Please explain steps to formulate the equation in (i) a) A planner in a small, open economy has a utility functionU = x1X2and production takes place according to the production functionsY1 =10L, – 0.5L?Y2 = 10L2 – LThe world prices of the goods are p1 = 10 and p2 = 5. The total amount of labouravailable in the economy is 5 units.(i)Formulate the Lagrange equation.(ii)Write down the Karush-Khun-Tucker conditions.(iii)Determine a possible solution.

In economics, a utility function is a term that expresses how satisfied or happy a person is after…

Answered: A planner in a small, open economy has…

A planner in a small, open economy has a utility function U = X1X2 and production takes place according to the production functions

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please explain steps to formulate the equation in (i)

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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Step 1: Define utility function and production function:

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Step 2: Calculate Lagrange function:

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Step 3: Determine Karush-Khun-Tucker condition:

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Step 4: Determine possible solution:

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