probset4

probset4 - Problem Set 4 EC720.01 - Math for Economists...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem Set 4 EC720.01 - Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Thursday, October 8 The two welfare theorems of economics tell us that optimal and equilibrium resource alloca- tions coincide but only under certain conditions. Sometimes when market failures prevent the theorems from holding, however, government policy can help improve equilibrium out- comes, as the questions below reveal. 1. Optimal Allocations Consider an economy in which output is produced with capital k and labor (hours worked) h according to the Cobb-Douglas specification k h 1- , where 0 < < 1. In this static model, the capital stock k is taken as given, but hours worked h and consumption c are chosen by a benevolent social planner in order to maximize the utility ln( c )- h of a representative consumer, where ln denotes the natural logarithm. Hence, an optimal resource allocation solves the problem max h,c ln( c )- h subject to k h 1- c. Find solutions for the optimal choices for h and c in terms of the parameters k and . 2. Equilibrium Allocations Now consider the same economy, but where perfectly competitive markets for inputs and outputs replace the social planner in allocating resources. a. Now, the representative consumer (standing in for a large number of identical consumers) is endowed with k s units of capital, and chooses labor supply h s and consumption c to maximize utility subject to a budget constraint, that is, to solve max h s ,c ln( c )- h s subject to rk s + wh s c, where r is the rental rate for capital, w is the wage rate for labor, and output is the economys numeraire, so that the price of consumption equals one and all other prices are expressed in real terms. Find solutions for the optimal choices ofprices are expressed in real terms....
View Full Document

This note was uploaded on 02/19/2010 for the course ECON 720 taught by Professor Ireland during the Fall '09 term at BC.

Page1 / 3

probset4 - Problem Set 4 EC720.01 - Math for Economists...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online