ans - Chapter 2: Measuring the Economy lnaz‘rucitw‘a...

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Unformatted text preview: Chapter 2: Measuring the Economy lnaz‘rucitw‘a Mamet Chapter 2: Measuring the Economy Problem 1 A closed economy is an economy without international trade, while an open economy is an economy that participates in international trade. The public sector refers to the portion of the economy controlled by the government, while the private sector refers to the portion of the economy controlled by households and firms. The government budget deficit refers to yearly borrowing by the government, while government debt refers to the total accumulated borrowing that is owed by the government. Aggregate income, aggregate expenditure, and aggregate production are each equal in value and are each measured by GDP. Problem 2 See Section 4 in the text and equation 2.9. From equation 2.9, you can see that a larger budget deficit, (TR +G)>T, will lead to a larger trade deficit, NX<0, everything else being equal. Looking at Figure 2.4 in the text, you can see that trade deficits in the US tended to be larger in the mid 19805 when the government budget deficit was at its the largest. Given that the budget deficit decreased dramatically and actually turned into a budget surplus in the late 19905, we should have witnessed a decrease in the US. trade deficit, everything else being equal. However, once again looking at Figure 2.4, you see that the trade deficit actually increased during the late 19905. The only explanation must be a change in one of the other variables in equation 2.9. The low private savings rate, S, in the US. is the most likely source of this decrease in net exports. (This will be discussed more fully in Chapter 6.) Problem 3 We know that the trade deficit is TD=G+TR-T. So rewriting this equation we can obtain G= TD + T — TR = 200—200+500=$500. The GDP accounting identity is Y=C+I+G+NX. So GDP equals 5,000+] ,000+500+600-800=$6,300. Given that NX=-$200, this country must also have a negative level of net foreign investment of -$200. Thus, this country is a net foreign borrower. C/Y=5,000/6,300= 79.4%. l/Y=1,000/6,300= 15.9%. Chapter 2: Measuring the Economy Instructor’s Manual Problem 4 Stocks are variables that are measured at a particular point in time, while flows are measure over a period of time. Stock variables are useful in giving you a snapshot of the overall level of assets and liabilities that have been accumulated over time. Flow variables allow you to investigate the rates of change in these stock variables. Problem 5 Flow variables are measured with respect to time (thus they have a "per unit time" dimension), while stock variables are measured at a point in time. Therefore, the stock variables are national debt and capital. The flow variables are Consumption, Gross Domestic Product, Net Domestic Product, the government budget deficit, transfer payments and interest payments on debt. Problem 6 a. From the GDP accounting identity, Y = C + I + G, it is possible to obtain the figure for gross investment. Since we have numbers for GDP (Y), consumption (C), and government spending (G), gross investment is I = Y - C - G = $5,000 — $2,600 - $1,200 = $1,200. b. Net Investment is simply Gross Investment minus the Depreciation cost of maintaining the existing capital stock. So, Net Investment = Gross Investment - Depreciation = $1,200 - (0.10)($10,000) = $200. c. The Net Domestic Product is obtained by subtracting depreciation costs from the Gross Domestic Product. Thus, NDP = GDP - Depreciation = $5,000 - $1,000 = $ 4,000. d. The capital stock in any year is the capital stock inherited fiom the previous year plus new investment that took place last year. We care only about net investment since a part of gross investment is used to cover for the depreciation of the existing capital stock. Hence, Capital Stock in 2002 = Capital Stock in 2001 + Net Investment in 2001 = $10,000 + $200 = $10,200. Chapter 2: Measuring the Economy Instructor’s Manual Problem 7 The table below shows the capital stock for the years 1994-1999. GROSS CAPITAL STOCK DEPRECIATION . - 199 _— 199 199 199 199 The second column is calculated as follows: In 1995, for instance, capital stock = capital from 1994 + gross investment - depreciation cost. YEAR Problem 8 John’s balance sheet: ASSETS ‘ ‘ LIABILITIES Car: $20,000 Mortgage: $45,000 Credit Card: $2,000 Credit to Joan: $17,000 House: $50,000 Net Worth: $44,000 Joan’s balance sheet: ‘ Car: $1 1,000 Debit: $17,000 Jewelry: $2,000 Mortgage: $45,000 House: $50,000 Credit Card Debts: $700 Credit Card: $1,000 Net Worth: $1,300 The Brown family's balance sheet: ‘ Cars: $31,000 Mortgage: $90,000 Credit Card: $3,000 Credit Debts: $700 House: $100,000 Jewelry: $2,000 Net Worth: $45,300 Chapter 2: Measuring the Economy Instructor’s Manual Problem 9 3. GDP using