probset1

probset1 - Problem Set 1 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
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online