# f07 ec51 ps5 answers - Economics 51D Due 12 October 2007...

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Economics 51D Due 12 October 2007 Problem Set 5 Answers 1. Time on the Keynesian Cross A. The short-run equilibrium GDP is found where Y = Y E , or actual GDP = Planned Expenditure. Planned expenditure is given by Y E = C + I + G + X – M in the basic case, but C depends on disposable income (Y-T) and T may depend on Y as well (if it’s an income tax), and M may depend on Y, too. In the problem, we’ll only have C depend on Y-T and we’ll write C = a C + b C *(Y-T), so that the expenditure function is Y E = a C + b C *(Y-T) + I + G + X – M. Then we can set Y = Y E , and collect the terms with Y in them on the left-hand side, so we get Y*(1- b C ) = a C - b C *T + I + G + X – M. Finally, dividing both sides by (1- b C ) gives C C C b M X G I T b a Y - - + + + - = 1 * . Putting the numbers in from the problem gives 92 . 1 400 400 600 460 550 * 92 . 100 * - - + + + - = Y = 8175 billion or 8.175 trillion. The calculations are also done on the accompanying spreadsheet. Note that on the spreadsheet, C = a C + b C *(Y-T), T = a T + b T *Y, and M = a M + b M *Y. Thus, a lump-sum tax of 550 has a T = 550 and b T = 0, and lump-sum imports of 400 have a M = 400 and b M = 0. B. The graph is presented on the accompanying spreadsheet. C. If taxes are raised by \$100 billion, then we can simply replace the numbers in the answer to Part A and recalculate: 92 . 1 400 400 600 460 650 * 92 . 100 * - - + + + - = Y = 7025 billion or 7.025 trillion. This is a fall of 1150 billion, or 1.15 trillion. D. Now let’s use the tax multiplier to calculate the change in GDP. The tax multiplier is found by solving for GDP in terms of changes. Let the greek letter Δ in front of a letter represent the change in that quantity. Therefore, the equilibrium in terms of changes is given by ΔY = Δa C + b C *( ΔY- ΔT) + Δb C *(Y – T) + ΔI + ΔG + ΔX – ΔM. Now, the only variables that are changing are Y and T, so all the other “Δ” variables are equal to 0. Setting these equal to 0 and collecting terms gives ΔY*(1- b C ) = - b C *ΔT or C C b T b Y - - = 1 = - (92 / .08) = -1150, so equilibrium GDP will fall by 1150 billion. Note that the simple tax multiplier here is C C b b - - 1 = -.92 / .08 = -11.5. E. The diagram graphs the medium-run and long-run effects of this increase in lump-sum taxes. In the short run, we know that equilibrium GDP falls by 1150 billion. This means that the AD curve shifts to the right by 1150 billion. Since this is the only change to the graph, the MRAS and LRAS curves are initially unchanged. In the medium run, the fall in AD will lead to lower GDP and lower prices, though the medium-run GDP is higher than the short-run GDP because of 1

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the slope of the MRAS curve. Assuming that we started this exercise at a long-run equilibrium GDP of \$8175 trillion (that is, potential GDP = 8175 trillion), we know that in the short- and medium runs, actual GDP is less than potential GDP. This means that there will be downward pressure on wages, since the unemployment rate will rise as Y falls. Thus, W will fall over time, causing the MRAS curve to shift down because the marginal cost of production falls. As the MRAS curve shifts down, the medium-run equilibrium will move so that GDP begins to rise and the price level continues to fall. The MRAS curve will continue to shift down until long-run
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