Consider an economy as described in clas and is frther characterized by C =cY, with e=0.75, T= 0,G=250, NX= 250, and /=1-br, with = 500 and b=5,0. ote tha iwestment depends on the interest rate (). %3D %3D a. Calculate the income equilibrium of the economy b. Assume that, due to heincreasingly esisic expectaions of imestor, automomous investment decreases from 500 to 300. The iteres rate and all ther exogenous variables tay Constant. Calculate the reuling change in equilibrium income. C. At the same time the interest rate decreases from 0.06 to 0.05. Calculate the efect on equilibrium inome.
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- Suppose that firms produce according to the production function Y = AK1/2L1/2, where A = 5 andL = 400. Assume that the prices of capital and output are equal and that the real interest rate, r, isequal to 0.25 and the depreciation rate, δ, is equal to 0.1.1. If firms operate according to the neoclassical theory of investment, what is the optimal levelof capital stock, K (YP) to rich (YR).22. Suppose that the government offers an investment tax credit which changes the relative priceof capital. This results in Pk = 3 and P = 6. What is the new optimal level of capital stock,K??3. Does the investment tax credit have an expansionary impact on the economy? Explain whyor why not.4. Based on the optimal capital stock computed in part (2), what is the level of investmentneeded to sustain this level of capital stock?Assume a set of well-behaved (i.e. strictly monotone and strictly convex) intertemporal indifference curvesbetween period 1 and 2. Then suppose that the nominal interest rate r decreases. Explain what happens to thenew interior solution if current and future consumption are normal and inferior goods, respectively.The neoclassical consumption model, a retirement perspective: Consider thespecial case solved in the text where ! = 1 and utility takes the log form.Suppose the real interest rate is 5 percent. Let’s give this consumer a fnancial profle that might look like that of a middle-aged college professor contem-plating retirement: initial assets are ftoday = $50,000, and the path for labor income is ytoday = $100,000 and yfuture = $10,000.(a) What is the individual’s human wealth? Total wealth?
- We consider a two-periodendowmenteconomy. Suppose you have the following utility function U (c , c ′)=lnc +βlnc ′ where c and c ′ refer to consumption in the first and second periods, respectively, and β =0.5. The household income in the first and second periods is denoted by y and y ′. Assumegovernment collects lump-sum tax in both periods (T, T ′)to finance the public spending inboth periods (G , G ′)and issue bonds B in the first period. A real net interest rate r is 1. 1. Write down the household’s problem. Does the household perfectly smooth their con-sumption over lifetime? Show it using the optimality condition. 2. Solve for optimal c , c ′ and s (saving) when y −T > y ′−T ′. 3. Given the conditions in part (2), there is an increase in future income y ′ such that y −T =y ′−T ′. Find new optimal c , c ′ and s . Explain how c , c ′ and s change compared to part(2). 4. Focusing on part (3),(a) Suppose that the government increases T by a small amount and decreases T ′ bythe…What is meant by “excess sensitivity” of consumption? Is this view of consumption consistent with the permanent-income hypothesis? Explain. How does the stock market affect consumption according to the permanent-income hypothesis? Is this prediction in line with the empirical evidence? Explain.Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…
- Consider an economy called Xanadu for which desired aggregate consumptiondepends on income, Y. and the real interest rate, r, according toCd =100+0.7Y - 200r.Xanadu's GDP is Y = 1000 and government spending on goods and services is G=180. Xanadu's desired future capital stock is given byK* = 140 - 100ucwhere luCdenotes the user-cost of capital. The price of capital is PK =2, thephysical depreciation rate is d =0.1 and the existing capital stock is K0= 50. Trapital stock between any period t and the following period t+1 evolves accordng toKt+1 = It+(1-d)Kt where It the level of investment. Assume throughout that net factor payments from abroad (NFP) is equal to zero.Suppose instead that Xanadu is a small open economy facing a world interest rate of 1%. It follows that Xanadu's current account position is equal toA) -16B) -51C) -6D) -8Let the equilibrium condition for national income be ?(?) + ?(?) = ?(?) + ? (? ′ , ? ′ ,? ′ > 0; ? ′ + ? ′ > ? ′ ) Where S, Y, T, I and G stand for saving, national income, taxes, investment and government expenditure respectively. All derivatives are continuous a. Interpret the economic meaning of the derivatives ? ′ , ? ′&? ′ b. Check whether the conditions for the implicit function theorem are satisfied. If so, write the equilibrium identity c. Find ??̅ ?? and discuss its economic implications(A) Derive the equation for the IS curve and LM curve. (B) Compute the equilibirum levels of income, Y and interest rates.
- Looking at business fixed investment, elaborate on why investment is negatively related to theinterest rates.b. Using the Tobin’s q theory, elaborate on the relationship between investment and capitalstock?c. If the market value of firm A is $1.5 million and the replacement cost of capital is $450,000, find the Tobin's q.d. Should the firm replace capital? Elaborate on your response.a) Draw a consumption function and label the axes.b) Suppose that your friend has a consumption function of the form y=1.4x+200. Is this function sustainable in the long run? Why or why not?c) Suppose that your consumption function is y=0.75+1000. What is your marginal propensity to consume? What is your autonomous expenditure?d) State the permanent income hypothesis.e) Suppose that I raise your income today by $10, and lower it tomorrow by $10. How would your behavior change according to the consumption function (aka Keynesian, aka rule-of-thumb) model? And what about according to the permanent income hypothesis model?Consider the market for loanable funds. Suppose the demand for loans is given be i=9-Q+π, and the supply of loans is given by i=Q/2+π, where π represents inflation. Now suppose that π=5 (instead of 3, in the previous problem). What is the equilbrium quantity of loans and what is the corresponsing interest rate? Q*=8, i*=6 Q*=3, i*=6 Q*=6, i*=8 Q*=6, i*=6