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UW-Madison ECON 102 - Answers to Homework 4

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Economics 102Summer 2011Answers to Homework #4Due 7/6/11Directions: The homework will be collected in a box before the lecture. Please placeyour name, TA name and section number on top of the homework (legibly). Make sureyou write your name as it appears on your ID so that you can receive the correct grade.Please remember the section number for the section you are registered, because you willneed that number when you submit exams and homework. Late homework will not beaccepted so make plans ahead of time. Please show your work. Good luck!1. Use the loanable funds framework for this problem. Suppose that in an economy net taxes, T – TR, are equal to $500 while government expenditures are equal to $500. Furthermore, suppose you know that this economy is initially a closed economy. You are told that the demand for loanable funds by businesses is given by the equation r = 20 – (1/500)Iwhere r is the interest rate expressed as a percent rather than a decimal and I is investment spending by businesses. You also know that the supply of private savingscurve is given by the equation r = (1/1500)Spwhere Sp is the quantity of private savings. a. Calculate the initial value of government savings, Sg.Answer:Sg = (T – TR) – GSg = 500 – 500 Sg = 0b. Calculate the initial value of capital inflows for this economy.Answer:Since the economy is a closed economy there are no imports and no exports. Hence, X – M = 0 and that implies that capital inflows, KI, are also equal to zero. Recall that KI = M – X and since there are no imports and no exports that implies that KI = 0. c. Calculate the equilibrium interest rate, the equilibrium level of investment spending, and the equilibrium level of private savings given the above information. Answer:I = Sp since Sg = 0 and KI = 020 – (1/500)I = (1/500)SpOr, 1500(20) – 3I = SpRecall that I = Sp in this example So, 1500(20) = 4Sp17500 = Sp = Ir = (1/1500)(7500) = 5 = 5%d. Suppose that at every interest rate private savings increases by $1500. Holding everything else constant, calculate the new equilibrium interest rate, the new equilibrium level of investment spending, and the new equilibrium level of private saving. Answer:r = (1/1500)Sp + b5 = (1/1500)(9000) + b5 = 6 + bb = -1so, r = (1/1500)Sp – 1 is the new private savings equationUse this new private savings equation and the business demand for loanable funds to solve for the new Sp’, I’, and r.Thus, (1/1500)Sp’ – 1 = 20 – (1/500)I’Sp’ – 1500 = 20(1500) – 3I’4Sp’ = 20(1500) + 1500 since Sp’ = I’ when Sg = 0 and KI = 0Sp’ = 7875I’ = 7875r’ = 4.25%e. Suppose that the loanable funds market is described as it was initially (that is, forget the changes described in part (d). Suppose there is no change in imports or exports but government spending increases by $1000 while net taxes increase by $500. Use this information to calculate the equilibrium values of I, Sp, and r. Answer:r = 20 – (1/500)I initially but now there is demand for loanable funds from the government. Initially the equilibrium interest rate was 5% and the equilibrium amount of loanable funds was 7500. Now, at an interest rate of 5%, businesses demand 7500 worth of loanable funds while the government demands an additional 500 of loanable funds. So, you know one point on the new demand for loanable funds curve is (LF, r) = (8000, 5) and you know the the demand curve for loanable funds shifted to the right parallel to the initial demand curve for loanable funds. Thus, r = b – (1/500)LFd where LFd is the demand for loanable funds from both businesses and the government. Substituting the known point into this equation we get:5 = b – (1/500)(8000)b = 21Thus, the new demand for loanable funds curve is given as r = 21 – (1/500)LFd. Use this equation and the supply for loanable funds curve, r = (1/1500)Sp to solve for the new equilibrium values. Recall that in this example Sp = LFd since KI = 0. Thus, 21 – (1/500)LFd = (1/1500)Sp221(1500) – 3LFd = SpBut, LFd = Sp = LFs in equilibrium in this example.4LF = 21(1500)LF = 7875: that is the quantity of loanable funds demanded is equal to the quantity of loanable funds supplied when this quantity is 7875.Use, either equation to find the equilibrium interest rate: r = 21 – (1/500)(7875) = 5.25%. Or, r = (1/1500)(7875) = 5.25%I = Sp + Sg or I = 7875 + (-500) = 7375f. How much investment spending is crowded out by the government deficit in part (e)?Answer:I is initially equal to 7500 and after the deficit described in part (c), I is equal to 7375. The amount of investment crowded out by the deficit is equal to 7500 – 7375 = 125.g. Suppose that the information you were given in part (e) is true except that you now know that imports into this economy equal $500 while exports equal $200. Find the new equilibrium interest rate and quantity of loanable funds given this information. Answer:Now you have Sg = (T – TR) – G = 500 – 1000 = -500KI = M – X = 500 – 200 = 300I = Sp + KI + SgI = 10,000 – 500 r (this is just rewriting the demand for loanable funds curve for private businesses in x-intercept form)Sp = 1500r (this is just rewriting the supply of loanable funds curve from private savings in x-intercept form)KI = 300Sg = -50010,000 – 500r = 1500r + 300 – 50010,200 = 2000rr = 5.1%I – Sg = Quantity of LFOr Sp + KI = Quantity of LFAt r = 5.1%, I = 10,000 – 500(5.1)I = 7450-Sg = 500I – Sg = 7950Sp + KI at r = 5.1%, Sp = 1500(5.1) = 7650KI = 300So, Sp + KI = 7650 + 300 = 79503Thus, I – Sg = Sp + KI when the loanable funds market is in equilibrium.2. Use the simple Keynesian model to answer this set of questions. Assume that this is a closed economy. Assume TR equals zero and that the aggregate price level is constant. You are provided the following information.Y T C I G UnplannedInventory ChangeDirection of Change in Real GDP100 20 98 10 10200 20 158 10 10300 20 10 10400 20 10 10500 20 10 10a. What is the consumption function with respect to aggregate output, Y, for this economy?Answer:C = a + b(Y – (T - TR))C = a + b(Y – 20)b = MPC = (change in consumption)/(change in disposable income) So, Y T – TR Disposable Income C100 20 80 98200 20 180 158Thus, b = C/ Disposable Income = 60/100 = 0.6Δ ΔC = a + 0.6(Y – T)But, we know T = 20 and (Y,C) = (100, 98) or (200, 158)Thus, 98 = a + 0.6(100 – 20)Or a = 50C = 50 + 0.6(Y – 20)C = 38 + 0.6Yb. Fill in the missing values in the above table. Answer:Y T C I G


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UW-Madison ECON 102 - Answers to Homework 4

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