Hw 1 - f- Write the constraint(s). g- Write the inequality...

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1 Problem Set 1 Please write legibly and show all your work. THE DUE DATE OF THIS PROBLEM SET IS JANUARY 28. 1- ChapelJet is a commercial aircraft manufacturer. The factors of production of this production process are labor and capital. If ChapelJet hires L units of labor and rents K units of capital, it can produce up to L 1/2 K 1/2 units of aircraft. Hence, the production function is f(L,K)= L 1/2 K 1/2 . Suppose ChapelJet wants to minimize total expenditures on the factors of production. However, to be able to survive in the hostile commercial aircraft market ChapelJet must produce at least 10 units of aircraft. Suppose the per unit price of labor, w, is $1 and the per unit price of capital, r, is $4. a- Identify the exogenous and the endogenous variables in this cost minimization problem. b- What is the objective function? c- What is the constraint on the cost minimization problem of ChapelJet? d- Form the Lagrangian. e- Find the first-order conditions with respect to L and K.
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Unformatted text preview: f- Write the constraint(s). g- Write the inequality constraint(s) for the multiplier(s). h- Write the complementary slackness condition(s). i- Find the optimal L and K. Econ 410 Spring, 2010 Baak Altan 2 2- Suppose the market demand for mineral water in the United States is given by I P P Q bw mw mw d 20 5 15 35 where mw P is the price for mineral water, bw P is the price for bottled water, and I is the average consumer income. The market supply curve for mineral water in the United States is given by T P Q mw mw s 5 10 30 where T is the total import tax on mineral water. Assume that 2 I dollars, 3 T dollars and 1 bw P dollar. a- What are the equilibrium price and quantity in this market? b- At the equilibrium values calculate the price elasticity of demand. c- At the equilibrium values calculate the income elasticity of demand. d- At the equilibrium values calculate the cross price elasticity of demand. Good Luck...
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This document was uploaded on 10/28/2011 for the course ECON 410 at UNC.

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Hw 1 - f- Write the constraint(s). g- Write the inequality...

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