Tutorials3Solutions - ECMA06 Tutorial#3 Week 3 Answers 1(a...

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Unformatted text preview: ECMA06 Tutorial #3 - Week 3 Answers 1(a) Because r is fixed at .05, investment is given by I = 100. This economy with no foreign sector and no (13) (C) (d) (6) government (and in which the price level remains fixed) has desired Aggregate Expenditure given by: AB = C + I = 60 + 0.75Y +100 2160 + 0.75Y The equilibrium condition is given by AB = Y (in other words, the desired level of spending is just equal to the current level of total national income or output). Therefore, 160 + 0.75Y = Y or 0.25Y = 160 or Y* = (1!0.25)(160) = 4 x 160 = 640. If national output were somehow set accidentally at 600 (i.e., Y = 600), AB = 160 + 0.75Y = 610 and AE > Y (that is, the economy is trying to purchase more output than is being produced, which in microeconomic terms can be seen as excess demand). Prices are fixed (by assumption) at their current level. Firms satisfy the excess demand by drawing down their inventories, which leaves inventories below their desired levels. There is pressure for firms to increase their current level of output in order to build inventories back up. This pressure will not cease until output is increased to the equilibrium level of 640. When Y = 600, C = 60 + .75Y = 510 and I = 100. In terms of GDP accounting, consumption is 510 and investment is 90 (because investment includes both I, which is intended investment, and changes in inventories, which in this case will be —10). Ifnational output were somehow set accidentally at 7‘00 (i.e., Y = 700), AB = 160 + 0.75Y = 685 and AE < Y (that is, the economy is producing more output than can be sold, a situation of excess supply). In contrast to part b, firms now begin accumulating inventories because they are producing more than they are selling. There is therefore pressure for firms to decrease their current level of output in order to reduce inventories to their normal level. These pressures will not cease until output is decreased to the equilibrium level of 640. When Y = 700, C = 60 + .75Y = 585 and I = 100. In terms of GDP accounting, consumption is 585 and investment is 115 (because investment includes both I, which is intended investment, and changes in inventories, which in this case will be +15). The multiplier shows us how the equilibrium level of Y changes when some element of autonomous expenditures changes. Since AB = C + I, it is convenient to write this as AB = 60 + 0.75Y + I, where "I" is (autonomous) investment spending. When we solve for equilibrium, we have AB = Y, or Y — 0.75Y = 60 + 1. Thus Y = (1/0.25)(60 + l) = 240 + 41. Therefore, dY/dI = 4, which is the multiplier. When investment increases, the transmission mechanism that causes output to increase is the one that is described in part (b) above. The increase in Investment spending increases Aggregate Expenditure, so that at the original level of output, there is now Excess Demand. Producers notice these unintended decreases in inventories and increase the level of output to the new equilibrium level in order to restore them. In the original problem Y* = 640. Thus C = 60 + 0.75Yd = 60 + 0.75(640) = 540. Since S = Yd - C = Y - C, therefore S = 100. Ifconsumers try to save more by reducing consumption to C = 50 + 0.75Yd, then AE will have fallen to AB = 150 + 0.75Y and, through the multiplier, equilibrium Y will fall to 600. In this new equilibrium, C = 500 and savings is still 100, so savings have not risen. In this model, increased savings reduce spending, so equilibrium Y falls until savings are back at 100. Consumers will have been unsuccessful in their attempt to save more. You may notice that savings are equal to investment in this model. That is because this simple model has no government and no foreign sector, so we derive equilibrium by setting Y = AB = C + I. Therefore, in equilibrium, Y — C = I. But here, Y — C is the same as savings, so S = I in equilibrium. However, you should keep in mind that this will not always be true in more complicated models. ...
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