1. Consider an economy in which all taxes are autonomous and the following values of autonomous consumption, planned investment, government expenditure, autonomous taxes, and the marginal propensity to consume are given: Ca = 1,400Ip = 1,800G = 1,950Ta = 1,750c = 0.6 (a) What is the level of consumption when the level of income (Y) equals $10,0007 (b) What is the level of saving when the level of income (Y) equals $10,000?. (c) What is the level ofplanned investment when the level of income (Y) equals $10,000?What is the level of actual investment? What is the level of unintended inventory investment? (d) Show that injections equal leakages when income (Y) equals $10,000. (e) Is the economy in equilibrium when income (Y) = $10,0007If not, what is the equilibrium level of income forthe economy described in this question? (f) Is there a surplus or deficit in the government budget at the equilibrium level of income? How much? 2. Consider an economy is which taxes,planned invest- ment, government spending on goods and services, and net exports are autonomous, but consumption and planned investment change as the interest rate changes. Youaregiven the following information con- cerning autonomous consumption, the marginal propensity to consume, planned investment, govern- ment purchases of goods and services, and net exports: Ca = 1,500- lOr c = 0.6 Ip = 2,400 - 50r G = 2,000 T = 1,800 NX = -200 (a) Compute the value of the marginal propensity to save. (b) Compute the amount of autonomous planned spending, Ap, given that the interest rate equals 5. (c) Compute the equilibrium level of income, given that the interest rate equals 5. (d) Suppose that autonomous consumption changes by 4 percent of any change in household wealth and that the decline in the housing market in 2006-07 and drop in the stock market in the sum- mer of 2007 reduces household wealth by $750 billion. Compute the decrease in autonomous consumption that results from the decline in household wealth. (e) Calculate thenew amount ofautonomous planned spending, Ap, and the new equilibrium level of income, given that the interest rate equals 5. () Using your answers to parts c-e, compute the value of the multiplier. (g) Fiscaland monetary policymakers can respond to the declinein household wealth by taking actions that restore income to its initial equilibrium level. Fiscal policymakers can increase government spending or cut taxesor do both. Monetary policy- makers can reduce interest rates. Given the values of the multiplier, the tax multiplier, and the balanced-budgetmultiplier,computebyhow much: Government spending must be increased in order to restore the initial equilibrium level of income, given no change in taxes or the inter- est rate. Taxesmust be cut in order torestore the initial equilibrium level of income, given no change in government spending or the interest rate. Government spending and taxes must be increased in order to restore the initial equilib- rium level of income, given no change in the government budget balance or the interest rate. The interest rate must be reduced in order to restore the initial equilibrium level of income, given no change in government spending or taxes. 3. Consider an economy is which taxes, planned invest- ment, government spending on goods and services', and net exports are autonomous, but consumption and planned investment change as the interest rate changes. Youare given the following information con- cerning autonomous consumption, the marginal propensity to consume, planned investment, govern- ment purchases of goods and services, and net. exports: Ca = 1,500 - 20r c = 0.6 Ip = 2,450 - 60r G = 1,980 NX = -200 T = 1,750 (a) Compute the value of the marginal propensity to save. (b) Compute the amounts of autonomous planned spending, Ap, when the interest rate equals 0,2,4, and 6. (c) Compute the equilibrium levels of income when the interest rate equals 0,2,4,and 6.Graph the IS curve. (d) Suppose that policymakers decide to reduce the number oftroops in Iraq, which results in a reduc- tion in government spending of $160 billion. Compute the new amounts of autonomous planned spending, Ap, when the interest rate equals 0,2,4,and 6. (e) Compute the equilibrium levels of income when the interest rate equals 0,2,4,and 6and graph the new IScurve. 