ECONOMICS 301 PROBLEM SET 2

# ECONOMICS 301 PROBLEM SET 2 - ECONOMICS 301 PROBLEM SET 2...

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ECONOMICS 301 PROBLEM SET 2 BYUNG-CHEOL KIM SPRING 2007 This problem set will be collected at the beginning of March. 21, 2007 (Wed) class with no excuse. The grade for this problem set is worth of 5% for your total grade. You can work on this paper or separate papers. Name: Last First ID# 1. A paper company dumps non-degradable waste into a river that flows by the firm’s plant. The firm estimates its production function to be: Q=6KW where Q = annual paper production measured in pounds, K = machine hours of capital, and W = gallons of polluted water dumped into the river per year. The marginal products of capital and labor are given as follows: MPk=6W, MPl =6K The firm currently faces no environmental regulation in dumping waste into the river. Without regulation, it costs the firm \$7.50 per gallon dumped. The firm estimates a \$30 per hour rental rate on capital. The operating budget for capital and waste water is \$300,000 per year. a. Determine the firm’s optimal ratio of waste water to capital. We want MP K /P K = MP W /P W , where P w is the price of labor and P k the price of capital. Graphically,   At the point shown on the graph, the optimality condition is 6W/30 = 6K/7.5 or  K = .25 W, so that W/L = 4.  Note that water dumping and machine hours have

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the same marginal productivity (at the same levels of input).  However, capital  is 4 times as expensive as dumping water.  As a result we will always dump 4
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## This note was uploaded on 03/19/2008 for the course ECON EC 301 taught by Professor Byung-cheolkim during the Spring '08 term at Michigan State University.

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ECONOMICS 301 PROBLEM SET 2 - ECONOMICS 301 PROBLEM SET 2...

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