Urban Economics Lab Assignment

1) Assume that your metropolitan area has an aggregate private industry production function which follows a constant returns to scale Cobb-Douglas form: VA_i = AK_i^α L_i^1-α, where VA is real private metropolitan value-added, A is the autonomous growth factor, K is metropolitan capital, L is private metropolitan hours worked (a measure of labor), and α is an exponent. The subscript i refers to your metropolitan area.

1) Using the equation of growth:

ΔVA_i/VA_i = ΔA/A + E_K*ΔK_i/K_i + E_L*ΔL_i/L_i,

(where E_K is the elasticity of private value-added with respect to capital and E_L is the elasticity of private value-added with respect to private labor) and data available online for the years 2007 and 2016, estimate the cumulate percent growth in capital in your metropolitan area from 2007 through 2016.

To make the estimate, obtain data on real private value-added in your metropolitan area in 2007 and 2016 from the U.S. Bureau of Economic Analysis website (Real GDP in Chained Dollars) and data on private metropolitan employment and private weekly hours worked (used to calculate annual private hours worked) in 2007 and 2016 from the U.S. Bureau of Labor Statistics website. Assume that the value of the exponent α is 0.5 and the cumulative growth rate of the autonomous growth factor (ΔA/A) is 2% from 2007 through 2016. Show your work in calculating the estimate and the data you use to make your calculation.

2) Compare the growth rate of annual private hours worked in your metropolitan area between 2007 and 2016 with the national growth rate. What factors (focusing on factors discussed in this course) might have caused private hours worked to grow as it did in your metropolitan area?