88 Chapter 3 0 Spending, Income, and Interest Rates (f) Suppose that policymakers decide to expand health care to those currently without health insurance, which results in an increase in govern- ment spending of $SObillion from $l,9S0 billion to $2,060 billion. Compute the new amounts of autonomous planned spending, Ap, when the interest rate equals 0, 2,4, and 6. (g) Compute the equilibrium levels of income when the interest rate equals 0,2,4, and 6and graph the new IS curve. (h) Suppose that initially the interest rate equals 4 and the economy is in equilibrium at natural real GDP, which equals 10,900. If monetary policy- makers want to maintain income at natural real GDP,explain by how much they will change the interest rate as a result of either the Iraqi troop reduction or the expanded health care coverage. *4.Assume an economy in which the marginal propen- sity to consume, C, is O.S, the income tax rate, t, is 0.2, and the share of imports in GDP, nx, is 0.04. Autonomous consumption, Ca, is 660; autonomous taxes, T", are 200; autonomous net exports, NX",are 300; planned investment, Ip, is 500; and government spending, G,is 500. (a) What is the value of autonomous planned spend- ing (Ap)? (b) What is the value of the multiplier? (c) What is the equilibrium value ofincome (Y)? (d) What is the value of consumption in equilibrium? (e) Show that leakages equal injections. (f) Suppose government expenditures decline by 150. Describe the economic process by which the new equilibrium value of Yis attained. (g) What is the new equilibrium value of Y? 5. Consider an economy in which taxes, planned invest- ment, government spending on goods and services, and net exports are autonomous, but consumption and planned investment change as the interest rate changes. Youare given the followinginformation con- cerning autonomous consumption, the marginal propensity to consume, planned investment, govern- ment purchases of goods and services, and net exports: Ca = 1,400 - 15r; C = 0.5; Ip = 2,350 - 35r; G = 1,940; NX = -200; Ta= 1,600. (a) Compute the value of the multiplier. (b) Derive the equation for the autonomous planned spending schedule, Ap. (c) Derive the equation for the IS curve, Y= kAp. (d) Using the equation for the IS curve, calculate the equilibrium levels of income at interest rates equal to 0,3, and 6. (e) Using your answers to part d, calculate the slope of the IS curve, b.r/ IlY. (f) Suppose that autonomous consumption rises by $40 billion, so that Ca = 1,440 - 15r. Explain whether this increase in autonomous consump- tion is caused bya rise or fall in consumer confi- dence. Derive the new equation for the IS curve. (g) Using the equation for the new IS curve, calculate the new equilibrium levels of income at interest rates equal to 0,3, and 6. (h) Using your answers to parts d and g, explain whether the IS curve shifts to the left or right when autonomous consumption rises. Explain why the horizontal shift ofthe IS curve equals the multiplier times the change in autonomous planned spending. 6. The purpose ofthis problem is to study how the slope of the IS curve changes as the multiplier changes and the responsiveness of autonomous planned spending to interest rate changes. Initially, use the same infor- mation as given in problem 5. (a) Suppose that the marginal propensity to consume increases from 0.5to 0.6. Compute the new value ofthe multiplier. (b) Derive the equation for the new autonomous planned spending schedule, Ap. (c) Derive the equation for the new IS curve, Y= kAp' (d) Using the equation for the new IS curve, calculate the new equilibrium levels of income at interest rates equal to 0,3, and 6. (e) Using your answers to part d, calculate the slope of the new IS curve, M/ 6.y. (f) Given that C = 0.6, suppose that the equation for planned investment expenditures is now Ip = 2,350 - 45r. Derive the equation for the new autonomous planned spending schedule, Ap' (g) Derive the equation for the new IS curve, Y= kAp. (h) Using the equation for the new IS curve, calculate the new equilibrium levels of income at interest rates equal to 0,3, and 6. (i) Using your answers to part h, calculate the slope of the new IS curve, Ilr / IlY. (j) Using your answers to part e of problem 5, and parts e and iof this problem, explain whether the IS curve gets flatter or steeper as (1), the multi- plier increases, and (2), the responsiveness of autonomous planned spending to the interest rate increases. *7. Consider an economy in which consumption, taxes, and net exports all change as income changes. In addition, consumption and planned investment change as the interest rate changes. Youare given the following information concerning autonomous con- sumption, the marginal propensity to consume, planned investment, government purchases ofgoods and services, and net exports: C = Ca + 0.S5(Y - T); C, = 225 - lOr; Ip = 1,610 - 30r; G = 1,650; NX = 700 - O.OSY;T = 100 + 0.2Y. (a) Compute the value ofthe multiplier. (b) Derive the equation for the autonomous planned spending schedule, Ap. (c) Derive the equation for the IS curve, Y= kAp' (d) Using the equation for the IS curve, calculate the equilibrium level of income at an interest rate equal to 3. (e) At the equilibrium level of income at an interest rate of3, show that leakages equal injections