In the classical model the supply of money and the demand

Question

Homework 4-

Problem 1 - Suppose there are only two countries, Macronia and Micronia and that these two countries trade with each other. Use the Classical Model and the following information to answer this problem.

Hint:  You will find it helpful to be very organized in your work on this problem: I would suggest that you make two columns on your page and in the left-hand column compute the calculations for Macronia (please label the top of the column with the country's name) and in the right-hand column compute the calculations for Micronia (label the top of the column with Micronia's name).  This will help you keep track of all the various details involved in this problem.

Use this Classical Model:

Y = C + SP + T - TR

Y = C + I + G + (X - M)

KI = M - X

SG = T - TR - G

NS = SP + SG = Y - C - G

I = Y - C - G + KI

Leakages = Injections in Equilibrium or SP + T - TR + M = I + G + X

Note: in the table below iR is the real interest rate and in the problem it is expressed as a decimal: e.g. if the real interest rate is 10%, then iR enters the mathematical expression as .1.

Country	GDP	C	G	T - TR	SP	I
Macronia	$6,000	4,700	700	200	1000+2000 iR	400-4000 iR
Micronia	4,000	2,800	600	200	800+4000 iR	1100-2000 iR

a. Calculate the equilibrium real interest rate for both Macronia and Micronia.

b. Calculate the value of net exports for Macronia and Micronia.  What do you notice about the relationship between the level of net exports for Macronia and Micronia?

c. Calculate the supply of loanable funds and the demand for loanable funds in the two countries. Does the market for loanable funds clear in each country?

d. Calculate NS + KI for each country and compare this sum with the value of investment for each country.

Problem 2 - The private saving and investment spending of Macronia, which is a closed economy, can be described by linear equations (e.g.,  i_R = mI + b or I = (1/m)i_R - (1/m)b). Use the information in the following table and the Classical Model in problem (1) to answer this series of questions.  Assume the private saving and investment functions are stable and linear from year to year (e.g., once you have an equation that describes private saving, this equation will hold true for 2003, 2004, and 2005).

Year	iR	I	SP
2003	.02	$1,030	$1240
2004	.04	$1,010	$1480

a. Derive the equations for private saving and investment spending in Macronia (you will find it easier to write these equations as I = f(i_R) and S = f(i_R)).

b. In 2005,  C = $10,000, G = $800, T = $300, and TR = $100. Find the equilibrium interest rate, the level of private saving in 2005, and the level of investment in 2005.

c. Calculate the level of GDP in Macronia for 2005.

d. Calculate the value of leakages and injections in 2005 in Macronia.

e. An economist suggests that the government of Macronia should spend $130 more (i.e., G = $930). Holding everything else constant, what is the new equilibrium interest rate, the new level of private saving, and the new level of investment? Does this policy increase total output? Why or why not?

Problem 3 - In the Classical model, the supply of money and the demand for money are equal. Let k denote the percentage of income that people desire to hold as money, which is assumed to remain constant. In 2004 the money supply was $5,000 and the nominal GDP was $10,000. The inflation rate from 2004 to 2005 was 10%. In 2005 the money supply was $6,600.

a. Calculate the value of  k.

b. Calculate the nominal and real GDP in 2005 (using 2004 as the base year).

c. What is the growth rate of real GDP from 2004 to 2005?

d. Suppose that the money supply in 2005 is $13,200 (and not $6,600). Given this level of the money supply, what is the inflation rate, the level of nominal GDP and the level of real GDP in 2005? (Hint: you know the level of real GDP for 2005 since we are using a Classical Model.)

e. Suppose the government wants the inflation rate from 2004 to 2005 to be 5%.  What level of money should the government supply in 2005 to achieve this goal?

Problem 4 - Use the following Keynesian Model of a closed economy to answer problem (4):

Y = C + S + T where T is net taxes (we will not worry about transfers in this problem)

AE = C + I + G

Y = AE in equilibrium

C = a + b (Y - T)

The aggregate consumption function of Macroland (a closed economy) is linear in the aggregate current disposable income, that is, C = a + b × (Y-T). We may divide the investment into planned and unplanned investments. And the total investment is I = I_Planned + I_Unplanned. The planned aggregate spending AE_Planned is the sum of C, G, and I_Planned.

Year	Y	T	Y-T	C	G	IPlanned	AEPlanned	IUnplanned
2002	$8,000	500		4150	1,000		5850
2003		500		4650	1,000	700		2,650
2004	10,000	1,000			4,000	800

a. Calculate the missing values in the above table.

b. What are the values of aggregate autonomous consumer spending and the marginal propensity to consume in Macroland?

c. In 2005, T= 1300, G=5,000, and I = 100. What is the equilibrium GDP for 2005 using the Short Run Keynesian Model?