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Given the production function Y=AK^{^{\alpha }}L^{_{1-\alpha }} , if the rental price of capital is 0.133, Y=690, and K=1,728, what is the value of the exponent \alpha ? If A=1, and the real wage is 1.15, is this economy in a long-run equilibrium?

I know rental price of capital equals the marginal product of capital, but I have no idea how to solve MPK, and progresses afterward.

Please give your solution in detail.

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Answer #1

Date Y = AK? (1-2 Rental price of capital (c) = 0.133 K = 178 e = MPK + Osunan vnitas MP k ayo svako lagunen Y = 690 & . 1. dLong run MPL M PK equilibrium condition = we e To findd MPL MP = 24 IL Aka (1-0) T-a-X AK (1-x) L- = = MP MPK(1-x) AK* L-a. PhotoGrid - CÁ ký- |- - |- 0.133 II-a K X-K+1 +1 = d.15 o rate 00123 = K L - Put 1.15 X o.133 x=0.333 60 333 (Long run MPL M PK equilibrium condition = we e To findd MPL MP = 24 IL Aka (1-0) T-a-X AK (1-x) L- = = MP MPKLong run MPL M PK equilibrium condition = we e To findd MPL MP = 24 IL Aka (1-0) T-a-X AK (1-x) L- = = MP MPK(1-x) AK* L-a. PhotoGrid - CÁ ký- |- - |- 0.133 II-a K X-K+1 +1 = d.15 o rate 00123 = K L - Put 1.15 X o.133 x=0.333 60 333 (

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