ANSWER OUTLINE SIXTH TAKE-HOME EXERCISE SET [14 Points Total] L. Tesfatsion DUE DATE: Tuesday, April 30, 9:30 A.M. Econ 302/Spring 96 ---------------------------------------------------------- EXERCISE 6.1 [6 Points Total]. This exercise extends the previously assigned "balanced budget" exercise 3.4 on the Third Exercise Set. Consider an economy described by the following six relations, where D denotes an exogenously set target level for the government budget deficit: (1) Y = C + I + G + NE (2) C = a + b[1-t]Y (3) I = e - dR (4) NE = g - mY - nR (5) M/P = kY - hR (6) G - tY = D Period T endogenous variables: Y, C, I, NE, R, G Exogenous variables (positive): a,b,t,e,d,g,m,n,M,P,k,h,D, with t,b less than 1 Part A: Define what is meant by an IS curve for the economy described by relations (1) thru (6). Derive an algebraic expression for the IS curve for this economy and illustrate this curve graphically. Determine whether or not an increase in D affects the IS curve, and illustrate any effects graphically. Part B: Define what is meant by an LM curve for the economy described by relations (1) thru (6). Derive an algebraic expression for the LM curve for this economy and illustrate this curve graphically. Determine whether or not an increase in D affects the LM curve, and illustrate any effects graphically. Part C: Using Parts A and B, graphically determine how an increase in D affects the IS-LM equilibrium values Y^o and R^o for GDP Y and the real interest rate R. Provide an economic interpretation for your findings. In particular, do your findings suggest that an increase in D (i.e., an increase in the size of the government budget deficit) has negative short-run implications? negative long-run implications? Explain carefully. ------------------------------------------------------ EXERCISE 6.2 [4 Points Total]. Hall and Taylor, Chapter 9, ANALYTICAL exercise 9, page 262. #Be sure to justify your assertions and label all graphs carefully.# -------------------------------------------------------- EXERCISE 6.3 [4 Points Total]. Hall and Taylor, Chapter 9, MACROSOLVE exercise 5, page 264. #Be sure to justify your assertions and include with your answer any MacroSolve data referred to in your answer#. NOTE: The "price shock" referred to in part b is a term Z(T) appended to the usual expectations augmented Phillips curve that is treated as an exogenous variable (a disturbance to the economy from "outside"): INF(T,T+1) = INF^e(T,T+1) + [Y(T)-Y*(T)]/Y*(T) + Z(T) . The effect of Z(T) is to cause a sudden change in P(T+1) not due to either inflationary expectations or GDP gap pressures. ------------------------------------------------------------------ ------------------------------------------------------------------ ANSWER OUTLINE FOR EXERCISE 6.1: [6 Points Total] ANSWER OUTLINE FOR PART A: [2 Points] The IS Curve shows all combinations of the real interest rate R and real GDP Y that are consistent with product market equilibrium, in the sense that demand for newly produced goods and services equals supply and all expectations are fulfilled. For the economy at hand, the relations dealing with the product market are relations (1), (2), (3), (4), and (6)---that is, all relations except the money market relation (5). As explained in HT7, these relations can be interpreted as the partially reduced down expressions for demand, supply, and equilibrium relations in the product market. The only difference between the product market relations for the HT7 economy and the product market relations for the economy at hand is relation (6), which specifies that G is an endogenous variable for the economy at hand. [REMARK: Specifically, G takes on whatever value is necessary in order to guarantee that the current government budget deficit stays at the exogenously given target level D. Note that the tax rate t is still given as an exogenous variable, but of course the amount tY of total tax **revenues** is determined endogenously.] The IS curve is obtained from the product market relations (1)-(4) and (6) as follows. ------------- #Step 1#: Reduce down relations (1)-(4) and (6) to one equation in the two unknowns R and Y by substituting out for the other endogenous variables C, I, G, and NE that appear in these relations. Y = (a + b[1-t]Y) + (e - dR) + (D + tY) + (g - mY - nR) ------------- #Step 2#: Collect terms in Y and in R (1 - b[1-t] - t + m) x Y = (a + e + D + g) - (d+n) x R or equivalently (d+n) x R = (a + e + D + g) - (1-b[1-t] - t + m) x Y = (a + e + D + g) - ([1-t] - b[1-t] + m) x Y = (a + e + D + g) - ([1-t][1-b] + m) x Y -------------- #Step 3#: Solve for R as a function of Y (slope-intercept form) .ls 2 (a + e + D + g) ([1-t][1-b] + m) R = --------------- - ----------------- Y (d+n) (d+n) ............... ..................... R-Intercept (+) Slope dR/dY (-) --------------- #Graphical Illustration#: R | (a+e+D+g)| ---------.is (d+n) | is | is | is <-------------IS Curve for any given D | is | is | is | is |----------------------------------------------- Y 0 IS Curve with positive R-intercept and negative slope dR/dY. #Effects of an Increase in D#: The exogenous target deficit