1.Food push carts cost $1000 each. The Cho Dofu night market food vender company is trying to decide how many of these push carts to buy. Cho Dofu expects to produce the following numbers of meals each week for each level of capital stock shown.

                Number of Push Carts                                                                    Number of Meals

Produced per Week

0                                                                                                                                                                     0

1                                                                                                                                                                     320

2                                                                                                                                                                     480

3                                                                                                                                                                     560

4                                                                                                                                                                     600

5                                                                                                                                                                     620

6                                                                                                                                                                     630

 

Meals have a real value of $1 each. For simplicity, let us assume Cho Dofu has no other costs besides the cost of push carts.

a.       Find the expected future marginal product of capital (in terms of dollars) for each level of capital. The MPKf for the third push cart, for example, is the real value of the extra output obtained when the third push cart is added

b.      If the real interest rate is 2% per year and the depreciation rate of capital is 5% per year, find the user cost of capital (in dollars per push carts per week). How many push carts should Cho Dofu buy?

c.       Repeat Part (b) for a real interest rate of 3% per year

d.      Repeat Part (b), with the original interest rate, with a 20% tax on Cho Dofu sales revenues.

e.       Cho Dofu found that by rearranging the configuration of the cart they could doubles the number of meals a push cart can produce. With this technological improvement. how many push carts should Cho Dofu buy when the real interest rate is 2% per year? 3% per year? Assume that there are no taxes and that the depreciation rate is still 5% per year.

 

2. Stuteslandia has full-employment output of 5000. Government purchases, G, are 1200. Desired consumptions and desired investment are

                                Cd =2100 – 2000r + 0.10Y, and

                                Id = 1500 – 4000r,

Where Y is output and r is the real interest rate.

a.       Find the real interest rate that clears the good market. Assume that output equals full-employment output.

c.       Government purchases rise to 1440. How does this increase change the equation describing desired national saving? Show the change graphically. What happens to the market-clearing real interest rate?

 

3. Suppose that the economywide expected future marginal product of capital is MPKf = 20 – 0.02K, where K is the future capital stock. The depreciation rate of capital, d, is 20% per period. The current capital stock is 900 units of capital. The price of a unit of capital is 1 unit of output. Firms pay taxes equal to 50% of their output. The consumption function in the economy is C= 100 + 0.5Y-200r, where C is consumption, Y is output, and r is the real interest rate. Government purchases equal 200, and full-employment output is 1000.

                a. suppose that the real interest rate is 10% per period. What are the values of the tax-adjusted user cost of capital, the desired future capital stock, and the desired level of investment?

                b. Now consider the real interest rate determined by goods market equilibrium. This part of the problem will guide you to this interest rate.

                                i. Write the tax-adjusted user cost of capital as a function of the real interest rate r. also write the desired future capital stock and desired investment as functions of r.

                                ii. Use the investment function derived in Part (i) along with the consumption function and government purchases, to calculate the real interest rate that clears the goods market. What are the goods market-clearing values of consumption, saving, and investment? What are the tax-adjusted user cost of capital and the desired capital stock in this equilibrium?

 

 

4.  Use the saving-investment diagram to analyze the effects of the following on national saving, investment, and the real interest rate. Explain your reasoning.

a.       Consumers become more future-oriented and thus decide to save more.

b.      The government announces a large, one-time bonus payment to veterans returning from a war. The bonus will be financed by additional taxes levied on the general population over the next five years.

c.       The government introduces an investment tax credit (offset by other types of taxes, so total tax collections remain unchanged).

d.      A large number of accessible oil deposits are discovered, which increases the expected future marginal product of oil rigs and pipelines. It also causes an increases in expected future income.

 

5.  In a small open economy, output (gross domestic product) is $25 billion, government purchases are $6 billion, and net factor payments from abroad are zero. Desired consumption and desired investment are related to the world real interest rate in the following manner:

World Real Interest Rate                     Desired Consumption                   Desired Investment

5%                                                          $12 billion                                            $3 billion

4%                                                          $13 billion                                            $4 billion

3%                                                          $14 billion                                            $5 billion

2%                                                          $15 billion                                            $6 billion

 

For each value of the world real interest rate, find national savings, foreign lending, and absorption. Calculate net exports as the difference between output absorption. What is the relationship between net exports and foreign lending?

 

 

 

Here are 2 extra problems that push the that are trick given the size of the equations.  Easy math, but you need to be careful.

 

In a small open economy,

Desired national saving, Sd = $10 billion +(100 billion)rw ;

  Desired investment, Id = $15 billion -($100 billion)rw

                                                Output, Y = $50 billion;

                Government purchases, G = $10 billion;

              World real interest rate, rw  = 0.03.

 

a.       Find the economy’s national saving, investment, current account surplus, net exports, desired consumption, and absorption

b.      Owing to a technological innovation that increases future productivity, the country’s desired investment rises by $2 billion at each level of the world real interest rate. Repeat part (a) with this new information

 

Here is one more that is even larger.  Simple math, but easy to drop a negative.

Consider two large open economies, the home economy  and the foreign economy. In the home country the following relationships hold:

Desired consumption Cd  = 320 + 0.4(Y-T) – 200rw ;

        Desired investment, Id = 150 – 200rw ;

                         Output, Y = 1000

                        Taxes, T = 200;

Government purchases, G = 275

 

In the foreign country the following relationships hold:

Desired consumption, Cd For  = 480 + 0.4(YFor – TFor ) -300rw

   Desired Investment,  IdFor  =225 – 300rw

                                        Output, YFor = 1500;

                                Taxes, TFor = 300

Government purchases, GFor  = 300

 

a.       What is the equilibrium interest rate in the international capital market?  What are the equilibrium values of consumption, national saving, investment, and the current account balance in each country?

b.      Suppose that in the home country government purchases increase by 50 to 325. Taxes also increase by 50 to keep the deficit from growing. What is the new equilibrium interest rate in the international capital market? What are the new equilibrium values of consumption, national saving, investment, and the current account balance in each country?