4 solution

# Higher real interest rates choke off some investment

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ot be the short run macroeconomic equilibrium since the increase in output will increase the transaction demand for money, which is also an excess supply of bonds. The excess supply of bonds pushes bond prices lower and so interest rates rise via the present value formula. Higher real interest rates choke off some investment, which in turn, chokes off some output. That is, investment is crowded out even though the government budget deficit does not change. Put another way national savings (Y – C – G) falls even though government saving (T – G) does not change because private saving (Y – C – T) falls due to the fall in output. To see this note that the Keynesian consumption function is C = a + b(Y – T). The change in consumption is ΔC = b(ΔY – ΔT). From the above we know that initially the IS shifts right by an amount equal to ΔG = ΔT = ΔY. We’ve seen that this is not the equilibrium since the interest rate will rise and crowd out investment and output. So equilibrium the increase in output is less than the increase in taxes, ΔY < ΔT. This implies that consumption falls in equilibrium ΔC = b(ΔY – ΔT) < 0. Since private saving is Sp = Y – C – T the change in private saving is ΔSp = ΔY – ΔC – ΔT. Putting in the change in consumption we have ΔSp = ΔY – b(ΔY – ΔT) – ΔT. Collecting terms we get ΔSp = (1 – b)ΔY – (1 – b)ΔT = (1 – b)(ΔY – ΔT) < 0 since b < 1 and ΔY < ΔT. Overall private saving falls and government saving is constant, so national savings falls and so must investment. 5. Chapter 11 Problem #2 Answer: a. The invention of the new high-speed chip increases investment demand, which shifts the IS curve out. That is, at every interest rate, firms want to invest more. The shift in the IS curve raises income and employment. The increase in income increases interest rates because the higher income raises demand for money for transaction purposes. Since the supply of money is not changing the interest rate must rise to keep the money market (and the bond market) in equilibrium. The rise in interest rates partially offsets the increase in investment demand, so that output does not rise by the full amount of the rightward shift of the IS curve. Overall income, interest rates, consumption and investment all increase. LM1 r IS2 IS1 Y1 Y3 Y2 Y b. The increased demand for cash shifts the LM curve up. This happens because households and firms wish to hold more cash and the way they do this is to sell off some bonds. The excess supply of bonds pushes bond prices lower, which increases interest rates by the present value formula. The upward shift of the LM curve and the rise in interest rates lowers investment and income. Consumption falls since income is lower. LM2 LM1 r r2 r1 IS1 Y Y2 Y1 c. At any given level of income, consumers now wish to save more and consume less. Since consumption falls and the IS curve shifts to the left. Since output is lower the demand for money for transaction purposes falls so households and businesses convert their money into bonds by buying more bonds. This is excess demand for bonds pushes bond prices up so interest rates fall by the present value formula, Pbonds = FV/(1 + r). Lower interest rates increase investment. Overall income, consumption and interest rates fall while investment increases. Consumption falls for two reasons: first because consumers are saving more; second, because income falls. Notice that the increase in investment due to lower interest rates offsets some of the fall in consumption and acts as a shock absorber so that output does not fall by as much as the leftward shift of the IS curve. r LM1 IS1 IS2 Y2 Y Y1 6. Chapter 11 Problem #3 Answer: a. The IS curve is given by: Y = C (Y – T ) + I(r) + G . We can plug in the consumption and investment functions and values for G and T as given in the question and then rearrange to solve for the IS curve for this economy: Y =200+0.75(Y–100)+200–25r+100 Y – 0.75Y = 425 – 25r (1 – 0.75)Y = 425 – 25rY = (1/0.25) (425 – 25r) Y = 1,700 – 100r. b. The LM curve is determined by equating the demand for and supply of real money balances. The supply of real balances is 1,000/2 = 500. Setting this equal to money demand, we find:  500 = Y – 100r. Y = 500 + 100r.  Answers to Textbook Questions and Problems c. If we take the price level as given, then the IS and the LM e...
View Full Document

## This note was uploaded on 10/01/2013 for the course ECON 302 taught by Professor Alvero during the Winter '09 term at UBC.

Ask a homework question - tutors are online