Consider a firm minimising the cost of production under the following Cobb-Douglas production technology constraint: q = KL where q is the output level, K is the quantity of capital used and L is the quantity of labour used. Let w be the wage rate and r be the rental rate of capital. 31. The Lagrangean for this optimisation problem is: a) wL + rK + µ[q – KL] b) KL – [wL + rK] c) wL + rK + µ[KL] d) wL + rK + µ[q – K¢L²-«] 32. The demand function for capital obtained from the cost minimisation problem would be: a) K = L" b) K = ]q. c) K = ? d) K = qla" 1-a

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please answer the both questions 31,32!!!!!

For Questions 31 and 32, use the following information:
Consider a firm minimising the cost of production under the following Cobb-Douglas
production technology constraint:
q = KL
where q is the output level, K is the quantity of capital used and L is the quantity of labour
used. Let w be the wage rate and r be the rental rate of capital.
31. The Lagrangean for this optimisation problem is:
a) wL + rK + µ[q – KL]
b) KL – [wL + rK]
c) wL + rK + µ[KL]
d) wL + rK + µ[q – KªL²¬«]
32. The demand function for capital obtained from the cost minimisation problem would be:
a) K = L"
b) K =
c) K = !
1-a
d) K = ql
Transcribed Image Text:For Questions 31 and 32, use the following information: Consider a firm minimising the cost of production under the following Cobb-Douglas production technology constraint: q = KL where q is the output level, K is the quantity of capital used and L is the quantity of labour used. Let w be the wage rate and r be the rental rate of capital. 31. The Lagrangean for this optimisation problem is: a) wL + rK + µ[q – KL] b) KL – [wL + rK] c) wL + rK + µ[KL] d) wL + rK + µ[q – KªL²¬«] 32. The demand function for capital obtained from the cost minimisation problem would be: a) K = L" b) K = c) K = ! 1-a d) K = ql
Expert Solution
Given information

Given information

q = KL  -----------> Production function

Where q is output level, K is the quantity of capital used and L is the quantity of labor used. 

-----

w is wage rate and r is rental capital

C = wL + rK   --------> Cost

 

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