Question: For the shadow - wage - rate model, let ( p _ { 1 } = 1 , p _ { 2 } =

For the shadow

-

wage

-

rate model, let

\ (

_{1} = 1,

_{2} = 2,

_{1} = 100,

_{2} = 50 \) \ (

= 0.5 \),

and

\ (

^{0} = 1000 \) .

Calculate the optimal labor allocations, outputs, and the shadow wage rate. Write out the value function and confirm the results for the derivatives of this function numerically.

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