Question

Total production in Victoria is described by the production function Yt At (Kt)a (Lt) ¹-a where At is total factor productivity, L₺ is labour, and K₁ is capital. Let a = 0.5. Assuming that the growth rate of per capita capital stock is equal to 2 percent and that the growth rate of per capita output is equal to 1 percent, the growth rate of total factor productivity is

1 percent
0.5 percent
2 percent O
0 percent

Answer 1

According to the given production function, Yt = At(Kt)^(a)(Lt)^(1-a)............(1)Given, a = 0.5Let the per capita capital stock is denoted by kt and the per capita output is denoted by yt, i.e.,Kt = K/L and Yt = Y/L Substituting these values in equation (1), we get: Yt/L = At(Kt/L)^(a)(Lt/L)^(1-a)Yt/L = At(Kt/L)^(0.5)(1/L)^(0.5)Yt/L = At(Kt/L)^(0.5) --------------- (2)Taking the logarithm on both sides of equation (2), we get:ln(Yt/L) = ln(At) + 0.5 ln(Kt/L)Hence, we can define the equation for the growth rate of per capita output as:gt = (1/t)Δ ln(Yt/L) = (1/t)Δ ln(At) + 0.5(1/t)Δ ln(Kt/L)Given, the growth rate of per capita capital stock is 2% i.e., Δ ln(Kt/L) = 2% = 0.02Given, the growth rate of per capita output is 1% i.e., Δ ln(Yt/L) = 1% = 0.01Substituting the given values in the above equation, we get:(1/t)Δ ln(At) = (0.01 - 0.5(0.02)) = -0.005So, the growth rate of total factor productivity is 0.5 percent.Option (B) 0.5 percent is the correct option.