Answer to Question #222462 in Macroeconomics for Ike

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 country's 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 the residual (a) equals 0, the annual labor force growth rate (g_L) equals 2.7%, the annual capital stock growth rate equals 1.8% (g_K), and labor’s share of national income (w_L) is 45% while capital’s share of national income (w_K) is 40%, then the growth rate of national income (g_Y) is:

$g _Y=a+(w_k\times g_k)+w(w_L\times g_L)\\=0+(0.40\times 0.018)+(0.45\times0.027)=0.01935=1.93\%$

b)

In this case, the growth of the inputs (capital and labor) is insufficient to explain the growth of the economy. The difference between the growth rate and the sum of the weighted factor growth rates is the residual (a). This residual can be calculated using the same equation as in part a:

$4.5\%=0.045=g_Y=a+(w_k\times g_k)+w(w_L\times g_L)\\=a+(0.40\times0.018)+(0.45\times0.027)$

Simplifying and solving this equation for a: . Thus, the residual equals -0.02565.