The appendix to this chapter shows how data on output, capi- tal, and labour can be used to construct estimates of the rate of growth of technological progress. We modify that approach in this problem to examine the growth of capital per worker: Y = K/3 (AN)2/3 The function gives a good description of production in rich coun- tries. Following the same steps as in the appendix, you can show that: (2/3)8A = SY-(2/3)gn - (1/3)gk (8y8N) (1/3) (8K - 8N) where gy denotes the growth rate of Y, 8x is the growth rate of capital, and g, is the growth rate of the labour input. a. What does the quantity gygy represent? What does the quantity gk-gn represent? b. Your download of the Penn World Tables in Chapter 11 includes the information needed to calculate the compo- nents of the growth accounting formula in the appendix. That formula is: residual gy [agN+ (1+ a)gk] From the Penn World Tables, you can fill in the table below: Year 2000 Year 2014 YN K Share of Y labour N K Share of labour China United States Use rgdpo for output (2011 US dollars); emp for number of employees' labour input; ck for the capital stock (2011 US dollars). The share of labour is labsh. These values are copied directly from the Penn World Tables version 9. Calculate annual growth rates of these variables over the 14 years of available data and answer these questions: a. Is the ratio of K/N rising or falling in China? b. In the United States? c. Which country has the highest labour share? d. Which country has the largest residual? (Use the average labour share over the two years to calculate the residual.) e. What does that residual represent? f. Are you surprised by any of your results?