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Juan Valdez owns a coffee farm in Colombia. His production function is:  f(x1​,x2​)=(x1​−1)^0.25 x2^0.5​   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 Juan wants to produce. (c)  Find Juan's cost function. (d)  What is the supply

Juan Valdez owns a coffee farm in Colombia. His production function is:  f(x1​,x2​)=(x1​−1)^0.25 x2^0.5​   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 Juan wants to produce. (c)  Find Juan's cost function. (d)  What is the supply

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Juan Valdez owns a coffee farm in Colombia. His production function is: 

f(x1​,x2​)=(x1​−1)^0.25 x2^0.5​

 

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 Juan wants to produce.

(c)  Find Juan's cost function.

(d)  What is the supply function of Juan's firm?

Juan Valdez owns a coffee farm in Colombia. His production function is: f(x₁, x₂) = (x₁ - 1)0.25 2.5. 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 Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?
Transcribed Image Text:Juan Valdez owns a coffee farm in Colombia. His production function is: f(x₁, x₂) = (x₁ - 1)0.25 2.5. 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 Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?
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