Answer to Question #222324 in Macroeconomics for Collins

Question

Consider an economy in which the labour force grows by 2.7 percent per annum, physical capital grows by 4 percent per annum and human capital grows by 1.8 percent per annum. Suppose 45 percent of national income goes to labour and 40 percent to capital. Use a constant returns to scale production function to answer the following growth accounting questions:
(a) If the Solow residual were zero what rate of growth would the economy achieve?
(b) The countrys actual rate of growth has been 4.5 percent per annum, which is faster than the growth rate generated by the accumulation of capital and labour stocks. Calculate the value of the residual.

Answer 1

a. If residual$(a)$ is equal to zero, annual labour force growth rate$(g_L)$ equals 2.7%, physical and human capital(gK​) equals 4% and 1.8% respectively ,and labors share of national income$(W_L)$ is 45% while capital share of national income $(W_K)$ is 40%

$g_Y=a+(W_K×g_K)+(W_L×g_L)=$0$+$ $($ 0.4$×$ 0.04$×$ 0.018$)$ $+$ $($ 0.45$×$ 0.027$)$ $=$ 0.012438

Economy will grow by 1.2%

b. Using the same equation as in question a:

$g_Y=a+(W_K×g_K)+(W_L×g_L)=$ 4.5%$=$ 0.045$=$ a$+$ $($ 0.4$×$0.04 $×$ 0.018$)$ $+$ $($ 0.45$×$ 0.027$)$

0.045$=$ a$+$ 0.012438

a$=$ 0.032562