Can you please explain what to do with p1=10 and p2=5 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. a) The lagrangian expression for the same is given by:Z=x1x2 + 21 (yı – 10L1 + 0. 5L¡²) + 2 (y2 – 10L2 + L2²)-where,21, 22 is the lagrangian multipliers

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Can you please explain what to do with p1=10 and p2=5

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

Can you please explain what to do with p1=10 and p2=5

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.

a) The lagrangian expression for the same is given by:
Z=x1x2 + 21 (yı – 10L1 + 0. 5L¡²) + 2 (y2 – 10L2 + L2²)
-
where,
21, 22 is the lagrangian multipliers

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