Suppose that an econometric study tells you that the following production function y=f(x1, x2) = xP 1× -P2 predicts well the behavior of the production side of the economy, where input 1 represents labor, input 2 represents capital, the output represents all consumer goods, and B E (0,1). Let w represent the price of labor and r the price of capital goods, and normalize the price of consumer goods to 1. (a) Write down an expression for the technical rate of substitution. (b) What happens to the ratio of labor costs to capital costs, WX1/rx2, if the price of labor over capital w/r increases? (C) Find the corresponding cost and pro fit functions. (d) Find the supply function for consumer goods.

Suppose that an econometric study tells you that the following production function y=f(x1, x2) = xP 1× -P2 predicts well the behavior of the production side of the economy, where input 1 represents labor, input 2 represents capital, the output represents all consumer goods, and B E (0,1). Let w represent the price of labor and r the price of capital goods, and normalize the price of consumer goods to 1. (a) Write down an expression for the technical rate of substitution. (b) What happens to the ratio of labor costs to capital costs, WX1/rx2, if the price of labor over capital w/r increases? (C) Find the corresponding cost and pro fit functions. (d) Find the supply function for consumer goods.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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