Using the consumption equation from point (a), what is the MPS for the corresponding saving curve?

Econ 100B: Macroeconomics

Problem Set #6

General Instructions:

• Late homework will not be accepted.
• put your name, student ID & your GSI’s name at the upper right corner of the front page.

 

• (25 points) Suppose we have a Keynesian consumption function where autonomous consumption is $600 and the marginal propensity to consume is 0.60.

 

1. (5 points) Write an algebraic expression for the consumption equation.
2. (5 points) Sketch a graph of this consumption curve that corresponds to the consumption equation above. Include the income line in your drawing and label autonomous consumption.
3. (5 points) Calculate the level of income at which income is equal to consumption, that is, where the consumption curve intersects the income line.
4. (5 points) Using the consumption equation from point (a), what is the MPS for the corresponding saving curve?
5. (5 points) At what level of income will saving be zero? (Hint: What is the level of income where consumption is equal to income?) Use this point and the MPS to sketch the saving curve in a graph.

 

• (35 points) Suppose you are given the following information about a closed economy:

Y = $40,000                      Real GDP = Income

T = $6,000                        Net tax collections

Spr = $1,000 + 0.15*(Y-T) + 1,000*r                       Private saving function; r = real interest rate

I = $5,600 – 2,000*r                     Total investment function

G = $6,800                                       Government purchases

Look carefully at the equations for private saving and total investment. Note that investment is a decreasing function of the real interest rate. That is, as the rate of interest increases, the level of desired investment (i.e. the demand for loanable funds) decreases. Also, private saving is an increasing function of both the real rate of interest and disposable income (Y–T).

The parameter 0.15 in the saving equation, which is multiplied by disposable income, is called the marginal propensity to save (MPS) and tells us how much extra saving is generated by an increase in disposable income.

1. (5 points) Give some intuition on why private saving might be increasing in the real interest rate.
2. b) (5 points) Does this government run a deficit or a surplus?
3. c) (5 points) What is the amount of national saving? That is, write an equation for national saving (S), showing how it depends on the interest rate.
4. d) (5 points) Without any calculations, what are the implications of changes in the amount of government deficit/surplus for the equilibrium interest rate in the economy?

Note that in this model, a reduction in investment in the economy does not change long run GDP. Here the level of GDP was given exogenously; that is, the model cannot explain changes in GDP. However, our simple model here makes predictions about changes in the composition of GDP.

1. e) (5 points) Suppose that the government increases its purchases without increasing its tax collection. What prediction does this model make about changes in the shares of consumption, investment, and government purchases in GDP?
2. f) (5 points) Calculate the equilibrium real interest rate in this economy. Also, if you are told that the rate of inflation in this economy is 2.5%, what is the nominal rate of interest?
3. g) (5 points) What are the total levels of saving and investment at this rate of interest? How much of the total saving is comprised of government saving and how much is private saving?

 

• (20 points) In a stunning result, the candidate of Le Tricolaire party wins the French election in the first voting round. The strong support received from voters allows the new president to implement large fiscal reforms that drastically reduce the government budget deficit.

 

1. (5 points) Does this change in policy shift the demand curve or the supply curve in the market for loanable funds? Why?
2. (5 points) Use a supply and demand diagram for loanable funds to show in which direction the relevant curve shifts.
3. (5 points) Does the interest rate rise or fall as a result of this change in policy? Explain why.
4. (5 points) What happens to private investment as a result of this change in policy?

 

• (20 points) Matt deposits $M 50,000 of currency into his new checking account at the Migronian Commercial Bank (MCB). The required reserve ratio is 10% and the liquidity ratio is 0 (nobody keeps cash).
  1. MCB required reserves increase by ________ and excess reserves (amount available to be lent) increase by
  2. The money multiplier in this economy is
  3. As a result of Matt’s deposit, checking account deposits in the banking system as a whole (including the original deposit) could eventually increase up to a maximum of
  4. If the liquidity ratio was 10% instead of 0%, the money multiplier in this economy would be