Homework 5-

1. Market of Loanable Funds:

Consider the country Romanovia. In 2012 this country is a closed economy and that implies that capital inflows (KI) are therefore equal to zero.  The loanable funds market is characterized by the following demand function DLF where the demand for loanable funds curve includes only investment demand for loanable funds: r = 10 - (1/2000)Q where r is the real interest rate expressed as a percent (e.g., if r = 10 then the interest rate is 10%) and Q is the quantity of loanable funds. The relationship between the supply of private savings (Sp) and the interest rate can be expressed by the equation: r = 2 + (1/2000)Q. In 2012 the government of Romanovia had government expenditures (G) of $8000, transfer payments (TR) of $2000, and collected taxes (T) equal to $14,000.

a) Calculate the value of government savings (Sg)? Is the government running a budget deficit or a budget surplus? Show how you got your answer.

b) Derive an equation that expresses this economy's supply of loanable funds curve. Make sure that you include not only private savings but also government savings in this equation.

c) Given the demand for loanable funds curve you were given and the supply of loanable funds curve you derived in (b) calculate the equilibrium interest rate and the equilibrium quantity of loanable funds in this market. Show your work.

d) What is the level of private investment (I) in this economy when the loanable funds market is in equilibrium? Is there any crowding out of private investment in this market? Explain your answer.

2013 starts with a natural disaster in Romanovia. A flood brings destruction in the south of the country.  The government decides to take care of the reconstruction. The government expenditure (G) in 2013 increases to $14000, the level of transfers (TR) is unchanged from 2012 and the level of taxes (T) is equal to $12,000. There is no change in the supply of loanable funds from private savings and there is no change in the demand for loanable funds for private investment.

e) Calculate the value of government savings (Sg) for 2013 in this economy. Is the government running a budget surplus or a budget deficit?

f) Consider your answer in (e). If you wanted to model the government's budget situation on the supply of loanable funds side of the market would your answer in (e) cause the supply of loanable funds curve to shift to the left or to the right? Explain your answer.

g) Consider your answer in (e). If you wanted to model the government's budget situation on the demand for loanable funds side of the market would your answer in (e) cause the demand for loanable funds curve to shift to the left or to the right? Explain your answer.

h) Write an equation expressing the new demand for loanable funds curve in this market assuming that you are modelling both the demand for loanable funds for private investment as well as the demand for loanable funds to finance the government budget deficit.

i) Given your equation in (h) and the information you have about private savings, find the new equilibrium interest rate in the loanable funds market as well as the new equilibrium level of loanable funds in this market. Identify how much of the equilibrium quantity in the loanable funds market goes to finance private investment.

j) What is the level of private investment in this market in 2013? Is there crowding out of private investment in this market? Explain your answer. In your answer provide a numerical measure of the amount of crowding out that occurs if there is crowding out.

k) Suppose that all of the changes described for 2013 occurred but in addition Romanovia decides to open its borders to capital inflows. In 2013 capital inflows into Romanovia equal to $4,000. Use this information to calculate the equilibrium interest rate, the equilibrium quantity of loanable funds and then compare the level of private investment in 2013 with the level of private investment in 2012.

2. Aggregate Consumption:

The following chart reports the aggregate consumption, savings, taxes and transfers in Macronesia in billions of dollars for 2011 and 2012.

a) We know that the aggregate consumption function of Macronesia can be written as a linear equation of the form C = a + b(Y - (T - TR)) where a is autonomous consumption and b is the marginal propensity to consume. Assume that autonomous consumption and the marginal propensity to consume are both constant. From the table derive the equation for this economy's consumption function.

b) What is the Marginal Propensity to Consume (MPC)? What is the Marginal Propensity to Save (MPS)?

c) Suppose in 2013 GDP will be $500 billion and Taxes and Transfer are the same as in 2012. Given this information, calculate the change in consumption between 2012 and 2013.

d) Suppose in 2013 GDP and Transfers are the same as in 2012 but that Taxes are increased to $150 billion. There is no change in the consumption function. Calculate the change in consumption between 2012 and 2013.

3. Data Analysis:

Let's work a bit with real data. We produced a graph using FRED, the data center of the St. Louis Fed. Your goal is to try to get a graph similar to ours, following our instructions. First, go on the St. Louis Fed data tools page:

• http://research.stlouisfed.org/datatools.html.

Select "create your own graph". Then select the following series (see instructions following this list).

• The growth rate of Real GDP (GDPC1)
• The growth rate of Real Private Investment (GPDIC96)
• The growth rate of Real Consumption (PCECC96)
• The growth rate of Real Government Expenditure and investment (GCEC96)

We've included the term you should search for in parentheses after each item. You can look for each series using the search box at the bottom of the page. Once you find the series you can adjust multiple options. We suggest the following setup:

• Frequency: Quarterly
• Units: Percentage Change
• Observation Date Range: from 1-1-1955 to 01-10-2012

You can also select additional options like color, width and type of the marker. You can change this setup, as you prefer. Once you are satisfied with your work, you can print out your graph or save it in pdf format (second and third option at the top of your graph).

a) Print the graph.

b) Given the data you found at FRED can you say anything about the relationship between private investment and GDP? What about the relationship between GDP and consumption? What about government expenditure and investment?

4. Keynesiam Model:

Say that consumption is determined by C = a + b(Y-T) for some constant value of a and b.  We have the following data on consumption and disposable income.

a) Find a and b using the above data.

b) Suppose that in this economy the government must always run a balanced budget (that is, T = G and for the sake of simplicity TR = 0). Suppose also that this is a closed economy and that the level of investment spending is autonomous, constant, and equal to 5. Given this information calculate the equilibrium level of consumption (C), and the equilibrium level of saving (S) for this economy.

c) What happens to the equilibrium quantities in (b) if the marginal propensity to consume (b) increases?  What is the effect of increasing autonomous consumption (a) in the consumption function?

5. Investment/Depreciation:

a. Suppose that an economy currently has a level of capital stock equal to 100 units. But, each year 10% of the capital stock depreciates. Suppose this economy does not engage in any investment spending: in the table below calculate what happens to this economy's capital stock over the next seven years. Round your answers to the nearest hundredth of a unit.

b. Given the information in (a), what is happening to this economy's labor productivity over these seven years holding labor and the aggregate production function constant? Explain your answer.

c. Given the information in (a), what is happening to this economy's capital productivity over these seven years holding labor and the aggregate production function constant? Explain your answer.

d. Suppose that this economy decides to increase investment spending so that it is equal to 20% of the current year's capital stock. Calculate the level of capital in this economy given this decision and incorporating the depreciation that is occurring. Put your calculations in the following table. Show how you calculated your values. Round your answers to the nearest hundredth.