Homework 4-
1. The economy of country A is described by the production function:
Y = √KL
In this equation the symbol Y stands for real GDP, K for capital and L for the employed individuals in this economy. The labor force at the beginning of time, period 0, is 100 individuals. Capital in each period is constant and equal to 100 units. Assume this economy is under full employment. (Suggestion: Use Microsoft Excel or some other computer program to do the calculations and the graphs of the questions posed below rather than a regular calculator.)
a. Complete the following chart using the above information. Calculate real GDP with at least 3 decimal places. Hint: this will be far easier if you use Excel to do these calculations and you may present your own Excel Chart as the answer to this question.
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Aggregate Variables
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Capital(K)
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Labor(L)
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Change in L
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Real GDP(Y)
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change in Y
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MPL
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Period 0
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100
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Period 1
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200
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Period 2
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250
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Period 3
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370
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Period 4
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480
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Period 5
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550
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Period 6
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640
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Period 7
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800
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Period 8
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890
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Period 9
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970
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Period 10
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1050
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b. Graph Real GDP and the labor level for this economy. Please measure real GDP on the y-axis and labor on the x-axis, when the amount of capital is fixed at 100 units. For this question it is fine to present your answer as an Excel Graph (hint: this is much easier to do with a program like Excel).
c. Graph the marginal product of labor each period for this economy. Measure the MPL on the y-axis and the amount of labor on the x axis. You will find this easiest to do using Excel and its graphing feature. Does the MPL you have calculated and graphed exhibit the property of diminishing return to labor? If not, why?
d. Suppose now that the capital increases to a constant level of 200 units from period 0. Nothing else changes about this problem. Present real GDP under both situations in the same graph: situation one, where capital is equal to 100 units and situation two, where capital is equal to 200 units. On your graph measure real GDP on the y-axis and the time periods on the x-axis. Remember to note clearly the label of each curve.
e. Suppose now that the technology changes, so that the productivity doubles. That is, the production function is now Y = 2√KL, and all other conditions remain the same. The amount of capital is fixed at 100 units. Present real GDP under both situations in the same graph: situation one, where Y = √KL ; and situation two, where Y = 2√KL.
Which production function has higher marginal return to labor? Why? (you can answer this question by analyzing the graph you have drawn)
2. Suppose that the demand for labor and supply of labor in Fantasyland are given by the following equations:
Demand for labor: w = 170 - LD
Supply of labor: w = 8 + LS
where w is the wage per week and L is the number of labor units hired per week. Assume that one labor unit is equal to one worker.
a. Suppose we have full employment, what is the equilibrium level of employment per week and the equilibrium wage rate per week in Fantasyland?
b. Suppose the aggregate production function in Fantasyland is given by the following equation:
Y = 2√KL
where Y is real GDP in unit of dollars, K is capital and L is labor. Furthermore, suppose that Fantasyland has 100 units of capital. Given this information, what is the full employment output for this economy?
c. Suppose we define labor productivity for Fantasyland as output divided by the level of labor used in a week. What is the value of labor productivity for Fantasyland if it produces the full employment level of output?
Suppose now, that the government implements a minimum wage rate of $95 per week. Use this information to answer parts (d) through (f).
d. Holding everything else constant and given this new information, what is the number of unemployed people in this economy?
e. Given this information, what is the new level of output for this economy and the new level of labor productivity?
f. From your answers in parts (d) and (e), discuss whether or not the government's minimum wage policy makes workers better off or not.
g. Go back to the initial situation (no minimum wage imposed by the government).Suppose that the demand for labor shifts to the right and results in the equilibrium wage increasing to $108. What is the value of labor productivity when this increase in wages occurs?
3. Using a diagram of the labor market and a diagram of an aggregate production function, illustrate and verbally describe what happens for the following cases. Be sure to identify what happens to the level of employment, the wage rate, the level of production, and labor productivity.
a. A baby boom 16 years ago drives the current labor force up.
b. The average education level has been dramatically increased. Assume that this change does not alter the demand for or the supply of labor.
c. Plants switch their labor-intensive job positions overseas, but the aggregate production processes in the U.S. do not change.
d. Technological improvement rebuilds production function.
4. Consider the market for loanable funds. Using the information below, graph the market for loanable funds. Measure the X-axis in millions of dollars of investment. Measure the interest rate (in percentage points) on the Y-axis. In the equations below r is the real interest rate, where the unit is percentage, and Q is the quantity of loanable funds, with the quantity measured in dollars. Assume the government initially has a balanced budget (that is, G = T - TR where G is government spending, T is taxes, and TR are transfers) and that this is a closed economy (that is, exports (x) are equal to zero and imports (IM) are equal to zero). The following two equations describe the supply of loanable funds from saving and the demand for loanable funds for investment:
Saving function: r = -0.5 + S/4000
Investment function: r = 25 - I/2000
a. What is the equilibrium interest rate and quantity of investment in this market?
b. Assume the government budget balance is zero (that is, G = T - TR). Suppose that at any given interest rate, consumers decide to decrease their saving by 2000 dollars. What is the new equilibrium interest rate and quantity of investment in the loanable funds market given this information?
c. Assume the government budget balance is zero, and the saving function is the same as it is in (a). Suppose businesses become very pessimistic about future profitability due to the financial crisis. Business executives decide to cut their investment spending by 50% at any given interest rate. Given this information, what is the new equilibrium interest rate and quantity of investment in the loanable funds market?
Now suppose that the government decides to run a deficit equal to $15,000. That is G - (T - TR) = 15,000. For this question assume that the government will finance the deficit by borrowing funds in the loanable funds market.
d. What is the new quantity of private investment and the new equilibrium interest rate in this market?
e. Draw a graph of the loanable funds market illustrating both the initial situation and the effect of the government deficit described in part (d) of this problem. Label your graph clearly and completely.