the expenditure methodl Y = value of finals goods and services = $5 + $80 = $85 b. Value added by firm A = $5 + $25 = $30. c. Value added by firm B = $80 - $25 = $55. d. Assume that all profits go back to the households. Profits of firm A = Revenue from sales - Cost of inputs = $30 - ($5 +$25) = $0. Fim‘. B spends $30 - $10 = $20 in wages. The problem is not specific about whether it employs capital too. Supposing that it does not, then Firm B's profits2 = $80 — $20 - $25 = $35. Thus total profits earned by hbuseholds from Firms A and B are $35. e. $25, the value of the goods that.me A sells to firm B. Problem 10 a. GDP per capita seems to be the most appropriate measure to compare the well being of these two countries. b. GDP per capita is $133.33 in Country A. GDP per capita is $102.86 in Country B, so Country A is better off. 0. Country A produces 91.7% of the world’s output and Country B produces 8.3%. Problem 11 1994-1995 inflation was ((129.96-126.35)/126.35)*100=2.86%. 1995-1996 inflation was ((132.37-129.96)/129.96)*100=186%. 1996-1997 inflation was (135.32-132.37)/132.37)*l00=2.22%. l Verify that you get the same answer using the value added and the income methods. By the value added method, Y = Sum of value added = $30 + $55 = $85. By income method, Y = Wages + Rent + Profit = $30 + $20 + $35 = $85. 2 If we assume that the firm employs capital too and that the production function exhibits constant returns to scale, these $35 are payments to capital so that Firm B makes zero profit like Firm A. Chapter 4: The Theory of Aggregate Supply Instructor’s Manual Chapter 4: The Theory of Aggregate Supply Problem 1 A representational agent economy is one in which each individual has identical preferences. The reason why economists make this assumption is that is simplifies their models and their analysis significantly. The problem is that it excludes the investigations of many sorts of issues, particularly distribution issues. For example, the effects that a specific policy might have on income distribution cannot be evaluated within a representational agent model. Problem 2 The nominal wage is the actual money amount paid to a worker for each hour of work. The real wage is the amount of goods and services that can be purchased with the proceeds from each hour of work. It is the real wage that matters to households because, ultimately, households do not care about the size of the numbers in their paycheck but about the amount of goods that they can buy with their wages. Similarly, it is the real wage that matters to firms because that is the true measure of a firm's cost of hiring labor. Problem 3 Diminishing returns refers to the fact that the additional amount of output produced by adding additional amounts of labor falls as larger amounts of labor are added to production. In other words, the marginal product of labor falls as the quantity of labor rises. Because the productivity of additional units of labor falls as a firm hires more labor, firms will only be willing to hire more labor if the real wage also falls. It is for this reason that the labor demand curve is downward sloping. Problem 4 a. The substitution effect refers to the fact that as the real wage rises, leisure becomes more expensive which, in turn, encourages households to work more hours. The wealth eflect refers to the fact that as the real wage rises, households become wealthier and can afford to work less and enjoy more leisure. b. The figure in Box 4.5 indicates that real wages have risen significantly in the US. while the employment rate (as a percentage of the population) has remained relatively constant. This seems to indicate that these two effects tend to offset each other, i.e., the substitution effect is approximately equal to the wealth effect, and that the long run labor supply curve is close to being horizontal. 317 Chapter 4: The Theory of Aggregate Supply Instructor’s Manual Problem 5 A tax on labor income will discourage work and reduce the supply of labor. Both the quantity of labor and the real wage will fall as a result. The reduction in the quantity of labor increases the marginal product of labor because of diminishing returns. As the quantity of labor falls, there is a movement along the existing production function and output falls. Problem 6 A tax on capital will reduce the amount of capital, which decreases the marginal product of labor and the demand for labor. This reduction in the demand for labor will lower the quantity of labor and the real wage. The production function will shift downward. At the same time, there is also a movement along this new production function as the quantity of labor falls. Both of these effects serve to reduce the level of output. Problem 7 The answer here is exactly the same as the answer to Problem 5 above. Problem 8 a. At t = .3 then I.S = (.7)(w /P). At t = .2 then L3 = (.8)(w /P). b. At t = .3, setting LS = Ld you can solve for the value of the real wage which is w / P = 2.39. At t = .2, setting L5 = Ld you can solve for the value of the real wage which is w / P = 2.23. c. An increase in the tax rate, t, should reduce the labor supply curve, which will increase the real wage and decrease the quantity of labor. d. Att= .3, L3 = .717. At t = .2, L3 = .446. e. The Lafler curve is a graph of tax revenue against the marginal tax rate. Looking at Box 4.4 in the text, you can see that there is a tax rate at which tax revenues are maximized. In this example, an increase in the tax rate increases tax revenue, so the current marginal tax rates must be below the tax rate that maximizes tax revenue. This example is not consistent with supply-side arguments that in the real world current marginal tax rates are above the revenue maximizing tax rate. 38 Chapter 4: The Theory of Aggregate Supply Instructor’s Manual Problem 9 a. The marginal product of labor is MPL = (l/2)L'”2. b. WhenL= l, MPL=.5. When L = 2, MPL = .35. When L = 3, MPL = .29. c. The labor demand curve is obtained by setting w / P = MPL, or w / P = (1/2)L'1/2. This can be simplified to Ld = l/(4(w /P)2). d. Setting LS = Ld, the equilibrium values of the real wage and labor can be calculated as w/P=‘/2andL= l, e. When L = 1, we can see from the production function that Y = 1. Problem 10 Real Business Cycle models assert that business cycles are created by changes in aggregate supply, specifically random technology shocks. As a result, business cycles do not represent inefficient uses of resources but are simply an optimal response by firms and households to unavoidable changes in the productivity of the economy. The attractiveness of RBC models is that they are simple, intuitive, and mimic business cycles in the real world fairly well (see Figure 4. 7 in the text). The problems with RBC models are twofold. First, it seems hard to satisfactorily explain all business cycles as decreases in technology (see the discussions on the Great Depression later in the text). Second, RBC models cannot explain involuntary unemployment, in which there are workers who would be willing to work for a lower real wage but are still unable to find work. In RBC models, all unemployment is voluntary and occurs when workers move in and out of the labor market in response to changes in real wages. 39 Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Instructor’s Manual Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Problem 1 a. The value of the propensity to hold money, k, is calculated according to the relationship k = M/PY and is shown in the table below. 1280"“ _1_981‘_ 198g“ 1983 1984 1985 0.152 ""'0.i4"1"”0.15'2' 0.153 0.145 0.155 b. Since k = M/PY, nominal GDP (PY) is a flow and M is a nominal stock, k has units of time. c. Figure l below illustrates the time-path of the propensity to hold money, k. Although k fluctuated a lot over the period, there is no discernible time trend. In fact, by eye-balling the graph we can think of k as being approximately constant at 0.149. 0.156 0.154 0.152 0.150 0.148 0.146 0. 144 1980 1981 1982 1983 1984 1985 Figure 1: Propensity to hold money Problem 2 The quantity theory of money says that MD = kxPYD, where PYD is the nominal demand for commodities and k is the marginal propensity to hold money. The intuition behind this equation is that people hold a constant fraction of their nominal demand for commodities as money. The quantity theory of money is a theory of aggregate demand because if the money market is in equilibrium, i.e. MD = M3, then the quantity theory equation can be rewritten as P = Ms/(kYD). From this equation, we can see that there is a negative relationship between P and YD. The intuition behind the downward sloping aggregate demand curve is that an increase in the price level reduces the real value of the money supply. As real money balances fall, the real demand for commodities also decrease. 49 Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Instructor’s Manual Problem 3 There should be a strong positive relationship between the money supply and the price level, and as a result a positive relationship between money growth and inflation. However, looking at the quantity equation you see that this relationship is not necessarily a perfect relationship if there is a change in one of the two other variables in the quantity equation. First, changes in k, the marginal propensity to hold money, affect the relationship between the money supply and the price level. An increase in k lowers the price level if the money supply is held constant. Second, a change in Y, or real GDP. changes the relationship between the money supply and the price level. An increase in Y also reduces the price level holding the money supply constant. Problem 4 Nominal variables are variables that are