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Midterm Review

# Midterm Review - ECON 101 Midterm Review Math Review •...

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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 Can’t 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 p’x1 +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

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o Ad valorem tax p 1 (1+ τ )x 1 +p 2 x 2 = m Tax revenue collected: τ 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 2) CONVEXITY averages are preferred to extremes

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Midterm Review - ECON 101 Midterm Review Math Review •...

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