level D enters into the numerator of the R-intercept for the IS curve with a positive sign, but it does not enter into the expression for the slope of the IS curve. Consequently, an increase in D increases the R-intercept without changing the slope. It follows that the IS curve undergoes a parallel **upward** shift, so that the new IS curve yields a higher level of R for each level of Y. This upward shift of the IS curve should be graphically depicted. ANSWER OUTLINE FOR PART B: [2 Points] The LM Curve shows all combinations of the real interest rate R and real GDP Y that are consistent with money market equilibrium, in the sense that the demand for money equals the supply of money and all expectations are fulfilled. For the economy at hand, the only relation dealing with the money market is relation (5). As explained in HT7, this relation can be interpreted as the partially reduced down expression for demand, supply, and equilibrium relations in the money market. The only difference between the money market relations for the HT7 economy and the money market relation for the economy at hand is that the expected inflation rate does not enter into this money market relation. (Money demand is assumed to depend on the real interest rate R rather than the nominal interest rate R+INF.) The LM curve is obtained from the money market relation (5) as follows. ------------- #Step 1#: Relation (5) is already one relation in the two endogenous variables of interest, Y and R; no other endogenous variables appear in relation (5). ------------- #Step 2#: Collect terms in Y and in R hR = - M/P + kY -------------- #Step 3#: Solve for R as a function of Y (slope-intercept form) R = - M/hP + (k/h) x Y ............... ............... R-Intercept (-) Slope dR/dY (+) --------------- .ls 2 #Graphical Illustration#: R | | | lm | lm | lm | lm | lm | lm | lm | lm |--------------lm--------------------------------- Y 0 lm | lm | lm -M/hP . lm | LM Curve with negative R-intercept and positive slope dR/dY. #Effects of an Increase in D#: The exogenous target deficit level D does not appear anywhere in the algebraic expression for the LM curve. It follows that the placement of the LM curve is **unaffected** by changes in D. ANSWER OUTLINE FOR PART C: [2 Points] From Part A and Part B, above, an increase in D shifts upward the IS curve but leaves the LM curve unchanged. It follows that the IS-LM equilibrium values for Y and R in the current period are **both increased** as a result of this increase in D. This should be illustrated graphically. #Economic Interpretation#: The increase in the IS-LM equilibrium level for real GDP Y in the current period T implies an increase in employment (a reduction in unemployment) in period T, which is a good short-run implication. However, the increase in the IS-LM equilibrium value for the real interest rate R decreases the period T investment level I(T). Economic agents are now buying more government bonds and putting less money into capital investment. [Recall that an increase in the government budget deficit will generally be financed by an increase in DB, i.e., an increase in the rate at which **newly** issued bonds are being sold to the HC private sector and to ROW in exchange for money.] Consequently, it follows from the identity K(T+1) = K(T) + I(T) - (Period T Capital Depreciation Expenditure) that the capital stock K(T+1) in the next period T+1 will be lower than it otherwise would have been. This in turn implies that potential GDP in period T+1, Y*(T+1) = F(N*(T+1),K(T+1),A) , will be lower than it otherwise would have been, a bad longer-run implication for the economy. This bad longer-run implication is the kind of prediction made by those who worry about growing government budget deficits. Note, however, that this negative impact on private investment could in principle be prevented by an appropriately accommodating monetary policy---an increase in the money supply M engineered by the Fed via an open market operation in which **existing** bonds currently in the hands of the private sector are purchased from the private sector in exchange for money. This increase in M could shift down the LM curve to prevent the rise in R. If the economy is currently in a state such that Y is less than Y*, then these accommodating downward shifts in the LM curve might be able to prevent rises in the real interest rate without causing inflationary pressures---that is, without causing Y to rise above Y*. ----------------------------------------------------------------- ----------------------------------------------------------------- ANSWER OUTLINE FOR EXERCISE 6.2: [4 points total] When the Reagan administration came into power in 1981, three of its primary objectives were to reduce inflation, lower taxes, and increase defense spending. ANSWER OUTLINE FOR PART A: [2 Points] Explain why the achievement of all three goals required an extremely restrictive monetary policy. Lowering income tax rates and increasing government defense expenditures are each **expansionary** fiscal policies in the sense that they rotate and shift upwards the IS curve, respectively, resulting in