This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: ECON 101 Midterm Review Math Review Second Derivatives o Tells us how first derivative changes as x varies o If negative, function is at a maximum o If positive, function is at a minimum Slopes of Level Sets o Level set: f(x,y)=c for some constant c o Sometimes can solve y=g(x,c) o Slope of level set = dg/dx Implicit Functions o Cant solve f(x,y)=c for y as a function of x Example: f(x,y)=xy 2 + x 2 ln(y) o Can still find slope of level set o Dy/dx=-fx/fy Budget Sets and Preferences A bundle (x 1 ,x 2 ) costs p 1 x 1 +p 2 x 2 = c Bundle is affordable if c< m o p 1 x 1 +p 2 x 2 < m Budget Constraint: p 1 x 1 +p 2 x 2 = m o Along the budget constraint line, consumer spends all money ***Graph: intercepts at m/p 2 and m/p 1 o Slope = -p 1 /p 2 Normalizing Prices o p 1 x 1 +p 2 x 2 = m o Divide by p 2 : (p1/p2)x1 + x2 = m/p2 Or px1 +x2=m Where p=(p1/p2) and m=(m/p2) o x2 is called the numeraire good Effects of Inflation o Initial budget: p 1 x 1 +p 2 x 2 = m o All prices and income double: 2p 1 x 1 +2p 2 x 2 =2 m o Yields same RELATIVE prices and income Income increases budget line shifts out Single price change Slope of budget line changes Tax on Good 1 o Original budget line: p 1 x 1 +p 2 x 2 = m o Quantity Tax (p 1 + t)x 1 +p 2 x 2 = m Tax revenue collected: tx 1 o Ad valorem tax p 1 (1+ )x 1 +p 2 x 2 = m Tax revenue collected: p 1 x 1 Rationing: consumption of good 1 restricted to be less than x bar o ***See graph Budget Kinks o Tax consumption of good 1 greater than x bar Slope of budget line changes after x bar o Food Stamps *** See graph o Income Tax No tax: budget constraint: c=y (45 degree line) Tax inclusive budget constraint: slope changes ***See graph (c,y) o Earned Income Tax Credit (EITC) ***See graph Preferences and Utility PREFERENCES Preferences: description of the RELATIVE utility of different bundles of goods Comparing two bundles X=(x 1 ,x 2 ) and Y= (y 1 ,y 2 ) o ***review symbols o X~Y: consumer is indifferent between X and Y Assumptions about Preferences o 1) Preferences are COMPLETE o 2) Preferences are REFLEXIVE o 3) Preferences are TRANSITIVE o ***Review in notes At-Least-as-good-as Sets o ***See graph in notes Indifference curve: Level set of utility functions o Indifference curves cannot cross o Examples: Perfect Substitutes: Indifference curves are straight lines Perfect Complements: Indifferences curves are L shaped Goods and Bads Satiation ***See graphs Properties of Preferences o 1) MONOTONOCITY more of one good, and not less of another, makes one better off indifference curves slope down and to the right o...
View Full Document
This note was uploaded on 05/01/2008 for the course ECON 101 taught by Professor Jack during the Spring '08 term at Georgetown.
- Spring '08