MACROECONOMICS SECTION


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1 MACROECONOMICS SECTION GENERAL TIPS Be sure every graph is carefully labeled and explained. Every answer must include a section that contains a response to WHY the result holds. Good resources include answers to the midterm and problem sets. A few sample answer outlines are included below. 1
2 1. Use the Solow growth model (neoclassical growth model) to derive the equation for the steadystate equilibrium. Assume initially that the growth rate of the labor force (g N ) and the growth rate of technical progress (g A ) both equal to zero. To derive the steadystate equilibrium, begin with the definition: in steady state, the change in capital per worker is equal to zero. The capital stock grows via investment (equal to savings in a closed economy as assumed in the Solow model); the capital stock declines when there is depreciation. The equation for SS is: sy = k, where y = f(k), and k = K/N and y = Y/N. In SS, what is added to the capital stock via investment (savings) matches the decline due to depreciation. a. What are the effects of a decrease in the saving rate on the level of output per worker and the growth rate of output per worker? Support your answer by presenting and referring to equations and/or carefully labeled graphs. Explain all reasoning and all details about the transition from the initial equilibrium to the new equilibrium. A fall in the saving rate means there is a smaller addition to the capital stock per worker at the initial steady state. The capital stock per worker will begin to decline. Since y = f(k), output per worker also falls until a new SS is reached. The new SS will be below the initial one and during the transition, the growth rate in the economy is negative. Once at the new SS, growth in k and y will equal zero (as at the initial SS). You can demonstrate with a graph such as the one on page 228 in Blanchard; shift the investment per worker curve down and then explain the transition to the new (lower) SS. b. Next, assume the both g N and g A are positive, and again analyze the effect of a decrease in the saving rate. Derive the new steadystate condition and draw a new graph of the steadystate condition. Carefully label all elements of the new graph, including the axes. The steadystate condition is where the capital stock per effective worker (k = K/AN) is constant. It can now be written as sy = ( + g N + g A )k. The required investment is needed for three reasons in the expanded model: to replace depreciated capital, to account for population (and labor force) growth and to account for higher quality workers (effective workers). See Figure 122 on page 250 for a diagram of steady state in the expanded model. To analyze the fall in the saving rate, shift the investment curve down, and explain the transition to the new lower steady state level of K/AN. During the transition, growth in K/AN is negative; once we reach the new SS, growth in K/AN is equal to zero (this is the balanced growth path ). Growth in K equals g N + g A in the new steady state (the same rate as in the initial SS) and growth in K/N = g A as shown in table 121 on page 253 in Blanchard. 2
3 c. If there is a rise in g N, what is the impact on the level of output per worker and the growth rate of output per worker? Present a graph showing the effects on the level and on the growth rate. Use Figure 122 in Blanchard to demonstrate the effect of the rise in g N. Rotate the line from the origin upwards to show a steeper slope for the required investment curve. The new SS level of K/AN will be lower (this is a change in the level; the growth rate in K/AN will return to zero in the new SS). The growth rate in K = g N + g A and it will be higher in the new SS since g is higher; the growth rate in K/N = g A and it is unchanged in the new SS. (Refer to Table 121 to see this.) d. The original Solow model was developed in the 1950 s. What accounts for its longevity? From a theoretical perspective, does it have any drawbacks? From an empirical perspective, does it have any drawbacks? If so, discuss them in detail. The longevity of the Solow model can be traced to its relatively simple formulation: it relies on three primary variables (the savings rate, the rate of population growth and the rate of technical change). One of its theoretical drawbacks is that technical change plays a key role in explaining economic growth in the model yet it is treated as exogenous (outside the model). One of its drawbacks from an empirical perspective is there are many nations that have failed to catchup or converge to growth rates found in many developed economies. 1. (A)Use the aggregate demand (AD) and aggregate supply (AS) model to analyze the following events (together): (a) (b) a decrease in the markup rate,, caused by a lower price of energy the reversal of the monetary expansion that has been in place for the past few years. Assume the economy begins at the natural level of output (Y N ). Include a discussion of the underlying relationships by using a graph of the labor market (wage setting and price setting) and the goodsfinancial markets (using the closed economy ISLM graphs). Show the short run equilibrium, the medium run equilibrium and the nature of the adjustment process. A detailed explanation is the most important part of your answer. First, show the impact on the labor market of the fall in the markup rate. In the pricesetting (PS) equation, P = (1+ W.; firms set prices as a markup over their cost of production (which is only the labor cost, W, in this model). Rearrange to show that W/P = 1/(1+ and draw this on the graph. Next, combine it with the wage setting (WS) curve: W = P F(u,z) where u is the unemployment rate (as un rises workers have less bargaining power and 3
4 wages fall at each price level) and z represents other factors that affect bargaining power of workers (such as, an increase in unemployment compensation makes workers less likely to accept a lower wage so equilibrium wages will be higher). See Chapter 6 in Blanchard for a review. Equilibrium in the labor market is at the intersection of PS and WS this determines the natural rate of unemployment. See the graph below. As the markup falls, the real wage rises in equilibrium (at each W, P is lower so W/P is higher) and the natural rate of UN falls. W/P 1/(1+ PS WS UN N UN In the goodsfinancial markets, the LM curve will shift back to the left as monetary contraction occurs. The fall in the money supply (or increase in the interest rate target) is carried out by an open market sale of bonds. 4
5 i LM 1 LM 0 IS Real GDP (Y) In the IS model, we assume the expected inflation rate is equal to zero so that real and nominal interest rates are the same; as nominal interest rates rise, demand for goods and services by consumers and firms declines and Y begins to fall. The fall in Y is one of the intended effects of contractionary monetary policy. Adjustment in the money market: as the money supply falls, there is an excess demand for money and people begin to rebalance their portfolios by selling bonds. Bond prices fall and interest rates begin to rise. This is shown by the shift to the left in the LM curve. Effect on the AD curve: it shifts left as Y falls at each price level. There is only one shift in the AD curve. See section 7.2 for a full discussion and equation for AD Effect on the AS curve: as shown with the labor market graph, the natural rate of unemployment falls so the natural rate of output rises (assuming a fixed labor force). Also, see equation 7.2 on page 137 in Blanchard. 5
6 P AS 0 AD 0 Y N Y N Y SHORT RUN: THE AD CURVE SHIFTS LEFT; AS THE PRICE LEVEL FALLS, P IS LESS THAN P E and workers begin to adjust their expectations lower; the AS shifts right. The net effect in the short run is the price level falls and the impact on Y is ambiguous. MEDIUM RUN: EXPECTED PRICES CONTINUE TO ADJUST DOWN SO THE AS CURVE CONTINUES TO ADJUST TO THE RIGHT UNTIL P = P E AND Y = Y N ; NET EFFECT IS THE PRICE LEVEL FALLS AND Y RISES. (B) How would you advise policymakers to adjust fiscal policy (if at all), given your analysis in part (A)? Explain in detail. Since the effect on Y in the short run is ambiguous, there may not be a need for fiscal policy in the short run if Y actually rises on net. If Y falls in the short run, there may be a need for expansionary fiscal policy. In the medium run, there is no need for fiscal policy since Y will be adjusting to a higher natural rate. However, policymakers may be concerned about an ongoing process of deflation which could be offset by expansionary fiscal policy. 6
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