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Macroeconomic Theory M. Finkler Suggested Answers to Spring 2007 Midterm Exam #1 1. W/P = d0 – d1*L + d2*K + d3*RM (1) Endogenous Ls = so + s1*(W/P)-s2*T (2) Variables L = Ls (3) W, P, L, Ls, Y, Y = 100*L^.75*K^.25 (4) AD, C, I AD = k*M/P (5) AD = C + I + G (6) C = .75*Y (7) Y = AD (8) a. To determine W/P plug (3) into (2) and then (2) into (1) W/P = d0 – d1*(so +s1*(W/P)-s2*T) + d2*K + d3*RM Exogenous Variables T, K, RM, G Distribute d1 across the terms and move the term with W/P to the left hand side. W/P + d1* s1*(W/P) = d0 –d1*s0 +d1*s2*T + d2*K + d3*RM thus, (A) W/P = d0 –d1*s0 +d1*s2*T + d2*K + d3*RM - equilibrium real wage 1 + d1*s1 The easiest way to determine L is to plug (3) into (2) and then (1) into (2) and solve for L (B) L = s0 + s1*d0 + s1*d2*K + s1*d3*RM -s2*T – equilibrium labor 1 + d1*s1 b. To obtain the AS curve, plug the equilibrium quantity of labor into (4) Y = 100*( s0 + s1*d0 +s1* d2*K + s1*d3*RM -s2*T).75*K.25 1 + d1*s1 This is the aggregate supply curve. It contains no price term and, thus, is vertical. c. Since there are no endogenous variables on the right side of C, that equation is also the reduced form equation for Y. (C) d. An increase in taxes would shift the labor supply curve toward the real wage axis, so real wages would rise and employment would fall. In equation A, the coefficient on taxes is positive, hence increases in taxes yield increases in W/P. In equation B, the negative sign on T means that an increase in T leads to a fall in L. The same result holds for equation C, so both Y and L would fall. Using equations 5 and 8, Y = k*M/P; since Y decreases (from C) and k and M are unchanged, P must rise. This result is consistent with a leftward shift in the AS curve. e. A decrease in (oil) raw materials decreases the demand for labor and thus the real wage and employment. The coefficients on RM in equations B and C are positive; thus, employment and output wound fall. Using equations 5 and 8, as in part d, P must rise. 2. a. Laspeyres index of output Pold*Qold = 10,000*100 + 20*10,000 + 25*5,000 = 1,325,000 - an index of 100 Pold*Qnew = 10,000*110 + 20*20,000 + 25*6,000 = 1,650,000 – an index of 124.5 Growth in output = (1650-1325)/1325 = .245 or 24.5% b. Paasche index of output Pnew*Qold = 14,000*100 + 12*10,000 + 50*5,000 =1,770,000 – an index of 100 Pnew*Qnew = 14,000*110 + 12*20,000 + 50*6,000 = 2,080,000 – an index of 117.5 Growth in output = (2080-1770)/1770 = .175 or 17.5% c. 3. chain index of output SquareRoot [1.175*1.245] - 1 = .209 so growth in output = 20.9% Based on the data in the table, the results would be as follows: Unemployment Rate = 100*(CLF – Employment)/ CLF = (2892-2782)/2892*100=3.8% Employment Rate = 100 – Unemployment Rate = 96.2% Employment Ratio = 100*Employment/ Civilian non-institutional Pop = 100*(2782/3510) = 79.3% Labor Force Participation Rate = 100*CLF/ Civilian non-institutional Pop = 100*2892/ 3510) = 82.4% Severity Index = 5*Unemployment Rate*Mean Duration = 5*(.038)*14.9 = 2.83 Days 4a. From Y = C + I + G + eX –Im , we can determine that eX = 4500 -2500-1000 -1000 + 450 = 450 Since I + G + eX = S + T + iM, we can determine that S = 1000 + 1000 + 450 -800 – 450 = 1200 The Trade Balance = eX – iM = 450 – 450 = 0; thus, there are no capital inflows or outflows. The excess of savings over investment (200) funds the excess of governmental spending over taxation. b. Expansionary fiscal policy would need to be funded either by a reduction in investment, a reduction in consumption, or a decrease in exports. 5a. Increase in payroll employment reflects the ability of firms to absorb growth in the labor force. Since the labor force grows by roughly 1% per year (See Econ Report of the President and class discussion), we need to add about 1% to payrolls each year. Given that payroll employment is around 146 million people, we need to add 1.46 million per year or roughly 122 thousand per month. 188 thousand is, thus, a very positive sign. An unemployment rate of 4.4% lies below the unemployment rates we have seen in recent years. Estimates of full employment or the natural rate (5.5%) as posited by Mankiw in Chapter 6 suggest that 4.4% is below relevant benchmarks. This implies that such a low rate is not sustainable. If the NAIRU (non-accelerating inflation rate of unemployment) notion is 5% or higher, 4.4% might suggest rising inflation is on the horizon. Consequently, this news cannot be viewed as uniformly positive. b. Payroll employment may not be an accurate indicator because it double counts people who exist on two payrolls and does not count self-employed or many who work for very small firms. The published unemployment rate (U3) captures those in the labor force and available and ready to work. It can be influenced by temporary jobs, movement into and out of the labor force, the benefits available to those unemployed, and the reservation wage. 6a. In the Neo-Classical Model, the only reason to hold money is to purchase goods and services. Such a desire to purchase is based on income that people have. Since income is determined on the supply side and since aggregate demand only influences the price level, changes in the stock of money have no influence on real variables including GDP, real wages, employment, investment, and consumption. b. Each measure of money conveys something different about the level of liquidity in the economy. The narrowest measure, M0 - currency plus reserves, provides some indication of what the central bank has direct control over. A broad measure, such as M2 which includes currency, demand deposits and a variety of other depository accounts, reflects assets that people can cash reasonably quickly and thus use for current purchasing. Furthermore, the velocity of M2 with respect to nominal GDP seems untrended which means that it has some desirable stability characteristics. 7a. One can calculate GDP by a) determining what it would cost to purchase all goods that were produced for final sale, b) determining the incomes paid to all factors of production plus depreciation allowances and indirect business taxes, or c) by adding together the value added at each stage in the production process. The first two are equivalent since they count opposite sides of the same transaction. For every transaction there would be both income and expenditure representation: double – entry bookkeeping. The value added approach looks at all stages of production rather than just goods produced for final sale. But, the sum of the values added for a given item equals its final sales value without double counting; thus, total expenditures on goods for final sale is equivalent to the sum of all values added. b. GDP does a better job of measuring economic welfare in advanced industrialized countries than it does in less developed economies because more goods flow through markets. To the degree goods are not recorded in the market place, GDP will undercount economy activity and, thus, economic welfare. An economy that only features barter will not show any recorded market activity. Additionally, some items add to economic welfare – for example, less pollution - but are not recorded as part of GDP. In contrast, the generation and clean-up of pollution both add to GDP, but the net addition to economic welfare would be zero. Protective expenditures (police and fire) have similar characteristics. Purchasing power parity (PPP) refers to the idea that traded goods should sell for the same price in all countries; thus, the exchange rate between any pair of currencies should adjust to ensure that this “law of one price” holds. Since the cost of living in relatively poor countries would be lower than would exist in relatively wealthy countries, PPP calculations would raise the calculated GDP in terms of a common exchange rate (such as the dollar and, thus, would more accurately represent material well-being than calculations based on market exchange rates alone.