According to the IS-LM model, what happens in the short run to the interest rate, income;consumption, and investment under the following circumstances? Be sure your answer includes;an appropriate graph.;a. The central bank increases the money supply.;b. The government increases government purchases.;c. The government increases taxes.;d. The government increases government purchases and taxes by the same amount.
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