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# homework4fall2007answers - Economics 102 Fall 2007 Homework...

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Economics 102 Fall 2007 Homework 4 Answer Key 1. You are given the following information about aggregate expenditures and output as well as the table below describing investment and savings behavior for a small open economy with a balanced budget. GDP = 50,000 C = 25,000 X = 8,000 M = 12,000 a. Assume a linear relationship, and find the demand equation for the loanable funds market. We have two points of (I,i), so we can find the slope equal to m = (i 2 – i 1 ) / (I 2 – I 1 ) = (8 – 3) / (7,900 – 21,900) = - 5/14,000 = - 1/2,800 Then we can plug into the slope intercept form, i = mI + b 8 = - 1/2,800 * 7,900 + b 8 = - 79/28 + b b = 303/28 i = - 1/2800 * I + 303/28 or if we rearrange we get the linear relationship of I = 30,300 – 2,800 * i double check to make sure both points work 8 = - 1/2800 * 7,900 + 303/28= -79/28 + 303/28 Checks 3 = - 1/2800 * 21,900 + 303/28= -219/28 + 303/28 Checks b. Assume a linear relationship, and find the supply equation for the loanable funds market. (Note: Check capital inflows (KI)) We have two points of (S p ,i), so we can find the slope equal to m = (i 2 – i 1 ) / (S p2 – S p1 ) = (8 – 3) / (30,000 – 15,000) = 5/15,000 = 1/3000 Then we can plug into the slope intercept form, i = mI + b 8 = 1/3000 * 30,000 + b 8 = 10 + b b = - 2 i = 1/3000 * S p - 2 i I S p 8 7,900 30,000 3 21,900 15,000

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or if we rearrange we get the linear relationship of S p = 3000*i + 6000 double check to make sure both points work 8 = 1/3000 * 30,000 - 2 = 10 – 2 Checks 3 = 1/3000 * 15,000 -2 = 5 – 2 Checks This however is only the private savings function, which is only part of the loanable funds supply curve as we have capital inflows equal to KI = M – X = 12,000 – 8,000 = 4,000, which we know is horizontally added to the private savings function we just found. S p = 3000i + 10,000 or i = 1/3000 * S p – 10/3 c. What is the equilibrium investment spending in this economy? Set supply equal to demand in the loanable Funds Market which implies I = S p Demand : (Private Investment) I = 30,300 – 2,800 * i Supply : (Private Savings plus Kapital Inflows) S p = 3,000i + 10,000 30,300 – 2,800 * i = I = S p = 3,000 * i + 10,000 20,300 = 5,800*i i = 203/ 58 = 3.5 I = 20,500 = 30,300– 2,800*3.5 = 30,300– 9,800 d. What is private savings in this economy? Use the information above, from parts c and b to calculate from the private savings function, or use the fact that private savings is equal to total investment less capital inflows. S p = 16,500 = 3000*i + 6000 = 3,000 * 3.5 + 6,000 = 20,500 – 4,000 e. What is government expenditure for this economy? We know that Y = C + S p + (T-TR) and that the budget is balanced, or G = (T-TR), implying G = Y – C – S p = 50,000 – 25,000 – 16,500 = 8,500 = G Alternatively, we could have calculated government expenditure from the GDP relationship, Y = C + I + G+ X – M, implying G = Y – C – I – X + M = 50,000 – 25,000 – 20,500 – 8,000 + 12,000 = 8,500 2.
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homework4fall2007answers - Economics 102 Fall 2007 Homework...

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