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ARE YOU IN YOUR ASSIGNED SEAT

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ARE YOU IN YOUR ASSIGNED SEAT

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    1. ARE YOU IN YOUR ASSIGNED SEAT? 1/4/2008 1

    2. ARE YOU IN YOUR ASSIGNED SEAT? A Yes B No C Don’t know 1/4/2008 2

    3. More problems? A yes B no 1/4/2008 3

    4. 1/4/2008 4 No Clicker (as of Yesterday)

    5. 1/4/2008 5 Announcements for Exam Week Extra O.H. posted on webpage. These are in addition to normal O.H. on syllabus Practice Midterm Posted Review Session Chem 1179 Fri 4-5:30 Bring ID to exam Please sit in assigned seat

    6. 1/4/2008 6 Review For Midterm 1

    7. 1/4/2008 7 Preferences Defined over bundles: (x1, x2) ?(x1’, x2’) Plot in coordinate system Monotonicity Indifference curves Marginal rate of substitution Slope of indif curve at a given bundle

    8. 1/4/2008 8 Utility U(x1,x2) “Represents” preferences Attaches a number to a bundle Indif curves are level curves of U(x1,x2) U(x1,x2) not a unique representation. Increasing transformations of U(x1,x2) represent same preferences It’s like renumbering indif curves

    9. 1/4/2008 9 Marginal Utility MU1(x1,x2)= : How much utility you get form one more unit of good 1. MU2(x1,x2)= : How much utility you get form one more unit of good 2. Depends on how much you already have of both goods Also depends on form of utility function

    10. 1/4/2008 10 Utility and Marginal Rate of Substitution To calculate MRS for differentiable utility function u(x1,x2): Diminishing MRS: As you go down an indif curve, slope gets flatter x1?x2? ? MRS ?

    11. 1/4/2008 11 Utility : Case 1 (Linear) U(x1,x2)=ax1+bx2 Goods are perfect substitutes Exxon gas, Mobil gas Coke, Pepsi

    12. 1/4/2008 12 Utility : Case 2 (Cobb-Douglass) U(x1,x2)=ax1ax2ß Diminishing MRS Describes many types of goods that are neither perfect subs nor perfect comps

    13. 1/4/2008 13 Utility : Case 3 (Leontief) U(x1,x2)=min[x1/a, x2/b] Goods are perfect complements Need them in strict proportions, must be used together Left shoes, right shoes

    14. 1/4/2008 14 Budget Line Shows affordable bundles Determined by p1, p2, I. Slope=

    15. 1/4/2008 15 Altering Budget Lines I? I?

    16. 1/4/2008 16 Altering Budget Lines p1? p1?

    17. 1/4/2008 17 Altering Budget Lines p2? p2?

    18. 1/4/2008 18 Road Map Prefs and utility give us a way to express the trade-offs we desire to make Budget line expresses trade-offs we are able to make. We use both to do utility maximization

    19. 1/4/2008 19 Two conditions for solution Tangency condition (x1*, x2*) solves: slope indif curve = slope budget line This yields : MRS (x1*, x2*)=p1/p2 Budget condition On budget line p1x1*+p2x2*=I Utility Maximization - PUTTING IT ALL TOGETHER :

    20. 1/4/2008 20 And the Point of All this Was…. … to derive Demand This lets us characterize consumer choice, given prices and income. (A little later, we will carefully characterize changes in consumption choices in response to price changes.) It gives us a way to think very precisely about choices, given scarcity.

    21. 1/4/2008 21 What is demand? Demand is the solution function: x1*(p1,p2, I), x2*(p1,p2, I) of maximization problem max u(x1, x2) x1,x2.. s.t. p1x1 + p2x2 = I x1*(p1,p2, I) expresses how much of good 1 consumer chooses when facing prices p1 and p2 and income I Maps out responses for ALL POSSIBLE prices and incomes Demand

    22. 1/4/2008 22 U(x1,x2)=ax1ax2ß Has nice properties (differentiability, diminishing MRS) and solution obtained from Tangency Condition And Budget condition: p1x1*+p2x2*=I Demand Functions: Cobb Douglass

    23. 1/4/2008 23 Demand Functions: Linear U(x1,x2)=ax1+bx2 Corner solutions x1*(p1,p2, I)=I/p1 if p1/p2<a/b x1*(p1,p2, I)=0 if p1/p2>a/b x2*(p1,p2, I)=0 if if p1/p2<a/b x2*(p1,p2, I)= I/p2 if if p1/p2>a/b

    24. 1/4/2008 24 Demand Functions: Leontief U(x1,x2)=mn[x1/a, x2/b] Tangency must occur at “kink” point Kink means x1*/a= x2*/b Use this to solve for x2, then sub in budget constraint

    25. 1/4/2008 25 Demand Curves

    26. 1/4/2008 26 Properties of Demand – Income Porperties Good 1 Normal Good 1 Inferior

    27. 1/4/2008 27 Properties of Demand – Scale Invariance Demand Functions are scale invariant Algebraically: x1*(?p1, ?p2, ?I)= x1*(p1,p2, I) x2*(?p1, ?p2, ?I)= x2*(p1,p2, I) Intuition: If prices double and income doubles, the set of allowed tradeoffs is exactly the same as before. Like renumbering the dollar bills as “2-dollar” bills. Graphically

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