Economics 876909

4. Suppose there is a decrease in the price level from P to P'. Given the stock of nominal money, M. this leads to an increase in the real money stock, M/P, which shifts the LM curve down. This implies that the AD curve shifts to the right. 5. In terms of changing output, monetary policy is relatively more effective when the AS curve is relatively flat, while fiscal policy is more effective when the AS curve is relatively steep. 6. The neutrality of money means that monetary policy cannot affect output. Part II. Aggregate Demand and Aggregate Supply In the first quiz, you have found that the IS relation is given by Y = Co +b. + G 1-c,(1-1 1-c(1-1) and that the LM relation is given by i = -(mo mz P +m, Y) in the Republic of Keynesia. Let 1-c,(1-1) -= A for simplicity. 1. Derive the expression for aggregate demand using the above equations. Is the AD curve upward- or downward-sloping? 2. Show (mathematically) that output, Y, is an increasing function of the real money stock, M/P, and an increasing function of government spending. G. 3. Let: Co = 200 mo = 400 G =100 CI = 0.5 m =1 1= 0 by = 300 mz =0.8 Y.=550 by = 0.4 M = 200 Derive the AD equation using these figures. (All figures are in millions of US dollars.) 4. Suppose the aggregate supply takes the following form: P = (1.5)P* +(1/50)(Y -Y_ )and P=1. Assume we are in the short-run for now. What is the equilibrium output, Y*? What is the expected price level, P*? Draw the AS-AD diagram. 5. The Keynesian government is up for reelection soon, and so it wants to achieve the natural level of output. (We are still in the short run.) Propose two different policy options that would do the job. For each policy option, draw the IS-LM and the AS-AD diagrams, and show how the first translates into the second. Calculate by how much the government must increase/decrease government spending to achieve the natural level of output. 6. The Keynesian government decides not to listen to you, and raises government spending by more than would be required to achieve the natural level of output. Its argument is that higher output is better. The voters apparently think so too, and the government gets reelected. What happens as time passes and we get to the "medium run"? (You do not have to do any calculations, just draw diagrams and give some intuition.) 7. Suppose the world price of oil increases. Use a diagram to show what will happen in the Republic of Keynesia, starting with the new medium run equilibrium you found in part 6. Part III. The Phillips Curve Suppose the Phillips curve is given by a, = , +0.2-5u, where n' = On,_ 1. What is the natural rate of unemployment in this economy? 2. For now assume that =0. (What does that mean?) Suppose that the government decides to lower unemployment to 3% and keep it there forever. What is the rate of inflation for t=100? Is this realistic? Why? 3. Assume that only for the first three periods (t=1, t=2, and t=3) people form their expectations using 0=0. After the third period, from =4 on, they start using =/ forever. Also, the government still wants to keep unemployment at 3%. What is the rate of inflation for t = 4, 5, and 6? What is the expected rate of inflation for t=4, 5, and 6? Is this setup more realistic? Why?4. Suppose there is a decrease in the price level from P to P'. Given the stock of nominal money, M. this leads to an increase in the real money stock, M/P, which shifts the LM curve down. This implies that the AD curve shifts to the right. 5. In terms of changing output, monetary policy is relatively more effective when the AS curve is relatively flat, while fiscal policy is more effective when the AS curve is relatively steep. 6. The neutrality of money means that monetary policy cannot affect output. Part II. Aggregate Demand and Aggregate Supply In the first quiz, you have found that the IS relation is given by Y = Co +b. + G 1-c,(1-1 1-c(1-1) and that the LM relation is given by i = -(mo mz P +m, Y) in the Republic of Keynesia. Let 1-c,(1-1) -= A for simplicity. 1. Derive the expression for aggregate demand using the above equations. Is the AD curve upward- or downward-sloping? 2. Show (mathematically) that output, Y, is an increasing function of the real money stock, M/P, and an increasing function of government spending. G. 3. Let: Co = 200 mo = 400 G =100 CI = 0.5 m =1 1= 0 by = 300 mz =0.8 Y.=550 by = 0.4 M = 200 Derive the AD equation using these figures. (All figures are in millions of US dollars.) 4. Suppose the aggregate supply takes the following form: P = (1.5)P* +(1/50)(Y -Y_ )and P=1. Assume we are in the short-run for now. What is the equilibrium output, Y*? What is the expected price level, P*? Draw the AS-AD diagram. 5. The Keynesian government is up for reelection soon, and so it wants to achieve the natural level of output. (We are still in the short run.) Propose two different policy options that would do the job. For each policy option, draw the IS-LM and the AS-AD diagrams, and show how the first translates into the second. Calculate by how much the government must increase/decrease government spending to achieve the natural level of output. 6. The Keynesian government decides not to listen to you, and raises government spending by more than would be required to achieve the natural level of output. Its argument is that higher output is better. The voters apparently think so too, and the government gets reelected. What happens as time passes and we get to the "medium run"? (You do not have to do any calculations, just draw diagrams and give some intuition.) 7. Suppose the world price of oil increases. Use a diagram to show what will happen in the Republic of Keynesia, starting with the new medium run equilibrium you found in part 6. Part III. The Phillips Curve Suppose the Phillips curve is given by a, = , +0.2-5u, where n' = On,_ 1. What is the natural rate of unemployment in this economy? 