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# Econ 104 Problem Set 2 Econ 104

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This 6 page Class Notes was uploaded by Jieun Son on Tuesday October 4, 2016. The Class Notes belongs to Econ 104 at University of Massachusetts taught by Mehrene Larude in Fall 2016. Since its upload, it has received 16 views. For similar materials see Introduction to Macroeconomics in Macro Economics at University of Massachusetts.

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Date Created: 10/04/16

Problem set 2 NOTE: You will need to write/type at least some of your answers on a printout of this problem set. For instance, you will need to draw directly on the graphs on the last page, and you’ll probably want to fill in the tables below and on page 3 on a hard copy of this, too. The Feb. 16 lecture will explain saving functions and related issues. 1. Suppose that in 2016, investment spending is (and has been each year for a couple of years) $2.5 trillion. Meanwhile, households consume out of aggregate income Y according to the function C = 2 + 0.75Y. Assume there is no government and no trade. When the table below is fully filled in, each row will show, for a given level of Y, how much households will spend on consumption (C) out of the Y they receive, and how much firms will spend on investment (I). It will also show the level of Aggregate Expenditure (AE = C + I). Another column shows, for given Y, whether the resulting AE is greater than, equal to, or less than Y. The final column shows how many trillions of dollars of saving happens for a given level of Y, given that S = Y – C in an economy that has no government. 1a. Fill in the blank cells, using the information above. Y < AE? Y = AE? Y C I AE Y > AE? S 6 6.5 2.5 9 Y < AE 0.5 8 8.0 2.5 10.5 Y<AE 0 10 9.5 2.5 12 Y<AE 0.5 12 11.0 2.5 13.5 Y<AE 1 14 12.5 2.5 15 Y<AE 1.5 16 14 2.5 16.5 Y<AE 2 18 15.5 2.5 18 Y=AE 2.5 20 17 2.5 19.5 Y>AE 3 22 18.5 2.5 21.0 Y>AE 3.5 24 20 2.5 22.5 Y > AE 4 1 1b. What is the level of equilibrium GDP? You can read this from the table if you know how. Here, show how you would find Y* by writing the right equation and solving it for Y. S = I when Y = Y* (in equilibrium). As you can read from the table above, I = S = 2.5 when Y = AE = 18. The level of equilibrium GDP is that output level at which the total amount of goods produced, GDP, is just equal to the total amount of goods purchased. In a world with no government or foreign sector, the amount purchased is C + I .gIn other word, equilibrium GDP Y* is when aggregate income Y is equal to aggregate expenditure and saving is equal to income. That is, Y = AE = C + I. Hence; Y = AE = C + I = 2 + 0.75Y + 2.5 when Y = 18, so equilibrium GDP or Y* = 18. 2. In 2017, investment spending rises to $3.0 trillion, and the consumption function remains the same. By how much will equilibrium GDP (Y*) rise in response to the $0.5 trillion increase in investment spending? Equilibrium GDP (Y*) will rise by $ 2 trillion in response to the $0.5 trillion increase in investment spending. Then what will the new level of equilibrium GDP be (the new Y*)? Hence the new level of equilibrium GDP will be $20 trillion. Briefly explain why the increase in GDP is more than the increase in investment spending, using the concept of the multiplier and describing successive rounds of spending. The reason the increase in GDP is more than the increase in investment spending is the multiplier effect in market. Multiplier is the number of times a rise in national income exceeds the rise in injections of demand that caused it. With injections of new demands for goods and services into circular flow of income stimulate successive rounds of spending. With successive rounds of spending investment increases income as it 2 transfers to another company as income. A portion of this income is spent on consumption, which increases GDP. GDP increases with each successive round of spending. Leading it to increase more than the initial increase in investment. 3. Now return to the situation in question 1. 