Suppose The Real Money Demand Function Is Where Y Is The

Suppose That The Real Money Demand Function Iswhere Y Is The Real O

Suppose that the real money demand function is where Y is the real output, r is the real interest rate, and is the expected inflation rate. Real output is constant over time at Y=150. The real interest rate is fixed in the goods market at r=5% per year. A) Suppose that the nominal money supply is growing at the rate of 10% per year and this growth rate is expected to persist forever. Currently, the nominal money supply is M=300. What are the values of the real money supply and the current price level? (Hint: For finding the expected inflation rate, use the equation which relates inflation rate to the growth rate of nominal money supply and the growth rate of output. Suppose people are rational and realize this relationship when they form their expectations.) B) Now, suppose the real output is not constant over time, and that the real output is growing at the annual rate of 4% and this growth rate is expected to persist forever. As in part (A), M=300 and the nominal money supply is growing (and expected to be growing) at the rate of 10% per year. Moreover, the income elasticity of money demand equals 2/3. What are the values of the real money supply and the current price level? Compare your result to part (A) and provide your intuition. C) Suppose that the money supply is M=300 and output is constant. The central bank announces that from now on the nominal money supply will grow at the rate of 5% per year. If everyone believes this announcement, and if all markets are in equilibrium, what are the values of the real money supply and the current price level? Compare your result to part (A). Explain the effects on the real money supply and the current price level of a slowdown in the rate of money growth. 2. How does each of the following factors affect the LM curve? Start your argument from the diagram of MD-MS and show how the associated change will affect LM curve. - An increase in nominal money supply. - An increase in the risk of non-monetary assets relative to the risk of holding money. 3. How does each of the following factors affect the IS curve? Start your argument from the diagram of I d -S d and show how the associated change will affect IS curve. - An increase in government purchases (when it does not affect the productivity). - An increase in marginal productivity of capital. 4) The production function in an economy is Y = A(5N-0.0025N^2), where A is productivity. Accordingly the marginal product of labor is MPN = 5A-0.005AN. Also, let A=2. The labor supply curve is N s =55+10(1-t)w, where N s is the amount of labor supplied, w is the real wage, and t is the tax rate on wage income, which equals 0.50. Desired consumption and investment are: C d = 300+0.8(Y-T)-200r; I d = 258.5-250r. Taxes and government purchases are: T=20+0.5Y; G=50. Money demand is M d /P = 0.5Y-250(r+ ). The expected rate of inflation is 0.02, and the nominal money supply M is 9150. A) Find the general equilibrium levels of the real wage, employment, and output. B) Find IS and LM. Then find the general equilibrium level of price, real rate of interest, consumption, and investment. C) Suppose that the government purchases increase to G=72.5. What are the general equilibrium values of real wage, employment, output, real interest rate, consumption, investment, and price level?

Paper For Above instruction

The assignment encompasses multiple core macroeconomic concepts, focusing initially on the analysis of money demand, inflation expectations, and their influence on the price level and real money balances, progressing toward effects on the LM curve, and extending into general equilibrium analysis involving the IS-LM model incorporating production functions, labor market, and fiscal policy changes.

Part 1: Money Demand and Inflation Dynamics

The crux of the first part pertains to understanding how money demand interacts with nominal money supply growth and how expectations about inflation influence the real money balances and price levels. When the real money demand function is held constant, with a given output level and fixed interest rate, the growth of the money supply directly influences the expected inflation rate. The classic equation tying the growth rate of the nominal money supply (μ), the growth rate of output (g_Y), and the inflation rate (π^e) is expressed as: π^e ≈ μ - g_Y, assuming rational expectations and perfect foresight.

In part (A), with a static output (Y=150), a fixed interest rate (r=5%), and a money supply M=300 growing at 10%, the expected inflation rate (π^e) is roughly 10% - 0% = 10%. The real money supply (M/P) can be computed once the price level P is found. The classic money demand function (not explicitly specified here but generally given as M^d/P = L(Y, r, π^e)) suggests that the real money demand is proportional to real output and depends inversely on interest rates and expected inflation. Under the assumption of equilibrium (money demand equals money supply), we solve for P, then derive the real money supply as M/P.

In part (B), with growing output at 4% annually, the inflation rate adjusts accordingly, based on the money supply growth. The income elasticity of money demand being 2/3 indicates a less than proportional response of demand to income growth. It implies that the changes in the real money demand are affected by both income growth and interest rate adjustments, which influence the price level. The faster-growing output relative to the money supply growth exerts downward pressure on inflation, potentially increasing the real money balances. The comparison with part (A) shows how output growth impacts the inflation rate and real balances, illustrating the importance of expectations and elasticity of demand.

Part (C) considers a slowdown in the growth rate of the money supply from 10% to 5%, assuming constant output. The anticipated decrease in inflation pressure leads to a lower inflation rate, increasing the real money balances and reducing the price level. This results in higher real balances and a salutary effect on the economy's price stability, demonstrating how monetary policy (slowing growth) influences price levels and money demand.

Part 2: Effects on the LM curve

The LM curve reflects equilibrium in the money market, where money demand equals money supply. An increase in the nominal money supply shifts the LM curve rightward because, at any given interest rate, the higher supply increases real balances, facilitating increased spending and investment. Conversely, an increase in the risk of non-monetary assets reduces their attractiveness relative to money, leading to increased demand for money, shifting the LM curve rightward as well, since the higher demand balances with the given money supply at lower interest rates.

Part 3: Factors affecting the IS curve

The IS curve illustrates equilibrium in the goods market, balancing investment and saving. An increase in government purchases (\(G\)) when productivity is unaffected raises aggregate demand, shifting the IS curve to the right, indicating higher output at every interest rate. An increase in the marginal productivity of capital enhances the profitability of investments, which also shifts the IS curve rightward, reflecting increased investment demand at any given interest rate, resulting in higher equilibrium output.

Part 4: General Equilibrium with Production, Labor, and Fiscal Policy

The production function \(Y = A(5N - 0.0025N^2)\) exhibits diminishing returns with increasing labor input. The marginal product of labor (MPN) illustrates this, decreasing as N rises, dependent on productivity A=2. The labor supply curve \(N_s = 55 + 10(1 - t)w\), with t=0.50, indicates how wages influence labor supply, factoring in taxation. Desired consumption and investment are functions of income and interest rates, and taxes directly affect disposable income, influencing consumption behavior. Money demand depends on income and interest rate, with an expected inflation rate of 2% and a money supply of 9150.

Solving for the general equilibrium involves setting money demand equal to money supply for the goods and money markets, then finding equilibrium wages, employment, and output. This requires simultaneously solving the labor market, goods market, and money market equations, considering the fiscal parameters and the production function. The interdependence of these variables dictates the equilibrium levels of real wages, employment, and output.

When government purchases increase to G=72.5, the fiscal expansion shifts demand outward, leading to higher output, wages, and employment. The increased government spending fosters economic activity, raising the equilibrium price level and real interest rate through enhanced demand pressures. The analysis exemplifies the interconnectedness of fiscal policy, monetary variables, and productive capacity within the macroeconomic framework.

Conclusion

The comprehensive analysis demonstrates how money supply dynamics, expectations, fiscal policy, and production functions shape the macroeconomic environment. Monetary policy speed and direction influence inflation and the real money supply, which in turn affect the LM curve and the overall equilibrium. Fiscal policy changes impact the IS curve, affecting output and employment levels. The incorporation of production functions and labor supply behaviors determined by taxation further refines the understanding of macroeconomic equilibrium variables, highlighting the multifaceted nature of economic analysis.

References

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