Workbook For Chapter 3 Of Blanchard Macroeconomics. Problem 4 For both political and macroeconomic reasons governments are often reluctant to run budget deficits. Here, we examine whether policy changes in G and T that maintain a balanced budget are macroeconomically neutral. Put another way, we examine whether it is possible to affect output through changes in G and T such that the government budget remains balanced. a. First, let’s investigate the effect on Y when G increases by one unit, ∆G = 1. Write down the equation for equilibrium output. (That is, write “equilibrium output = the multiplier * autonomous expenditure” in symbols. This is equation 3.8 in the text.) _________________________________. Now suppose that autonomous expenditure rises by one unit. Notice that G is a part of autonomous expenditure, so it affects expenditure directly. How much does equilibrium output increase by? ∆Y = ____________________. b. Second, by how much does Y decrease when T increases by one unit, ∆T = 1? Here you have to be more careful. T affects expenditure through its effect on Consumption. If T increases by one unit, Disposable Income _______ (rises/falls), so that ∆(Y – T) = _____ unit(s). Now write down the Consumption Function, equation 3.2. _________________________. Given the consumption function, if disposable income decreases by the amount you found above, what happens to consumption? ∆C = ______. Given this change to consumption, and using equation 3.8, what will happen to equilibrium output? ∆Y = __________________. c. Why are your answers to (a) and (b) different? __________________________________ ______________________________________________________________________________. Suppose that the economy starts with a balanced budget: G=T. If the increase in G is equal to the increase in T, then the budget remains in balance. Let us now compute the “balanced budget multiplier.” d. Suppose that both G and T increase by one unit, ∆G = ∆T = 1? Using your answers to (a) and (b), we’re going to find the change in equilibrium GDP.You found above that when ∆G = 1, ∆Y = __________; and that when ∆T = 1, ∆Y = __________. If both G and T change at the same time, then it makes sense to think that the total change will be the sum of both changes.1 ∆Y = ∆G + ∆T = ________ + ________ = ________________. This result is called the balanced budget multiplier. Given what happens to Y when G and T change by the same amount, would you say that balanced budget changes in G and T are “macroeconomically neutral”? ______________. This answer turns out to be tremendously useful. Chapter 3 has implied that if a country is in a recession, the government should run a budget deficit, raise equilibrium output, and return the economy to full-employment. But budget deficits mean accumulating government debt, higher interest rates, and potentially macroeconomic instability. So countries around the world have learned to try to avoid budget deficits and rather to stay within a balanced budget. Does this mean that they have had to give up fiscal policy? The answer depends on whether changes to G and T that leave the budget balanced are macroeconomically neutral. e. Finally, think about whether the specific value of the propensity to consume affects your answer to (d). Suppose that the mpc were higher. What would that do to the balanced budget multiplier? It would ___________(raise it/lower it). Why? Give your answer in terms of what a balanced budget does to the multiplier. ____________________________ ______________________________________________________________________________. Problem 5 So far in this chapter we have been assuming that the fiscal policy variables G and T are independent of the level of income. In the real world, however, this is not the case. Taxes typically depend on the level of income, and so tend to be higher when income is higher. In this problem we examine how this automatic response of taxes can help reduce the impact of changes in autonomous spending on output. Consider the following behavioral equations TYYYttTYccCDD−=+=+=1010 G and I are both constant. Assume that t1 is between zero and one, 0 < t1 < 1. 1 The reason the total change is equal to the sum of the partial changes is that G and T are joined together by addition in equation 3.8 (i.e., they “enter additively into equilibrium output”). We could not use this trick if the two changing terms were multiplying each other (e.g., T and c1) changed at the same time. In that case, instead of being able to use the sum rule of differentiation, we would have to use the product rule of differentiation. This is fairly basic if you know Calculus. eq. 1 eq. 2 eq. 3a. First, let’s solve for equilibrium output. Plug equation 3 into equation 1 ___________________________. Now plug equation two into the combined 1-3 equation ________________________________. Call this the Equation 4. Write down the expenditure function by substituting the Equation 4 into Z = C + I + G. Z = C + I + G = ________________________________ + I +G. Call this Equation 5. Substitute the Equation 5 into Y = Z. Y = ________________________________+I+G. Now solve the result for Y (that is, put all the “Y’s” on the left hand side of the equation). ____________________________________________________________________________________________________________________________________________________________. By setting the expenditure function and Y = Z equal to each other and then solving for Y, you have “solved the system of equations” formed by those two equations. The result is equilibrium output. Your result should look like (but not be the same as) equation 3.8: equilibrium output is equal to a multiplier times autonomous expenditure. b. In (a), you found that equilibrium output was the product of the multiplier times autonomous spending and that multiplier has a t1 term in it. In the case we are considering, when the multiplier depends on the average tax rate (t1), what is the multiplier? __________________. Suppose that government changed t1 so that t1 = 0. What would the multiplier be in that case? _________. You know that if the denominator of a fraction is larger, the fraction itself is smaller. Given this, which of the two multipliers you just found is larger in absolute value? ______________________________. Suppose that