Chapter 3 - Chapter 3 National income: Where It Comes From...

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Unformatted text preview: Chapter 3 National income: Where It Comes From and Where It Goes 17 7. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c) national saving can be analyzed by using the following relationships: National Saving = [Private Saving] + [Public Saving] = [Y— T— C(Y— T)] + [T— G] = Y— C(Y— T) ~ G. a. Public Saving—The tax increase causes a 1-for—1 increase in public saving. T increases by $100 billion and, therefore, public saving increases by $100 billion. b. Private Saving——The increase in taxes decreases disposable income, Y — T, by $100 billion. Since the marginal propensity to consume (MP0) is 0.6, consumption falls by 0.6 x $100 billion, or $60 billion. Hence, APrivate Saving = — $1001) — 0.6 (— $10013) = — $4013. Private saving falls $40 billion. 0. National Saving—Because national saving is the sum of private and public sav- ing, we can conclude that the $100 billion tax increase leads to a $60 billion increase in national saving. Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y — C(Y — T) — G. The $100 billion tax increase reduces disposable income and causes consumption to fall by $60 bil- lion. Since neither G nor Y changes, national saving thus rises by $60 billion. d. Investment—To determine the effect of the tax increase on investment, recall the national accounts identity: in Y: C(Y— T) + 10‘) + G. Rearranging, we find Y— C(Y— T) — G = 10'). The left-hand side of this equation is national saving, so the equation just says that national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion. HOW does this increase in investment take place? We know that investment depends on the real interest rate. For investment to rise, the real interest rate must fall. Figure 3—1 illustrates saving and investment as a function of the real interest rate. r 51 52 Figure 3~1 ‘: a. Real interest rate r? aid the ime I (r) rian reen even duct 1, S Investment, Saving The tax increase causes national saving to rise, so the supply curve for loan- able funds shifts to the right. The equilibrium real interest rate falls, and invest- ment rises. 18 Answers to Textbook Questions and Problems 8. If consumers increase the amount that they consume today, then private saving and, therefore, national saving will fall. We know this from the definition of national saving: National Saving = [Private Saving] + [Public Saving] = [Y— T— C(Y— T)] + [T— G]. An increase in consumption decreases private saving, so national saving falls. Figure 3—2 illustrates saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment. Figure 3—2 Real interest rate 1 (r) I,S Investment, Saving 9. a. Private saving is the amount of disposable income, Y— T, that is not consumed: ; Sprivate = y_ T_ C { = 5,000 — 1,000 — (250 + 0.75(5,000 — 1,000)) = 750. “ Public saving is the amount of taxes the government has left over after it makes its purchases: Spublic = T_ G = 1,000 — 1,000 = 0. Total saving is the sum of private saving and public saving: V S = Sprivate + Spublic ‘ = 750 + 0 i = 750. b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already know that national saving is 750, so we just need to set it equal , to investment: s = I 750 = 1,000 — 50r 4 Solving this equation for r, we find: r = 5%. c. When the government increases its spending, private saving remains the same as before (notice that G does not appear in the S Viva” above) while government saving decreases. Putting the new G into the equations above: Chapter 3 National Income: Where It Comes From and Where It Goes 19 Sprivate = Spublic = T_ G = 1,000 — 1,250 = —250. Thus, S: Sprivate + Spublic : + = 500. Once again the equilibrium interest rate clears the market for loanable funds: S = I 500 = 1,000 — 50r Solving this equation for r, we find: r = 10%. To determine the effect on investment of an equal increase in both taxes and govern- ment spending, consider the national income accounts identity for national saving: National Saving = [Private Saving] + [Public Saving] = [Y— T— C(Y— T)] + [T— G]. We know that Y is fixed by the factors of production. We also know that the change in consumption equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us that ANational Saving = [— AT — (MPC >< ( — ATM] + [AT — AG] = [—AT+(MPC><AT)l +0 = (MPC — 1) AT. The above expression tells us that the impact on saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MP0 is to 1, the smaller is the fall in saving. For example, if the MP0 equals 1, then the fall in consumption equals the rise in government purchases, so national saving [Y — C(Y— T) — G] is unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved rather than spent for a one—dollar change in disposable income), the greater is the impact on saving. Because we assume that the MP0 is less than 1, we expect that national saving falls in response to an equal increase in taxes and govern- ment spending. The