a) A planner in a small, open economy has a utility function U = x1x₂ and production takes place according to the production functions y₁ = 10L₁ - 0.5L²2 Y2= 10L₂ - L2 10 and P2 The world prices of the goods are p₁ = available in the economy is 5 units. (i) (ii) = 5. The total amount of labour Formulate the Lagrange equation. Write down the Karush-Khun-Tucker conditions.

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a) A planner in a small, open economy has a utility function
U = x1X2
and production takes place according to the production functions
Y1 =
10L, – 0.5L?
Y2 = 10L2 – L
The world prices of the goods are p1 = 10 and p2 = 5. The total amount of labour
available in the economy is 5 units.
(i)
Formulate the Lagrange equation.
(ii)
Write down the Karush-Khun-Tucker conditions.
(iii)
Determine a possible solution.
Transcribed Image Text:a) A planner in a small, open economy has a utility function U = x1X2 and production takes place according to the production functions Y1 = 10L, – 0.5L? Y2 = 10L2 – L The world prices of the goods are p1 = 10 and p2 = 5. The total amount of labour available in the economy is 5 units. (i) Formulate the Lagrange equation. (ii) Write down the Karush-Khun-Tucker conditions. (iii) Determine a possible solution.
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