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Consider the cost function

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Dottorato di Ricerca in Economia Politica, XVIII ciclo

Microeconomics: production and cost functions March 21st, 2019

Consider the cost function

ln C(y, w, r) = (α ln y + β ln w + γ ln r)

θ

,

where y is the production (output), while w and r are the costsof inputs, namely the salary and and the cost of capital.

1. Is it possible to assign specific values to all parameters in order to obtain a translogari- thmic cost function?

YES, the parameters should be

α > , β > , γ > , θ = .

NO, because

2. Set θ = 1 and prove that the above function exhibits constant return to scale when α = 1 3. Set θ = 1 and tick the cases where the [ ln C(y, w, r) ] cannot be a cost function:

α > 1, β + γ > 1, γ = 1.5 β + γ < 0.5 α = 0.01 4. Set θ = 1 and tick the conditions that must be respected for being [ ln C(y, w, r) ] a cost

function

β = 1, γ + β = 1 α = 1 5. Set θ = 1. Given [ ln C(y, w, r) ], compute C(y, w, r).

Assume perfect competion, with p the price of the output. Write the profit function.

π(p, y, w, r) =

1

(2)

6. Which restriction on parameters must be set in order to have a profit maximising plan?

Restriction: =

7. Write the maximum profit function, π(p, w, r).

π(p, w, r) =

8. Compute the elasticity of profits to price.

ε

π,p

= .

2

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