Let α represent labor's share of total output.The Solow residual is,therefore,represented by
A)αgᵧ.
B)αgA.
C)αgK.
D)αgN.
E) 1 / α.

Question

Quizplus · Accepted Answer

The Solow residual is represented by the formula y = Ak^αn^(1-α), where A represents technology, k represents capital stock, n represents labor input, and α represents the share of output going to labor. Taking the natural logarithm of both sides and differentiating with respect to time, we get: 
(1/ y) (dy/dt) = (1/ A) (dA/dt) + α (dk/dt)/k + (1-α) (dn/dt)/n 
The term (1/ A) (dA/dt) represents the growth rate of technology, which is exogenous and not explained by the inputs used in production. The other two terms represent the contributions of capital and labor inputs to output growth. Dividing both sides by α and rearranging, we get: 
(y/α) (dy/dt) = (gA) + (gK) 
where gA = (1/ α) (dA/dt) represents the exogenous component of growth (not explained by capital and labor inputs), and gK = α (dk/dt)/k + (1-α) (dn/dt)/n represents the endogenous component of growth (explained by capital and labor inputs). Therefore, the Solow residual is equal to αgA, which is choice (B).

Let α Represent Labor's Share of Total Output