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Unformatted text preview: Economics 51D Due 19 October 2007 Problem Set 6 Answers 1. CrowdedOut House, a forgettable 80s band A. If the government increases G by $150 billion without increasing taxes, then this will reduce national saving by $150 billion. National saving is Y – C – T – (XM) + T – G, so when G increases without an increase in T, saving falls. The supply of Saving shifts to the right by $150 billion. Now, the only part of Saving that could be sensitive to the interest rate is C. But the problem specifies that C is not sensitive to changes in r, so that Saving function is vertical—it has interest elasticity of 0. Since Investment = Saving in equilibrium, this means that the equilibrium quantity of Investment must fall by the full $150 increase in G. That is, there is full crowding out of private investment by government spending. 1 Then we need to figure out how much the interest rate rises. We are given that the interest elasticity of investment demand is 1.2, so when the interest rate rises by 1%, investment demand falls by 1.2%. Recall that, according to our definition of elasticity, % change in I = 2 / ) ( 1 2 1 2 I I I I + , and we know that I must fall by $150 billion, so I falls from 1600 to 1450 billion. This means that the percent change in I is given by 150 / 1525, or .0984. Since % change in I = interest elasticity * % change in r, .0984 = 1.2 * % change in r, or % change in r = .0984 / 1.2 = . 0820. The formula for % change in r is simply 2 / ) ( 1 2 1 2 r r r r + , so we have .0820 = 2 / ) 075 . ( 075 . 2 2 + r r . This implies that r 2 = .0814. So the interest rate must rise from 7.5% to 8.14% in order to reduce investment enough. B. Now if the consumption function is somewhat sensitive to the interest rate, we will get less than full crowding out. That means that the increase in G will be matched partly by a decrease in I and partly by an increase in S due to a fall in C as interest rates rise. In other words, we know that the Saving function shifts to the left by 150 billion. But the new equilibrium quantity of Investment will drop by less than 150 billion, because as the interest rate increases, Saving will increase a bit as Consumption falls. So it is as if Saving falls 150 billion, then rises a bit. We can picture this in the diagram. The saving function shifts left, but we see that we also move up the saving function to the new equilibrium. To put this in numbers, we know that in equilibrium, Saving must be equal to Investment and the change in Saving must equal the change in Investment. The total change in Saving is a fall of 150, plus an increase due to the effect of the increased interest rate on Consumption. The total change in Investment is simply a fall in Investment due to an increase in the interest rate....
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 Fall '07
 Fullenkampf
 Economics, Inflation, Monetary Policy, Supply And Demand, Fed, discount window

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