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Dottorato di Ricerca in Economia Politica, XIX ciclo

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Dottorato di Ricerca in Economia Politica, XIX ciclo

Microeconomics: production and cost functions May 4th, 2017

Given the production function:

q = 100 [0.6L ρ + 0.4K ρ ]

1ρ

Where q is total production, L is labor utilisation and K capital utilisation.

Write the general formula for the marginal rate of technical substitution and the elasticity of substitution.

Condider the three cases:

a ρ = 1 b ρ → 0

c ρ → −∞

In the three cases:

1. write the production function;

2. compute the marginale rate of technical subsitution (MRTS);

3. given w and r the unitary cost of labor and capital, compute the con- ditional demand function for L and K;

4. compute the total cost function, the average cost function and the marginal cost function.

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