2. For now assume that =0. (What does that mean?) Suppose that the government decides to lower unemployment to 3% and keep it there forever. What is the rate of inflation for t=100? Is this realistic? Why? 3. Assume that only for the first three periods (t=1, t=2, and t=3) people form their expectations using 0=0. After the third period, from =4 on, they start using =/ forever. Also, the government still wants to keep unemployment at 3%. What is the rate of inflation for t = 4, 5, and 6? What is the expected rate of inflation for t=4, 5, and 6? Is this setup more realistic? Why?Part III. Solow Model of Growth Suppose that the production function is given by Y=0.5 VK VN. Assume that the size of the population, the participation rate, and the unemployment rate are all constant. 1. Is this production function characterized by constant returns to scale? Explain. 2. Transform the production function into a relationship between output per worker and capital per worker. 3. Derive the steady state level of capital per worker in terms of the saving rate (s) and the depreciation rate (o ). 4. Derive the equations for steady-state output per worker and steady-state consumption per worker in terms of s and o 5. Let 5 =0.08 and s = 0.16. Calculate the steady-state output per worker, capital per worker, and consumption per worker. 5. Let 6 =0.08 and s = 0.32. Calculate the steady-state output per worker, capital per worker, and consumption per worker. 7. What is the effect of an increase in the saving rate on output per worker over time? Show the transition from so to s, graphically. 8. Explain what happens to the level of output per worker and the growth of output per worker when the saving rate increases from So to $1.Part L. True/False/Uncertain Justify your answer with a short argument. 1. A higher saving rate alone can sustain higher growth of output forever. 2. The golden-rule level of capital tells us that the highest level of consumption in steady-state is achieved when the saving rate is equal to 0. 3. A flexible exchange rate regime is superior to a fixed exchange rate regime. Part II. Open-Economy AS-AD Real exchange rate: EP * P I- rate parity condition: E IS: Y=((Y, T)+ 1(Y.1)+ 0 + NX (Y, Y' 8) LM: M=M (Y.I)P 1. Suppose the economy is al paint A where You YN. II E = E . what happens to Y. NX. P. and cover time? Explain the intuition and also show graphically using IS-LM. AS-AD, and i- parily curves. 2. Now. suppose the central bank wants to intervene to speed up the adjustment process from point A to point C. the medium-run (long-run) equilibrium. What can it do? Explain with words and also show graphically. 3. Now, assume that this economy is where P=P and E= E. What happens to Y, i, and P if the government decreases G in the short-run and medium-run (long-run)? Explain with words and also show graphically.Part III. Expected Present Discounted Values 1. Suppose that the interest rate is 5% today and is expected to stay at 5% for the next three years. Calculate the present discounted value of a security that pays $10,500 in one year, $11,025 in two years, $23,152.5 in three years, and nothing thereafter. 2. Suppose the security in part 1 sells for $38,342.08 today. Would its discount rate need to be smaller or higher than 5%? Answer without computing it first. Then calculate the discount rate. Assume again that the interest rate is expected to remain the same for the next three years. 3. What is the constant payment required to achieve the same present discounted value over three years as in part 2 (i.e. $38,342.08), at the same constant interest rate as you found in part 2? 4. Suppose that the security pays the annual payment you calculated in part 3 forever at the constant interest rate from part 2. Calculate the present discounted value of this security.Part I. True/False/Uncertain Justify your answer with a short argument. 1. In an economy with technological progress, the saving rate is irrelevant in the long-run. 2. The rate of technological progress declined in the mid-1970s due to the rise of the service sector. 3. There is much theoretical and empirical support for the idea that faster productivity growth leads to higher unemployment. 4. Increased globalization and technological progress can both be blamed, at least to some extent, for the increase in wage inequality in the United States. 5. The Fisher hypothesis states that, in the short-run, the nominal interest rate increases one for one with inflation, while the real interest rate remains unchanged. Part II. The Solow Model Revisited The Republic of Solowakia has the following production function: Y = F(K,N) = AK"'N'- , where axl. Let ga be the growth rate of A, gy be the growth rate of N, and o be the rate of depreciation in this economy. 1. Interpret the parameter A. Empirically, what has happened to A over time? 2. Verify that the above production function has the property of constant returns to scale. 3. Verify that the above production function is concave in capital (which means that the second derivative is negative). What does that mean in economics terms? 4. What is effective labor in this economy? 5. At what rate do output and capital grow in Solowakia in the long run? (Hint: use g, for the transformed gA-) 6. Rewrite the production function in terms of only capital per effective worker. 7. Draw the diagram that plots required investment and investment for this economy. Label the steady-state level of capital per effective worker k,*. Label the steady state as point A on the diagram. 8. Suppose the rate of population growths falls. Use a diagram to analyze what happens in Solowakia. Label the new steady state capital per effective worker k,*. Label the new steady state as point B. 9. Starting at the steady state in part 7 (point A), suppose the saving rate increases and the depreciation rate decreases at the same time. Use a diagram to analyze what happens in Solowakia. Label the new steady state capital per effective worker ka*. Label the new steady state as point C. 10. Starting at the steady state in part 7 (point A), suppose a neighboring country gives Solowakia a gift of new capital equipment. Use a diagram to analyze what happens in the long run. Label the new steady state capital per effective worker k,*. Label the new steady state as point D