What is the long-run cost function if the production function is qequals=33Lplus+22K? Let the cost of each unit of L be w and the cost of each unit of K be r. The long-run cost function is A. C(q)equals=wplus+r. B. C(q)equals=(w/33)q if (w/33)less than or equals≤(r/22), and (r/22)q otherwise. C. C(q)equals=q. D. C(q)equals=wq if wless than or equals≤r, and rq otherwise. E. C(q)equals=(w/33)q if (w/33)greater than or equals≥(r/22), and (r/22)q otherwise.

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akindelemf akindelemf · Answer 1 · 2020-06-15T17:07:34+02:00

Answer:

C(q)equals=(w/33)q if (w/33)greater than or equals≥(r/22), and (r/22)q otherwise.

Step-by-step explanation:

The production function is q = 33L + 22K

Cost function is then, C = wL+ rK

Minimising the functions, we get:

σ = wL+ rK+ λ(q -33L -22K)

dσ/dL = w - λ33 = 0 ----------(1)

dσ/dK = r - λ22 = 0 -----------(2)

dσ/dλ = q -33L -22K ---------(3)

From equation (1) and (2)

w/r ⇒ λ33 / λ22 ⇒ ³³/₂₂

Or, w = r(³³/₂₂)

Substitute for 'w' in C

C = r(³³/₂₂)L + rK

C = r [(³³/₂₂)L + K]

Or, (³³/₂₂)L + K = C / r

So, C/r = q or r = C/q

recall that w = r(³³/₂₂)

∴ w = (³³/₂₂)C/q

So, cost function C = wL+ rK

Substitute for 'w' and 'r' in the equation