reduction in saving means that the supply of loanable funds curve shifts to the left in Figure 3‘3. The real interest rate rises, and investment falls. r 52 31 Figure 3-3 Real interest rate I (r) I, S Investment, Saving 20 Answers to Textbook Questions and Problems 11. a. The demand curve for business investment shifts out to the right because the sub— sidy increases the number of profitable investment opportunities for any given interest rate. The demand curve for residential investment remains unchanged. b. The total demand curve for investment in the economy shifts out to the right since it represents the sum of business investment, which shifts out to the right, and residential investment, which is unchanged. As a result the real interest rate rises as in Figure 3—4. Figure 3—4 1. An increase in desired investment . . . Real interest rate 2. . . . raises the interest rate. Investment, Saving 0. The total quantity of investment does not change because it is constrained by the inelastic supply of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in residential investment. That is, the higher interest rate means that residential investment falls (a movement along the curve), whereas the rightward shift of the business investment curve leads busi- ness investment to rise_by an equal amount. Figure 3—5 shows this change. Note that IIB+I1R =I§3+IzR =S. Business Residential investment investment 12. In this chapter, we concluded that an increase in government expenditures reduces national saving and raises the interest rate; it therefore crowds out investment by the full amount of the increase in government expenditure. Similarly, a tax cut increases disposable income and hence consumption; this increase in consumption translates into a fall in national saving—again, it crowds out investment by the full amount of the increase in consumption. *2 t g Chapter 3 National Income:Where It Comes From and Where It Goes 21 If consumption depends on the interest rate, then these conclusions about fiscal policy are modified somewhat. If consumption depends on the interest rate, then so does saving. The higher the interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the interest rate might increase saving and reduce consumption. Figure 3—6 shows saving as an increasing function of the interest rate. r Sm Figure 3—6 Real interest rate Saving Consider what happens when government purchases increase. At any given level of the interest rate, national saving falls by the change in government purchases, as shown in Figure 3—7. The figure shows that if the saving function slopes upward, investment falls by less than the amount that government purchases rises by; this hap- pens because consumption falls and saving increases in response to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the less govern— ment purchases crowd out investment. r 520’) 510,) Figure 3-7 Real interest rate e +5 [(1') Investment, Saving 18. a. Figure 3—8 shows the case Where the demand for loanable funds is stable but the supply of funds (the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes in government spending, or changes in consumer confi- dence. In this case, when interest rates fall, investment rises; When interest rates rise, investment falls. We would expect a negative correlation between investment and interest rates. 22 Answers to Textbook Questions and Problems S10") Figure 3~8 r S; (F) (D E 0 .‘§ s m [(1’) I, S Investment, Saving b. Figure 3-9 shows the case Where the supply of loanable funds (saving) does not respond to the interest rate. Also suppose that this curve is stable, Whereas the demand for loanable funds varies, perhaps reflecting fluctuations in firms’ expec- tations about the marginal product of capital. We would now find a positive corre- lation between investment and the interest rate—When demand for funds rises, this pushes up the interest rate, so we see investment increase and the real inter- est rate increase at the same time. Figure 3—9 Real interest rate 12 (r) 110’) I, S Investment, Saving Chapter 3 National Income:Where It Comes From and Where It Goes 23 If both curves shift, we might generate a scatter plot as in Figure 3—10, where the economy fluctuates among points A, B, C, and D. Depending on how often the economy is at each of these points, we might find little clear relationship between investment and interest rates. 51(r) Figure 3—10 Real interest rate 12 (2-) [1(7) I, S Investment, Saving Situation (0) seems fairly reasonable—both the supply of and demand for loanable funds fluctuate over time in response to changes in the economy. ...
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This note was uploaded on 11/06/2010 for the course ECON 716-2 taught by Professor Prof.man-luilau during the Fall '10 term at University of San Francisco.

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Chapter 3 - Chapter 3 National income: Where It Comes From...

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