measured in monetary units and, as a result, have not been adjusted for changes in the price level over time. Real variables are variables that are measured in units of commodities and as a result are not distorted by changes in the price level. The proposition of money neutrality says that increases in the money supply will lead to proportional increases in all nominal variables but will not affect real variables. In other words, changes in the money supply only lead to proportional changes in the price level and those variables measured in prices. Problem 5 One of the implications of perfectly competitive markets is that prices will be perfectly flexible in these markets. If markets are not perfectly competitive and individuals have some control over setting prices, then prices most likely will not be perfectly flexible. As a result, in a response to an increase in the money supply it may not be the case that the price level will increase proportionally. Looking at the quantity theory you see that if the money supply rises without a proportional increase in the price level, one of two real variables must adjust to maintain equilibrium, either it or Y. This would violate the proposition of money neutrality in that changes in the money supply would affect real variables. Problem 6 fidgniamge refers to the revenue that a government generates by printing and issuing money. Many governments find themselves with severe budget problems. For example, many less developed countries have accumulated large amounts of foreign debt and loan payments. At the same time. many of these same countries have a very poor tax base from which to raise revenue. As a result, countries that have experienced a hyperinflation are typically countries that have had no other alternative but to meet their obligations through printing up large amounts of money, which produces high levels ofinflation. 50 Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Instructor’s Manual Problem 7 The price level is countercyclical in the classical model. Given that changes in output can only be created by changes in aggregate supply, when aggregate supply and output increase the price level must fall. While prices have been countercyclical over certain periods 0fU.S. history, prices were strongly procyclical during the Great Depression when both prices and output fell substantially. The classical model is unable to explain this procyclical movement in prices. Problem 8 a. An increase in natural resources would increase labor demand and aggregate supply. As a result of the increase in labor demandl the quantity of labor would rise and real wages would rise. As a result of the increase in aggregate supply the price level would fall and aggregate output would rise. b. A reduction in the money supply would only affect nominal variables and not real variables according to the proposition of money neutrality. There would be no change in the real wage, but nominal wages and the price level would both fall by 20%. Aggregate demand falls but aggregate supply remains unchanged so that aggregate output remains unchanged. c. Same answer as in part a. Problem 9 A large increase in labor force participation created by more women entering the labor force would result in a large increase in labor supply. Real wages would fall and the quantity of labor would rise. As a result, aggregate supply would rise, which would reduce the price level and increase output. If both the price level and the real wage fall, it must be the case that nominal wages fell as well and by more than the decrease in the price level. Problem ll) If we impose market clearing on the classical aggregate demand equation by equating aggregate demand YD to aggregate supply YE, we obtain the Quantity Equation of Money: Ms kYE ' This equation tells us what factors influence the average price level. Preferences affect the price level through the propensity to hold money, k. Although the classical theory assumes that the propensity to hold money is constant over time, as Figure 5-9 in the text shows, it has changed a lot over the years. Technology affects the price level through the full-employment output level YE, with a higher output leading to lower prices. Finally, as an example of endowments, we could think of the number of people in the economy. A shrinking labor pool would imply a shrinking real economy, and this would raise the price level. P: 51 Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Instructor’s Manual None of these factors can be considered as having hadany important consequence for prices in the US. history. In fact, as Figure 5-7 in the text demonstrates, the inflation rate in the US. has followed the rate of money creation quite closely. Problem 11 in the classical model, aggregate output is completely determined by changes in aggregate supply. As a result, the aggregate