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calculate the elasticity of substitution

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Dottorato di Ricerca in Economia Politica, XIX ciclo

Microeconomics: production and cost functions July 3rd, 2018

Given the production function

q =√ L +√

K,

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

1. classify the above function

Cobb-Douglas CES Translog Diewert other

2. calculate the marginale rate of techincal substitution.

MTRS(L, K) =

3. calculate the elasticity of substitution.

σ =

4. calculate the elasticity of scale (ε) and say if the returns to scale are increasing/constant/decreasing.

ε =

decreasing R.S. constant R.S. increasing R.S.

5. suppose that the cost of labour (the salary) is w = θr, where r is the unitary cost of capital, and θ is a scalar. Compute the value of the salary for which the marginal cost is linear with slope 1.

w =

1

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