(22 marks) Suppose that the marginal product of labour is MPN = 4.5K N , the capital stock is
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25 and labour supply is NS = 100[(1 – t)w] , where w is the relwage rate, t is the tax rate on labour
income and (1 – t)w is the after-tax real wage rate. To begin, assume that the tax rate on labour income is zero.
a. (2 marks) Write down the equation for labour demand, ND, as a function of w.
b. (2 marks) Calculate the equilibrium real wage rate.
c. (2 marks) Calculate the equilibrium level of employment.
d. (2 marks) Calculate the total after-tax wage income of all workers.
Now assume that the tax rate on labour income is increased to 0.6. e. (2 marks) Calculate the new equilibrium real wage rate.
f. (2 marks) Calculate the equilibrium level of employment.
g. (2 marks) Calculate the total after-tax wage income of all workers.
h. (2 marks) Briefly explain why employment and income fell by more than 60 percent in the presence of a 60-percent tax rate on labour income.
Now assume that the tax rate on labour income is eliminated and a minimum real wage of 2 is introduced instead.
i. (2 marks) Calculate the level of employment.
j. (2 marks) Calculate the total after-tax wage income of all workers.
k. (2 marks) Briefly explain whether the minimum wage increases the total income of all workers.
ff 2. (18 marks) Suppose that the expected future marginal product of capital is MPK = 20 – 0.02K ,
where Kf is the future capital stock. The depreciation rate of capital, d, is 20 percent, the current capital stock is 900 units and the price per unit of capital is 1. Firms pay taxes equal to 50 percent of their output, government purchases are 200 units, full-employment output is 1000 units and the consumption function is C = 100 + 0.5Y – 200r, where C is consumption in units, Y is output and r is the real interest rate. To begin, assume that the real interest rate is 10 percent.
a. (2 marks) Calculate the tax-adjusted user cost of capital.
b. (2 marks) Calculate the desired future capital stock.
c. (2 marks) Calculate the desired level of investment.
Now assume that the real interest rate is determined by equilibrium in the goods market.
d. (2 marks) Write down the equation for the tax-adjusted user cost of capital as a function of r.
e. (2 marks) Write down the equation for the desired future capital stock as a function of r.
f. (2 marks) Write down the equation for the desired level of investment as a function of r.
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g. (2 marks) Use part (f) along with the information provided about consumption and government purchases to calculate the equilibrium real interest rate.
h. (2 marks) Calculate the equilibrium levels of consumption, saving and investment.
i. (2 marks) Calculate the equilibrium tax-adjusted user cost of capital and desired capital stock.
3. (12 marks) Consider two large open economies (Home and Foreign). In Home, Cd = 320 + 0.4(Y – wdw!
300r , ! = 225 – 300r , YF = 1500, TF = 300 and GF = 300.
a. (2 marks) Calculate the equilibrium world real interest rate, r .
T) – 200r , I = 150 – 200r , Y = 1000, T = 200 and G = 275. In Foreign, ! = 480 + 0.4(YF – TF) – w!w
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w
b. (2 marks) Calculate the levels of consumption, national saving, investment and the current account balance in Home at the equilibrium world real interest rate.
c. (2 marks) Calculate the levels of consumption, national saving, investment and the current account balance in Foreign at the equilibrium world real interest rate.
d. (2 marks) If the Home government were to increase its spending by 50 and finance it fully by increasing taxes by 50, calculate the new equilibrium world real interest rate.
e. (2 marks) Calculate the new levels of consumption, national saving, investment and the current account balance in Home at the new equilibrium world real interest rate.
f. (2 marks) Calculate the new levels of consumption, national saving, investment and the current account balance in Foreign at the new equilibrium world real interest rate.
4. (10 marks) The population and workforce both grow by n = 1 percent per year in a closed economy. Consumption is C = 0.5(1 – t)Y, where t is the tax rate on income and Y is total output. The per-
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worker production function is y = 8k , where y is output per worker and k is the capital-labour ratio
and the depreciation rate on capital, d, is 9 percent. The government runs a balanced budget each year where its spending per worker is equal to the tax rate on income times output per worker. To begin, assume that there are no government purchases and the tax rate on income is zero.
a. (2 marks) Write down the equation for national saving per worker as a function of the capital- labour ratio.
b. (2 marks) Write down the equation for the steady-state level of investment per worker, i, as a function of the capital-labour ratio.
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