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Economics 102 Fall 2007 Answers to Homework #5 1. Complete the following table, and answer the questions that follow. Taxes are proportional to income, so T = tY. Assume that there are NO TRANSFERS. Hint: You should consider using the slope formula to calculate MPC. Y T Y-T C S 60 15 45 56 -11 100 25 75 80 -5 175 43.75 131.25 125 6.25 400 100 300 260 40 a) Determine the progressive tax rate t. 15 = t(60) t = .25 b) Determine the consumption and saving functions with respect to disposable income, and with respect to aggregate income. 2 . 8 . 1 1 8 . 45 75 56 80 ) ( ) ( ) ( 2 1 2 1 = - = - = = - - = - - - - = - = MPC MPS T Y T Y C C T Y C MPC C = 20 + .8(Y-T) C = 20 + .6Y S = -20 + .2(Y-T) S = -20 + .15Y c) Given the consumption function you determined in part (b), the tax rate you found in part (a), and the following information about the economy, determine the equilibrium output: I = 130 G = 100 + .16T X = 250 M = 200 Y = [20 + .8(Y-T)] + 130 + [100 + .16T] + [250-200] Y = 300 + .8(.75Y) + .16(.25Y) Y = 300 + .64Y .36Y = 300 Y = 833.33 d) Given equilibrium output, determine the equilibrium levels of consumption, savings, taxes, and government spending.

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C = 20 + .6(833.33) C = 20 + 499.99 C = 519.99 S = -20 + .15(833.33) S = -20 + 124.99 S = 104.99 T = .25*(833.33) T = 208.33 G = 100 + .16(208.33) G = 133.33 Notice, adding the values for C + S + T, you get 833.33 (approximately because of rounding errors). This is the value determined for Y in part C. This is consistent with the identity from class, Y = C + S + (T-TR). e) Is the government running a deficit or a surplus? Are there capital inflows or outflows? The government is running a surplus. T-G = 75 There are capital outflows M – X = -50. f) In terms of variables, determine the GDP multiplier. Hint: you should model the equations as follows: C = a + b(Y-T) I = I G = g + dT X = X M = M T = tY Y = [a + b(Y-T)] + I + [g + dT] + [X-M] Y = [a + b(Y-tY)] + I + [g + dtY] + X – M Y = a + bY –btY + I + g + dtY + X – M
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