Homework 3-

1. In this question you are asked to calculate the CPI and inflation rate in 4 different ways, varying the choice of the market basket and of the base year. Then you are asked to compare the results you calculated. Assume consumers in Badger Land only consume pears and watermelons. The following table provides the quantities produced and prices in 2005 and 2006.

 (a) Using the quantities produced in 2005 as the market basket and using 2005 as the base year, calculate the CPI in 2005 and 2006.  Calculate the inflation rate between 2005 and 2006.

(b) Using the quantities produced in 2006 as the market basket and using 2005 as the base year, calculate the CPI in 2005 and 2006.  Calculate the inflation rate between 2005 and 2006

(c) Using the quantities produced in 2005 as the market basket and using 2006 as the base year, calculate the CPI in 2005 and 2006.  Calculate the inflation rate between 2005 and 2006. 

(d) Using the quantities produced in 2006 as the market basket and using 2006 as the base year, calculate the CPI in 2005 and 2006.  Calculate the inflation rate between 2005 and 2006 

(e) Explain whether there is any substitution bias in the CPI depending upon the choice of market basket and base year.

2. Suppose that the demand for labor in Badger Land is characterized by the equation w = 170 - L while the supply of labor is given by w = 8 + L, where w is the wage per year and L is the number of labor units per year.

(a) What is the equilibrium level of employment per year and the equilibrium wage rate in Badger Land?

(b) Suppose the aggregate production function is given by Y = 2*(K^0.5)*(L^0.5), where K is physical capital and it is fixed at K=100 now. What is the full employment output for this economy?

(c) What is the value of labor productivity for Badger Land if it produces the full employment level of output? Labor productivity is defined as the level of aggregate output in the economy divided by the level of labor.

(d) 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?

(e) Now, assume that the labor demand and labor supply curves are the originally given curves (there has been no shift in labor demand). But, the physical capital available to this economy has been increased to K=196 due to capital accumulation. Re-compute the full employment level of output and labor productivity, given labor demand w = 170 - L and supply w = 8 + L.

(f) Using the answers found above, how does an increase in the capital stock affect output and labor productivity? 

3. Using a graph of the labor market and a graph of an aggregate production function, explain by graphs and words what happens for the following cases. Be sure to identify what happens to the level of employment, wage rate, output 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. Badgerland statistics is summarized in the table below.

 (a) Compute the inflation rate from 2005 to 2006.

(b) Compute the growth rate of GDP deflator from 2005 to 2006.

(c) Explain the reason of your result difference (if any) in (1) and (2).

5. Now it is time to do a combined exercise of CPI and long run growth model. In Macroland, competitive firms use capital and labor to produce Playstation 3. The production function is given by Y = 2*(K^0.5)*(L^0.5), where K is physical capital fixed at K=225 and L is the labor employed by firms. Labor supply is w = 8 + L in both 2005 and 2006, while labor demand switches from w = 170 - L in 2005 to w=208 - L in 2006. CPI in 2006 is 110 give 2005 as base year. The price of Playstation 3 increases from $100 in 2005 to $120 in 2006.

(a) Compute the nominal equilibrium wages and employment levels in 2005 and 2006.

(b) Compute the real equilibrium wages in 2005 and 2006.

(c) Compute the full employment output levels and corresponding nominal values of aggregate production in 2005 and 2006.

(d) Compute the real values of aggregate production in 2005 and 2006.

(e) Compute labor productivities under full employment level in 2005 and 2006.

(f) Compute nominal and real wage growth rates, and nominal and real product value growth rate.

(g) Explain your results in (6), considering the force of growth, and the difference between nominal and real growth rates.