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Homework answers / question archive / Derive the total, average and marginal long run cost functions for the production function F (L, K) = K + L, if input prices are wk = 3 and wL = 5

Derive the total, average and marginal long run cost functions for the production function F (L, K) = K + L, if input prices are wk = 3 and wL = 5

Economics

Derive the total, average and marginal long run cost functions for the production function F

(L, K) = K + L, if input prices are wk = 3 and wL = 5.

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Production function = F(L, K)= K + L

the Marginal rate of Technical Substituiton(MRTS) = MPL/MPk = 1 (MP = Marginal Product )

wL/wK   = 5/3 as, MPL/MPk <  wL/wK ( wL ,  wK  are the input prices)

Hence, the firm will make use of capital(c) and they will avoid the usage of labour(L).

C= wKK

let us now take from the production function:

Q = K

1 a) Total long run cost   C = 3Q

1 b) Average long run cost TC/Q = 3Q/Q = 3

1 c) Marginal long run cost dTC/dQ =3