a higher IS-LM equilibrium level for real GDP Y. On the other hand, to keep inflation in check, it follows from a Phillips curve argument that it is generally necessary to ensure that real GDP Y stays below or at potential real GDP Y*. As seen in Figure 9-12 in HT Chapter 9, the U.S. economy was close to potential GDP when Reagan was inaugurated in 1981. Thus, to reduce the inflation rate while at the same time cutting taxes and increasing defense expenditures required an extremely restrictive monetary policy to ensure that Y did not rise above Y*. In actuality, attempts were made by the Fed in 1981-2 to keep the **growth rate** of the money supply in check while the Reagan Administration increased the **growth rate** of defense expenditures and pushed through changes in the tax code that resulted in deep cuts in income tax rates across all income brackets. But the general qualitative implications of these policy choices can be captured within the HT8 IS-LM model by considering the combined effects of a sharp decrease in the money supply M, a sharp decrease in the tax rate t, and a a sharp increase in the level of government expenditures G, starting from a position of internal balance (IS=LM and Y=Y*) with a high but correctly predicted inflation rate (INF = INF^e). The big decrease in t rotates **up** the IS curve (higher R for each Y) and the big increase in G shifts **up** the IS curve (higher R for each Y); the LM curve is unaffected by the decrease in t and the increase in G. Thus the new IS-LM equilibrium point occurs at a level of Y that is sharply higher than Y*, so a large positive GDP gap opens up. It follows from the form of the expectations-augmented Phillips curve that the inflation rate will then increase unless there is an appropriately large offsetting **decrease** in the money supply M to push the LM curve **up** (higher R for each Y). Pushing the LM curve up means that the IS-LM intersection point is pushed back to a lower Y level; but note that the real interest rate is then at an even higher level than before. ADDITIONAL REMARKS: Hall and Taylor argue (pages 558-559) that there was a monetary policy error on the part of the Fed in 1982: they argue that the monetary policy followed by the Fed was too restrictive and resulted in unnecessarily high interest rates and an unnecessarily severe recession. You may want to take a look at this discussion; see also the empirical data reported in HT Chapter 13, in particular figure 13-5. Many Democrats have argued that it was the Reagan Administration's sharply expansionary fiscal policy in 1981 that was the primary policy mistake because this is what forced the Fed into a restrictive monetary policy stance. The short-run outcome was the severe 1981-82 recession and the longer-run outcome was the twin deficit problem---the simultaneous opening up of a large and persistent government budget deficit together with a large and persistent current account deficit. (Why?) Republicans counter that the primary policy mistake was the failure of the Democratically controlled Congress to enact other types of spending cuts to offset the effects of the reduced tax rates and increased defense expenditures. ANSWER OUTLINE FOR PART B: [2 Points] Could the same disinflation have been achieved with a less restrictive monetary policy and a more restrictive fiscal policy? If not, why not? If so, explain how the following variables would have been affected during the 1981-1984 period: output, inflation, interest rates, consumption, investment, the trade deficit, and the government budget deficit. Yes, according to the basic HT8 IS-LM model. By reducing the extent of the increase in G while at the same time reducing the extent of the decrease in t and reducing the extent of the decrease in M, the **same** real GDP level Y could be achieved (hence the same rate of disinflation) at a **lower** real interest rate. Comparing the effects of this milder course of policy action relative to the initial sharp increase in G and sharp decreases in t and M, one finds that: Output (real GDP) would be the **same**; Inflation would be the **same** because the real GDP gap would be the same; The real interest rate would be **lower**; Consumption would be **lower** due to higher t at the same level of Y; Investment would be **higher** due to lower R at the same level of Y; The trade deficit (Imports-Exports) would be **smaller** because of the lower R and the same level of Y (hence the higher level of exports with unchanged imports); The government budget deficit G-tY would be **smaller** due to higher t and lower G at the same level of Y. ----------------------------------------------------------------- ----------------------------------------------------------------- ANSWER OUTLINE FOR MACROSOLVE EXERCISE 6.3: [4 Points Total] **NOTE**** See the closed reserve version of this answer key (Reading Room, Heady 368) for the MacroSolve data figures and tables that supports the answer outlines given below. Note also that, in all MacroSolve exercises with the AD/PA, Closed Econ model, the default parameter settings for M and P are M=900 and P=1. Also, the