a) A planner in a small, open economy has a utility functionU = x1X2and production takes place according to the production functionsY1 = 10L, – 0.5LY2 = 10L2 – LThe world prices of the goods are p110 and p25. The total amount of labour%|%3Davailable 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 utility function represents consumer’s preferences for a set of goods and services…

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 - L²2 The world prices of the goods are p₁ = 10 and P2 available in the economy is 5 units. (i) (ii) (iii) = 5. The total amount of labour Formulate the Lagrange equation. Write down the Karush-Khun-Tucker conditions. 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 - L²2 The world prices of the goods are p₁ = 10 and P2 available in the economy is 5 units. (i) (ii) (iii) = 5. The total amount of labour Formulate the Lagrange equation. Write down the Karush-Khun-Tucker conditions. Determine a possible solution.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

show all working.
Please explain steps to formulate the equation in (i)
Suppose that Flamerock Tires must decide where to produce one million tires: the US, where wages are 30 and the cost of capital is 5; or China, where wages are 5 and the cost of capital is 25. Production in each location follows the same technology (production function) given by: Q = f(L, K) = L^0.25 K^0.75 Computationally solve the cost - minimizing input levels in each location to produce the goal of 1 million tires
The quantity, Q, of a certain product manufactured depends on the quantity of labor, L, and of capital, K, used according to the function 0 = 900LK¹³. Labor costs $100 per unit and capital costs $50 per unit. What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost? Round your answers to two decimal places.
Problem 2: Production economy Consider a production economy with two firms, X and Y, and two factors of production, labor and capital. Firm X produces the output good X with a technology that can be de- scribed by the following production function: fx(lx, kx) = lx + kx, where lx is the quantity of labor and kx is the quantity of capital. Firm Y produces the output good Y with a technology that can be de- scribed by the following production funetion: fr(ly, ky) = y + VAy, where ly is the quantity of labor and ky is the quantity of capital. The economy has a total endowment of labor L > 0 and a total endowment of capital K = L. The price of the good X is p > 0 and the price of good Y is q = 1. These output prices are determined on international markets and are not affected by the supply decisions of the firms. (a) Find the set of production efficient allocations in this economy. Illus- trate the set of efficient factor allocations in a Bowley box diagram. Describe and illustrate the…
Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost - minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale?f. The pharmacy plans to produce 40,000 prescriptions per week. At the…
Suppose that the economy's production function is given by Y=K²N¹-a where Y is output, K is capital, and N is labor. Assume that a = 1/3. The production function transformed into output per worker is (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with N character.)
!
Please solve b,c and d.
Problem B: The Production Model Consider the production model that we have seen in class with a production function for final output specified as Y = K1/4L3/4 Capital and labor available in the economy are, respectively, K = 40 and L = 50. B.1 Write down the profits maximization problem for firms in the production model (you can write profits in units of final output). Derive the first order conditions for the firm's maximization problem and provide the economic interpretation of the first order condition for labor. B.2 Please define the property of "Constant Returns to Scale" as we did in class. Does the production function above exhibit constant returns to scale? Show your computations. B.3 State the equations that constitute the competitive general equilibrium for the economy in the production model above. What are the variables that you need to solve for to obtain a solution to the equilibrium?
Consider an economy that has a labor endowment of L = 40 units. The production functions are x = 0.5L, and y = 4Ly, where x and y are consumption goods while L, and Ly represent the labor allocation. What is the equation for the PPF? 8x + y = 160 6x + 2y = 80 6x + y = 120 8x + 2y = 80
Which situation would most likely cause a nation's production possibilities curve to shift inward? The construction of more capital goods An increase in discrimination based on race An increase in the number of skilled immigrant workers The destruction from bombing and warfare in a losing military conflict