demand for output is determined solely by the amount of output that is supplied. Surpluses and shortages of output are not possible in the classical model because prices are perfectly flexible. As a result, supply does determine, or "create," its own demand and the classical model is consistent with Say’s Law. Problem 12 a. The marginal product of labor is MPL = 3L“. Setting the real wage equal to the marginal product, the labor demand curve is w / P = 3L“, which can be rewritten as LD = 9/((w / P)2). b. Using equation 5.4 in the text, the aggregate demand curve is P = lZ/YD. 0. Setting LS = LD and solving for the equilibrium wage, w /P = 1.65 and L = 3.31. d. Equilibrium output is YE : 66.31)"2 = 10.9. c. From the aggregate demand curve P = l2/10.9 = 1.1. Problem 13 a. The marginal product of labor is MPL = AL'm. Setting the real wage equal to the marginal product of labor, w / P = AL”, I w / P which can be rewritten as LD = (A/ (w / P))3"2. b. Setting L5 = L” and solving for the equilibrium wage, w / P = l and L = 1. Aggregate output is Y = 3. c. Using equation 5.4 in the text, the aggregate demand curve is P = lS/YD. Given Y = 3 then P = 5. d. When A = 4 then setting LS = LD, the equilibrium wage is now w /P = 2.30 and L = 2.30. Aggregate output increases to Y = l2(:2.30)1’/3= l5.84. The aggregate price level falls to P = l5/(15.84) = .95. 52 Chapter 5: Aggregate Demand and the Classical Theory of the Price Level Instructor’s Manual Problem 14 a. Set the real wage equal to the marginal product to obtain LD = 16/((w / P)2). Set labor supply equal to labor demand to obtain w / P = 2 and L = 4. Y = 8(4)“2 = 2. P = MS/kY = 16. b. The real wage, labor, and output all remain unchanged. When the money supply rises to MS = 120, the price level also rises so that P = Ms/kY = 20, which is also a 25% increase. c. The 25% increase in the money supply lead to a proportional increase in the price level but did not affect real variables such as Y or L. As a result, these results are completely consistent with the proposition of money neutrality. Problem 15 The production function for this economy is Y = L, while the representative agent's utility function is U = Iog(Y) + Iog(I-L). a. The simplest way to solve this problem is to maximize the representative agent's utility subject to the economy's production function, i.e., Max U = log Y+ log (I-L) subject to Y = L This can be rewritten as a problem of maximizing the function U = log Y + log (I-lO, by substituting for L from the production function into the utility function. The first order condition for the optimal choice of Y is 8U 1 1 t l —=————=0 => Y =—. aY Y 1 — Y 2 Thus 1/2 units of output are produced in equilibrium. b. Equilibrium employment is obtained from the production function; it is l/2 unit. c. If the labor market is perfectly competitive, the equilibrium real wage paid to workers will be equal to the marginal product of labor. Since the marginal product of labor is always one, the equilibrium real wage (w /P)* is also equal to 11. Hence, if the price level is P=$6, the equilibrium nominal wage is W* = PX (w / P) * =$6. d. If money supply is $20 and the propensity to hold money k = 1, from the quantity equation of money, the price level is P = M / (k Y *) = $40. Problem 16 A class discussion is helpful here. ‘ Recall from Chapter 4, that the labor demand curve is perfectly elastic at the real wage w/ P = 1. Hence the labor supply curve must intersect the labor demand curve at w/ P = 1. 53 Chapter 9: The Demand for Money and the LM Curve Instructor’s Manual Chapter 9: The Demand tor Money and the LM Curve Problem 1 As real balances rise, the marginal utility of money falls. As a result, interest rates must fall in order to encourage the holding of larger levels of real balances, which generates a downward sloping money demand curve. Problem 2 YMAX is the maximum possible income of a household if it chooses to hold all of its wealth in interest-bearing corporate bonds: YMAX — fl + 3L, P P where W/P is the household’s real wealth, w/P is the real wage rate, and L is the amount of labor supplied during a typical week. The price of a bond, PB, enters the variable YMAX through wealth, W, since w = M + PBB. ' Therefore, an increase in the price of bonds will increase the household's wealth, everything else remaining the same, and hence increase YMAX. The household's wealth increases because an increase in price of bonds increases the value of corporate bonds that the household already owns. Therefore, the bond price increase will shifi the budget line to the right, in a parallel fashion. Problem 3 The velocity of circulation is the number of times a year that the average dollar bill circulates in the economy and is measured in fractions of l/years. The propensity to hold money is the fraction of a year’s nominal income held as money and is measured in