economy begins in internal balance and stays in internal balance at Y=Y*=6000, where potential GDP Y* remains constant at 6000 in each time period. Suppose the Fed adopts a policy to fight inflation. What should it do in response to an increase in government expenditure? Select the "AD/PA, Closed Econ" model and increase government spending by $50 billion. ANSWER OUTLINE FOR PART A: [2 Points] What change in the money supply is required to maintain stability of the price level? Let us first examine what happens when G is increased by $50 billion in period 1 with **no** change in the money supply. Data generated for the resulting economy are presented in Table 1 and graphically depicted in Figure 1. As seen during the dynamic display of Figure 1, the increase in G by $50 billion in period 1 shifts **up** the IS curve (higher R for each Y) in period 1 but does not affect the LM curve in period 1. Consequently, both Y and R increase in period 1. Because the economy was originally in internal balance with Y=Y*=6000, the increase in Y in period 1 opens up a positive GDP gap in period 1 and puts upward pressure on the price level for period 2 through the expectations-augmented Phillips curve. As seen in Table 1, the price level ultimately increases from its original value of 1.0 to a final value of 1.03, attained when the GDP gap once again is zero; and the LM curve has shifted up in response to the increase in P. Consequently, the new IS-LM equilibrium is at the same Y level (Y=Y*=6000) but at a higher real interest rate R. A cut of $25 billion in the money supply M in period 1, the same period that G increases by $50 billion, shifts the LM curve **up** (higher R for each Y) and just offsets the effects on Y of the increase in G. That is, as seen in Figure 2 and Table 2, Y remains equal to Y*, implying that the GDP gap remains equal to zero. Consequently, there is no pressure on the price level to change. As seen in Figure 2, however, the cut in M in response to the increase in G does result in a higher real interest rate R. The fact that a cut in M of $25 billion is needed to maintain Y equal to Y*, and hence a constant price level, subsequent to a $50 billion increase in G can be determined either by trial and error or by doing an offsetting multiplier calculation along the lines of the previously assigned MacroSolve Exercise 1 (HT, p. 207) on the Fourth Exercise Set. ANSWER OUTLINE FOR PART B: [2 Points] Now suppose the economy suffers a 5 percent price shock (as opposed to the increase in government spending): (*) INF(0,1) = INF^e(0,1) + [Y(0) - Y*]/Y* + .05 How should you respond according to the inflation-fighting policy? What is the impact of your response on output? Are GDP fluctuations larger or smaller? It follows from relation (*) above that the 5 percent price shock at the end of period 0 (or equivalently, at the beginning of period 1) increases the price level P(1) in period 1. Thus, the real money supply M/P(1) in period 1 is smaller and the LM curve shifts **up** (higher R for each Y); the IS curve is not directly affected by price shocks. Consequently, IS-LM equilibrium in period 1 is re-established at a smaller level of Y. This opens up a negative GDP gap which puts downward pressure on the price level. The ultimate effects of the 5 percent price shock, assuming no policy response, are seen in Figure 3 and Table 3. Note, in particular, from Figure 3, that the price level does not start to decrease until period 3. **Cutting** the money supply M in period 1 shifts up the LM curve even further, thus opening up an even larger negative GDP gap and putting additional downward pressure on the price level. Consequently, the price level adjust back down more quickly if M is cut. See Figure 4 and Table 4, for example, which depict what happens when M is cut by $50 in period 1. Note that P now starts to decrease in period 2. Nevertheless, this faster downward adjustment of the price level due to a cut in M comes at the cost of greater volatility in GDP, in the sense that Y undergoes a more negative change than in Part A before finally returning once more to Y* as the price level drops. Note that Y in Figure 3/Table 3 drops only to 5867 whereas Y in Figure 4/Table 4 drops all the way down to 5773. Moreover, to the extent that M is cut, the price level will fall to a **lower** level than its original default value P=1. See Figure 4/Table 4, for example. The reason for this is that the 5 percent price shock shifts up the LM curve but leaves the IS curve unaffected. Consequently, in order for internal balance to be reestablished, the LM curve must return to its **original** position (so that the IS and LM curves again intersect at Y=Y*). But the LM curve will only return to its original position if the real money supply M/P returns to its original level---which is 900 under the MacroSolve default values M=900 and P=1. If M=900 is unchanged, this means that P must return to its original default value P=1. But if M is decreased to 850, then P must decrease to 850/900 = 0.9444... in order for the real money supply M/P = 850/P to again equal its original value 900.