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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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 Winter '10
 Dr.AtaMazaheri

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