fractions of a year. For example, if k=1/5 of a year's income, then v=5, which means that the average bill changes 5 times a year. Problem 4 See Box 9.2 in the text. In the data there is a cllose positive relationship between the nominal interest rate and Velocity, just like the utility theory of money demand predicts. This compares favorably to the predictions of the quantity theory, which assumed that velocity was constant and that there should be no relationship between interest rates and velocity. Chapter 9: The Demand for Money and the LM Curve Instructor’s Manual Problem 5 ln the utility theory of money demand, it is the nominal interest rate that determines the level of money demand. The nominal interest rate is the opportunity cost of holding real balances because the nominal interest rate incorporates notjust the lost real return of holding money as opposed to holding bonds but also incorporates inflation that decreases the real value of money holdings. Problem 6 in the classical model, the real interest rate is determined in the capital market, where saving supply and investment demand determine the equilibrium real interest rate. In the new—Keynesian model, it is the nominal interest rate that is matters. The nominal interest rate is the opportunity cost, or price, of holding money and is determined by equating money supply with money demand. Problem 7 In response to an increase in the money supply, nominal interest rates in the money market will fall. This is consistent with the real world behavior of interest rates in response toFederal Reserve policy, which will be discussed more fully in Chapter 10. Problem 8 In the classical model, changes in the money supply have no real effects because of money neutrality. Changes in the money supply only lead to changes in the price level. As a result of an increase in the money supply, the real interest rate remains unchanged but the nominal interest rate should increase as inflation increases. This is not consistent with what happens in the real world, where increases in the money supply lead to decreases in nominal interest rates. This is a big problem with the classical model’s explanation of interest rates. Problem 9 Usually money demand increases during the Christmas season because of the large increase in purchases. This increase in money demand will put upward pressure on nominal interest rates. To offset this, the monetary authority should increase the money supply to keep interest rates at their current level. Problem 10 The LM curve is upward sloping because an increase in output increases money demand, which in turn increases the equilibrium interest rate. See Figure 9.4 in the text. 94 Chapter 9: The Demand for Money and the LM Curve Instructor’s Manual Problem 11 According to the classical model, money neutrality holds and there is no relationship between the level of nominal variables and the level of real variables. As a result, the nominal interest rate has no efl‘ect on real output and the LM curve is a vertical line. In the utility theory of money demand, nominal interest rates do have an effect on the real demand for money balances and as a result money neutrality does not hold and the LM curve is upward sloping. Problem 12 A decrease in the price level increases the real supply of money. This increase in the real money supply reduces nominal interest rates. The LM curve shifts to the right towards lower nominal interest rates for a given level of output. See Figure 9.5 in the text. Problem 13 A proportional increase in both the price level and the money supply leaves the real money supply unchanged. As a result, there is no change in the money market, no change in nominal interest rates, and no change in the LM curve. ' Problem 14 Setting Md/P = MS/P, the LM curve is Y = 500 + 200i. Notice that there is a positive relationship between interest rates and output in the money market. 95 Chapter 9: The Demand for Money and the LM Curve Instructor’s Manual Problem 15 To derive the LM curve, first let us find the demand for money. Instead of obtaining the first-order conditions from the utility maximization exercise, we will make things simpler by setting the slope of the indifference curve (the MRS between M/ P and Y) equal to the slope of the budget line. (3’0 *2. 1 M P _ M D _ _ —~ — Y*=— 72—1: =(16)“Y. 6 P 3U p é’Y T Slope of the indifference Slope of the curve is the Marginal budget line is the Rate of Substitution. rate of interest. Having obtained the money demand function above, set money demand equal to money supply, and fix the price: MD = IllS = A7, P = 1—). Simplify the equation by expressing i as a fimction of Y, the (constant) money supply and the (constant) price level: i=—1—[£j Y‘" 6 P This is the equation of the LM curve. Note that it slopes upward, as it should. 96 ...
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