a) A planner in a small, open economy has a utility functionU = x1x2and production takes place according to the production functionsY1 = 10L, – 0.5L?Y210L2 – L3The world prices of the goods are p110 and P25. 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.b) Let aggregate national income be given byY; = C; + It + G;Where C, I and G are consumption, investment and government expenditure. Assumethat consumption is given byC = mY;%3DInvestment is given byI; = i + «(Y¢-1– Y;-2)%3DAnd government expenditure declines over time according toG¢ = Go(1 – 8)*,0 < 8 < 1Where 8 is the exogenous rate of decline of government expenditure(i)Derive the linear second order difference equation.(ii)Solve the difference equation.

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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 = 10L₁ - 0.5L² Y₂ = 10L₂ - L2 The world prices of the goods are p₁ = 10 and p₂ = 5. The total amount of labour available in the economy is 5 units. (1) Formulate the Lagrange equation. (ii) Write down the Karush-Khun-Tucker conditions. (iii) Determine a possible solution.

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 - 0.5L² Y₂ = 10L₂ - L2 The world prices of the goods are p₁ = 10 and p₂ = 5. The total amount of labour available in the economy is 5 units. (1) Formulate the Lagrange equation. (ii) Write down the Karush-Khun-Tucker conditions. (iii) Determine a possible solution.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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