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- . Consider the macroeconomic model of a two-sector economy (i.e. no government or trade) using standard notation. Assume that the consumption function is linear, i.e. of the form: C = a +bY . It is known that when ? = 110, the value of consumption, C , is equal to 160.8, and that when ? = 170, the value of C is 207.6. (a) Determine the consumption function and derive the savings ( S ) function for the model. What is the marginal propensity to consume? (b) Determine the equilibrium level of national income when planned investment ? = 255.Consider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Assume that in this economy consumption (C) is given by the equation C = 600 + 0.6(Y – T). Investment (I) is given by the equation I = 2,000 – 100r, where r is the real rate of interest in percent. Taxes (T) are 500 and government spending (G) is also 500. (Hint: use the GDP obtained in part a). What are the equilibrium values of C, I, and r? What are the values of private saving, public saving, and national saving?a. List all the equilibrium conditions of this model and Using the equilibrium conditions listed, write down an expression that describes the evolution of the aggregate capital stock, Kt over time. Briefly explain why this expression is not particularly convenient for our analysis of the model? b.Using your answer to the above question, derive the equation that describes the evo- lution of the the capital stock per effective unit of worker, kt. ' Why is the analysis in terms of the variables per effective unit of worker more useful than the one with the aggregate capital stock? c. Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label…
- Piketty (2014) argues that a fall in the growth rate of the economy is likely to lead to an increase in the difference between the real interest rate and the growth rate. This problem asks you to investigate this issue in the context of the Ramsey Cass Koopmans model. Specifically, consider a Ramsey Cass Koopmans economy that is on its balanced growth path, and suppose there is a permanent fall in g. (a) How, if at all, does this affect the k = 0 curve? (b) How, if at all, does this affect the c = 0 curve? (c) At the time of the change, does c rise, fall, or stay the same, or is it not possible to tell? (d) At the time of the change, does r - g rise, fall, or stay the same, or is it not possible to tell?Suppose that we have an economy whose production can be represented by a Cobb Douglas production function with parameter α=0.3. You may assume that there is no depreciation (i.e. δ=0). a. What fractions of income do capital and labor receive? b. For the following parts, describe what happens to output (in percent), the rental price of capital and the real wage from: i) Suppose that immigration increases the labor force by 10 percent. ii) Suppose that a gift of capital from abroad raises the capital stock by 10 percent. iii) Suppose that a technological advancement raises the value of the parameter A by 10 percent. Type out the correct answer ASAP with proper explanationQuestion: Consider the IS-LM model derived. Suppose the economy of Economica is initially at the general equilibrium. Suppose further that the government considers the increase of the effective tax rate on capital and hires you as a consultant. a. Explain and show graphically how an increase in the effective tax rate on capital would affect the labor, goods, or the asset market. b. Explain and show graphically how an increase in the effective tax rate on capital would affect the short-run equilibrium. c. Explain and show graphically how an increase in the effective tax rate on capital would affect the long-run equilibrium.
- The graphs below depict the initial market for labor (on the left) and the macroeconomic production function (on the right). You will use these graphs to identify the effect of an increase in the number of available workers on employment, Potential GDP, and per-worker productivity. Suppose that a substantial increase in labor force participation increases the supply of labor by 40,000 workers at every value of the real wage. (1) Identify the effect of this event on equilibrium employment in the market for labor, and identify the specific new equilibrium level of employment. (2) Identify the effect of this event on Potential GDP, and identify the specific new level of Potential GDP. (3) Finally, identify the effect of this event on per-worker productivity, and identify the specific new level of per-worker productivity. You should embed a graph that clearly depicts (1) the correct supply shift in the market for labor, (2) the new equilibrium real wage, and (3) the new equilibrium…Consider the intertemporal model of consumption studied in class, with two possible periods. Consider initially that an individual is a borrower. If the interest rate increases: (a)The individual will never become a saver. (b)The individual will always remain a borrower. (c)The individual will be worse off, provided she remains a borrower. (d)The individual can be better off, but only if she becomes a saver. Both c and d.Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, whereK is capital, L is the labor force, and u is the natural rate of unemployment. The national savingrate is s, the labor force grows at rate n, and capital depreciates at rate d.a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and thenatural rate of unemployment (u).b. Write an equation that describes the steady state of this economy. Find the steady state capitalper worker and steady state output per worker.c. Does this production function have constant returns to scale? Explain.
- Suppose a country has a production function Y=2K0.5L0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 400 units of capital and 625 units of labor. Find numerical answers to the following. Be sure to show your work. What is the real wage and the real rental price of capital? (Hint: Assume the firms are maximizing profit.) Suppose there is a natural disaster and half of the capital is destroyed. What is the new level of output? What is the new real wage and real rental price of capital? How much output does the economy produce? Please answer all part I will rateBriefly explain how one or more of the microeconomic components, namely consumption,investment, supply and demand for money influence macroeconomic outcomes and formulations of the following macroeconomic theories:a. Solow Growth Model b. The Mundell-Fleming model c. Neoclassical Model of Investment Use mathematical equations and graphs where necessary.Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate d. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u). Write an equation that describes the steady state of this Find the steady state capital per worker and steady state output per worker. Does this production function have constant returns to scale?