Consider a firm which produces a good, y, using two inputs or factors of product

Question

Consider a firm which produces a good, y, using two inputs or factors of production, x1 and x2. The firm's production function describes the mathematical relationship between inputs and output, and is given by BER (1) x1,x2 1- 23 (a) Derive the degree of homogeneity of the firm's production function. (4 marks (b) The set yo (2) x1,x2 is the set of combinations of Cx1x2) which produce output level yo Economists refer to S as the isoquant associated with output level yo.The isoquant implicitly defines x2 as a function of x1. i) Use implicit differentiation to derive the slope of the isoquant x1x2 yo That is, derive dx 1 (Note that along a given isoquant Ay 0). ii) Use implicit differentiation to derive d2x2 for the isoquant x1x2 yo iii) What conclusions do you draw regarding the slope and curvature of the isoquant? Briefly explain. 8 marks

Explanation / Answer

a) Degree of homogenity is calculated as degree of t in f(tx1, tx2) as multiple of f(x1,x2) . Here it is clear that f(tx1, tx2) = tlpha + eta (f(x1,x2)). Hence degree of homogeneity is lpha +eta .

(Other questions are independent from this question and according to policy of chegg I can solve only one question unless it has some parts.)

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