The total cost function of a firm is given by:Where q is total output, W and V are unit prices of labour (L) and capital (K) respectivelya. Find the conditional input demands for labour (L) and capital (K)b. From your result in (a), derive the underlying production function for qConsider a firm that produces cars with the following production function:q = min(ak, bL)a. Find the Marginal Rate of Technical Substitution of labour for capital for this firmb. If per unit prices of capital (K) and labour (L) are r and w respectively, find the inputdemand functions for K and L; as well as the long run cost functionc. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm)

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The total cost function of a firm is given by: C = q(W)¹³(V) Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively a. Find the conditional input demands for labour (L) and capital (K) b. From your result in (a), derive the underlying production function for q

The total cost function of a firm is given by: C = q(W)¹³(V) Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively a. Find the conditional input demands for labour (L) and capital (K) b. From your result in (a), derive the underlying production function for q

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Chapter1: Making Economics Decisions

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Problem 1QTC

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Question

The total cost function of a firm is given by:
Where q is total output, W and V are unit prices of labour (L) and capital (K) respectively
a. Find the conditional input demands for labour (L) and capital (K)
b. From your result in (a), derive the underlying production function for q
Consider a firm that produces cars with the following production function:
q = min(ak, bL)
a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm
b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input
demand functions for K and L; as well as the long run cost function
c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm)

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