probset1

# probset1 - Problem Set 1 EC720.01 Math for Economists...

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

Problem Set 1 EC720.01 - Math for Economists Peter Ireland Boston College, Department of Economics Fall 2009 Due Thursday, September 17 1. Proﬁt Maximization Consider a ﬁrm that produces output y with capital k and labor l according to the technology described by k a l b y, (1) where 0 < a < 1, 0 < b < 1, and 0 < a + b < 1. The ﬁrm sells each unit of output at the price p , rents each unit of capital at the rate r , and hires each unit of labor at the wage w . Hence it chooses y , k , and l to maximize proﬁts py - rk - wl subject to the constraint just shown in (1). a. Set up the Lagrangian for this problem, letting λ denote the multiplier on the constraint. b. Next, write down the conditions that, according to the Kuhn-Tucker theorem, must be satisﬁed by the values y * , k * , and l * that solve the ﬁrm’s problem, together with the associated value λ * for the multiplier. c. Assume that the constraint binds at the optimum (can you tell under what conditions this will be true?), and use your results from above to solve for

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

View Full Document
This is the end of the preview. Sign up to access the rest of the 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 / 2

probset1 - Problem Set 1 EC720.01 Math for Economists...

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

View Full Document
Ask a homework question - tutors are online