Solve all of the following
Consider the standard Solow growth model. Let productiv'rty be denoted lay A and let the production function be Y=A F{K,N]. For Simplicity, assume that there is no population growth [n={l so that N' = N}. let depreciation be denoted by d and the savings rate by s. a] Derive the per capita capital accumulation equation for k: K! N and the steady state level of capital per worker, ??\"ss . Please show the details of your derivation to earn points. Draw the Solow model graph showing the savings line and the depreciation line and marking the steady state level of k. b] Now, consider the \"AK model\" with production function '9? = 'E'??? , where A is the exogenous productivity level. Again, assume that there is no population growth in the economy. Follow the similar steps in part a. to derive the capital accumulation equation in terms of capital per capita ??. c} Ea sed on the equations you derived in part b, draw a graph similar to that of the Solow growth model to show the steady state of the model in part b. If you cannot nd such a steady state, please explain why. d} . Recall that Solow growth model implies convergence in capital per capita. Does the model in part b has this feature? Exercise 7.1 Suppose a government is established in a country where none previously existed. The government spends 100, financed by borrowing, to provide public services. If autonomous expen- diture before government is set up is 200 and induced expenditure is 0.6) (based on mpc = 0.75 and mpm = 0.15) what is the equilibrium value of real GDP before the government is established and what would equilibrium GDP be after government is established? Exercise 7.2 If the government expenditure in Exercise 7.1 were financed by imposing a net tax rate on income of f = 0.10: (a) Calculate and compare the slopes of the AE functions in Exercises 7.1 and 7.2. (b) Calculate and compare the multipliers in Exercises 7.1 and 7.2. (c) What is the equilibrium real GDP in Exercise 7.2 compared to Exercise 7.1? Exercise 7.3 If government expenditure is 100 and the net tax rate is t = 0.20: (a) Complete the following table: Y NT = tY G BB = NT -G 100 200 300 400 500 600 700 (b) In a diagram with national income Y on the horizontal axis and government revenue and expenditure on the vertical axis, draw the government expenditure and net tax functions. Explain the intercept on the vertical axis, and the slope you have given to the NT and G functions in your diagram. (c) Suppose the government cuts the tax rate to * = 0.15. Show the effects in your diagram. Exercise 7.4 Using diagrams illustrate an initial equilibrium national income, the effect of the increase in government expenditure on that equilibrium national income, and the government's budget functions and balances before and after the increase in government expenditure. 180 The government sector Exercise 7.5 Suppose the government raises its revenue by a net tax of 25 percent on income, 1 = 0.25. Further suppose that induced expenditure is 0.45Y (based on c = 0.8, f = 0.25 and m = 0.15). (a) What is the slope of the AE function? What is the size of the multiplier? (b) Autonomous expenditure by the non-government sectors (An) is 300 and government expen- diture is 400. What is the equilibrium income and output? What is the government's budget balance? (c) Now assume the government increases its expenditures by 100 to provide additional funding for national defense. What is the effect on equilibrium income and output? What is the effect on the government's budget balance? Exercise 7.6 An economy is in equilibrium at a real GDP of 750, but current estimates put potential output at Yp = 850. (a) Is there an inflationary or a recessionary gap, and, if there is either, what is its size? (b) Research suggests that induced expenditure is 0.5Y (based on c = 0.75, m = 0.10, and f = 0.20). If there is a gap, what change in government expenditure would eliminate the gap? (c) If the government preferred to change its net tax rate to eliminate the gap, and not change government expenditure, what new tax rate would be required to eliminate the gap?Exercise '1? (a) Draw a diagram that shows the government's budget balance relative to national income. Explain briey the vertical intercept of the budget inclicn and its slope. {b} Using your diagram from {a}, show the structural budget balance and a situation in which the actual balance is different from the structural balance. {c} Based on this diagram, show and explain the difference between the budget effects of auto- matic stabilization and discretionary scal policy. Exercise 13 Suppose m in Exercise 15 the government raises its revenue by a net tax of25 percent on income, 3' = I125. Further suppose that induced expenditure is {1451' {bamd on r.' = {18, r = [125 and m = [115}, autonomous private expenditure is 3m and government expenditure is me. {a} What is the government's budget balance? {b} If the government has outstanding public debt equal to see what is the public debt to GDP ratio? (c) Suppose the governmentinereases itsexpenditure by lll without any increase in the tax rate. What are the new equilibrium GDP and the new budget balance? Explain why the change in the government's budget balance is different titan the change in government expenditure. Exercises for Chapter 1' I 131 {d} What is the outstanding public debt and the public debt ratio in the new equilibrium. assum- ing the economy has reached its new equilibrium national income in one year? ExemkeiLl Ifthecurrent market interest rate is 3 peroentand abond promises acouponof$3 each year in perpetuity {forever}, what is the current market price of the bond? Suppose you were holding such a bond and current market interest rates fell from 3 percent to 2.5 percent. Would you be pleased or disappointed by the returnon your bond holding? Why? Exemke 9.2 Suppose you are holding a bond that will pay $5 each year for the next two years from today and mature two years from today. {a} Ii'current two-year market interest rates are 5 percent, what is the market price of your bond? {b} If market interest rates rise tomorrow to IE percent, what happens to the market price of your bond? {c} What is the \"market risk\" in holding bonds? Exercise 93 Draw a diagram to illustrate the relationship between the demand for real money balances [L], GDP [1'] and the interest rate [1'], L = H" Iii, when real GDP has a given value ii}. {:1} Explain your choice of the intersection of your demand for money function with the hori- zontal axis, and your choice of the slope of the inction. {b} Using your diagram. illustrate and explain the quantity of real money balances demanded for a specic interest rate, say in. Pay particular attention to the underlying motives for holding these money balances. {c} Suppose interest rates declined from your initial assumption of in to a new lower rate 11. Illustrate and explain the effect of the change in interest rates on the demand for money balances. {d} Holding interest rates constant at either in or i., suppose real GDP were to increase. Illustrate and explain the effect of the increase in real GDP on the demand function and the quantity of real money balances people hold. Exemke 9.4 Today it costs $1.25Cdn to buy SIUS. Suppose tomorrow US interest rates rise. What would happen to the foreign exchange rate between Canadian and US dollars? Explain why. Exemke 9.5 {:1} Draw a diagram to illustrate equilibrium in the money market. {b} Starting from your initial equilibrium, suppose real national income [1'] increased. Illustrate and explain how the money market would adjust to this change in economic conditions. {c} How does the interest rate in the new equilibrium compare with the interest rate in the initial equilibrium? Exercises for Chapter 9 I 13'? Exemke Elli Construct a set of diagrams that shows the monetary transmission mechanism linking interest rates to aggregate demand and output. Using these diagrams, show and explain: {a} How a reduction in the money supply would affect aggregate demand and output. {b} Alternatively, how an increase in the precautionary demand for money balances caused by terrorist activity, or severe weather events, or an increase in uncertainty in general would affect aggregate demand and output. Assume the money supply is held constant. {c} Alternatively, how would an increase in autonomous investment expenditure and exports affect aggregate demand, output, and interest rates