3a. What is the saving function S? Derive it from the consumption function in question 1, using the fact that S = Y – C in an economy that has no government. S = Y C, S = Y – [2 + 0.75Y], S = Y – 2 .75Y, S = .25Y – 2 S = 2 + .25Y 3b. In this question, however, assume that in 2017 investment spending does not change; instead, consumer spending declines, say because they hear news stories about a coming recession. Worried about losing jobs, consumers change their behavior. Now C = 1 + 0.75Y. What is the NEW saving function S? Derive it from the consumption function, as in 3a, using the fact that S = Y – C in an economy that has no government. S = Y – C S = Y – [1 + .75Y] S = Y – 1 .75Y S= .25Y – 1 S = 1 + .25Y 1 is autonomous consumption 0.75 is MPC. 3c. You calculated the original level of equilibrium GDP (Y*) in question 1. Now calculate the new level of Y* after the decline in consumption, using I = 2.5. Show your work; briefly explain what you did, and why. Y = AE equilibrium C + S = C + I (1 + 0.75Y) + Y – (1 + 0.75Y) = (1 + .75Y) + 2.5 -1 + .25Y = 2.5 .25Y = 3.5 Y* = 14 By combining the Y (GDP/income) and the aggregate expenditure equations I derived the equation C + S = C + I. As mentioned above, it was stated that consumption is equal to (1 + 0.75Y) and that S is equal to Y – (1 + 0.75Y). By adding those two together I got the Y end of the equation. The AE end of the equation was derived from consumption and investment. Both C’s cancel out leaving only, S = I, leaving me to 3 solve the equation using basic algebra. Y* equals 14. This means that the new level of equilibrium is 14 when there was the decline in consumption. 3d. Now fill in the table below similar to the one in question 1a, but this time based on the new consumption function C = 1 + 0.75Y introduced in question 3b. Y<AE? Y= AE? Y C I AE Y>AE? S 6 5.5 2.5 8 Y < AE 0.5 8 7.0 2.5 9.5 Y< AE 1 10 8.5 2.5 11 Y< AE 1.5 12 10.0 2.5 12.5 Y < AE 2 14 11.5 2.5 14 Y = AE 2.5 16 13 2.5 15.5 Y > AE 3 18 14.5 2.5 17 Y > AE 3.5 20 16 2.5 18.5 Y > AE 4 22 17.5 2.5 20.0 Y > AE 4.5 24 19 2.5 21.5 Y > AE 5 Briefly describe which columns of numbers changed (refer to them by the letter or letters at the head of the column), and whether they rose or fell. Columns such as consumption column, C, aggregate expenditure, AE, and saving, S decrease in numbers. All of the columns fell by $1 trillion. 3e. How can you tell just from looking at the table alone what is the new equilibrium level of GDP (which row is the one in which Y = Y*?) (There are two ways that you can tell, and you’re welcome to mention them both.) S = I when Y = Y* (in equilibrium). As you can read from the table above, I = S = 2.5 when Y = AE = 14. The level of equilibrium GDP is that output level at which the total amount of goods produced, GDP, is just equal to the total amount of goods purchased. In a world 4 with no government or foreign sector, the amount purchased is C + I g In other word, equilibrium GDP Y* is when aggregate income Y is equal to aggregate expenditure and saving is equal to income. That is, Y = AE = C + I. Hence; Y = AE = C + I = 1 + 0.75Y + 2.5 when Y = 14, so equilibrium GDP or Y* = 14. 3f. At this new equilibrium level of real GDP (that is, Y*), does saving equal planned investment? Look in the table. Explain briefly, in terms of leakages of demand from, and injections of demand into, the circular flow. At the new equilibrium level of real GDP(Y*), 14, saving (S) equals to planned investment (I), 2.5. Market only has equilibrium when the leakages of demand from the circular flow are equal to the injections of demand into the circular flow, so that the same amount of demand keeps going around and around. It’s like a hydraulic system, a system of fluid circulating in a physical system – and in fact one economist named Phillips actually had a hydraulic system built to illustrate the workings of the economy, many years ago when computers didn’t exist yet. 3g. Using the columns for Y, S, and I in the table in question 1a, plot the saving function on the bottom graph on the next page, and plot the investment function from question 1a on the same graph. Put S and I on the vertical axis. (Try drawing them in PENCIL first!) When you’re sure you have done this part correctly, then add another line for the (shifted) saving function from the table in question 3d (after households reduce their consumption spending and so increase their saving). The result should look generally like the graph in the one-page “Paradox of Thrift” explanation on page 160 – but of course the numbers and shape will be somewhat different. Also plot the AE functions (the one before the decline in consumption spending, and the one after) on the upper graph. Be sure to use a straightedge! Draw lightly the 45 degree line (Y = AE), too. The two graphs together will end up looking a bit like Figure 11 in the text; Y* in the top graph will be directly above Y* in the bottom graph (where S = I). 5 YOUR NAME__________________________________________________________ (in case you submit this page separately) 6

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