Answer to Question #96130 in Microeconomics for Subam thapa

Question

Suppose that a firm’s production function is given by Q = KL + K, with MPK = L + 1 and MPL = K. At point A, the firm uses K = 3 units of capital and L = 5 units of labor. At point B, along the same isoquant, the firm would only use 1 unit of capital. a) Calculate how much labor is required at point B.
b)calculate the elasticity of substitution between A and B.Does this production function exhibit a higher or lower elasticity of substitution than a Cobb -Douglas function over this range of inputs?
I need the diagram also

Answer 1

a) At point A: Q = 3×5 + 3 = 18 units.

If at point B, along the same isoquant, the firm would only use 1 unit of capital, then Q = 1L + 1 = 18,

L = 17 units of labor is required at point B.

b) Elasticity of factor substitution is defined as the proportionate change in the factor- proportions to the proportionate change in the marginal rate of technical substitution, so that the output remains the same.