Q6 1. Juan Valdez owns a coffee farm in Colombia. His production function is:f (x1, x2) = (x1 – 1)0.25 x9-5.Assume the price of input 1 is r and the price of input 2 is w..(a) Write down an expression for the technical rate of substitution.(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juanwants to produce.(c) Find Juan's cost function.(d) What is the supply function of Juan's firm?2. Show that the profit function is convex in (p, w).3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x"with A > 0, a1, ¤2 > 0 and a1 + a2 < 1.4. Verify Hotelling's Lemma for the Cobb-Douglas production function with a1+a2 < 1.5. Find the supply function and the input demand functions for the CES productionfunction:f(r1, F2) = A(ax{ + (1 – a)x2)8/e,%3Dwhere A > 0, B > 0, 0 < a < 1, and 0 + p< 1.6. Find the profit function for the CES production function.7. Verify Hotelling's Lemma for the CES production function with B < 1.

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Answered: 1. Juan Valdez owns a coffee farm in…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Let's say we have a game called "guess 2/3 of the average," where players can choose any number x ∈ [0, 100]. 5% of players are at level N0, 40% at level N1, 35% at level N2, 15% at level N3, and 5% at level N4. Players at level N0 choose a number randomly, while players at higher levels choose a number according to their beliefs, which are as follows: players at higher levels believe that all other players are one level lower than themselves. (a) What will be the winning number and which level players will be the winners? (b) Under the assumptions of classical game theory, the mentioned version of the game "guess 2/3 of the average" has exactly one equilibrium, in which everyone chooses the number 0. Prove that this outcome is indeed a Nash equilibrium of the game.
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