Econ 50 Unit 1
perfect complement indifference curves
L-shaped
cobb-douglas MRS shortcut
MRS = (a1/a2) x (x2/x1)
MRS equation
MU1/MU2
unit elastic
equal to one in absolute value
Steps to draw indifference curves
1) evaluate utility function at the point 2) set the utility function equal to the found value 3) solve for X2 4) plug in various values of X1 and plot
elasticity equation
Ey,x =(Change in Y/Change in X) * (X/Y)
indirect utility function
Function of prices and income that reflects the utility from the utility maximizing bundle given those prices and income
Special Elasticity Case
If F(x)=exponent form, Ey,x = the exponent (b).
Exogenous variable
Variables that go into the model; independent
monotonic transformations of utility functions
represent the same preferences; i.e. can multiply by a constant, raise to a power, or take the natural log of the util function and it won't affect MRS.
not monotonic
satiation point
cobb-douglas solution shortcut
X1 = aM/P1 X2 = (1-a)M/P2 where 0<= a <= 1
optimality
a choice is optimal if there is no other affordable choice that is also preferred
Preference assumptions
complete (any two can be compared) and transitive (if x>y and y>z, x>z)
hicksian demand function
cost minimizing bundle
elasticity definition
describes how responsive an endogenous variable is to an exogenous one in percentage changes
engel curve
fix both prices and plot (X1(m),m). X1 on the horizontal axis, M on the vertical one.
income offer curve for good 1
fix both prices; plot (X1(m),X2(m)) in X1-X2 space. If lagrange works, equation for the IOC is the MRS.
price offer curve for good 1
fix p2 and m, plot (X1(P1), X2(P1))
elastic
greater than one in absolute value
inelastic
less than one in absolute value
Perfect substitute indifference curves
linear because MRS is constant
well behaved preferences
monotonic and convex
monotonicity
more is better; no satiation; all MRS has the same sign.
if MRS < p1/p2
move left; IC flatter than BL; less willing to give up good 2 than the market requires
if MRS > p1/p2
move right; IC steeper than BL; more willing to give up good 2 than the market requires
Slope of BL
opportunity cost of consuming good 1. Amt. of good 2 the market requires you to give up to get another unit of good 1. (-P1/P2)
not smooth
perfect complements
not convex
perfect substitutes, concave utility
crosses axes
quasilinear
indifference curves
sets of bundles such that the consumer is indifferent between each bundle in the set. Every bundle defines an indifference curve; Set of all consumption bundles which are assigned the same number of utils by the utility function u(x1, x2).
price ratio
slope of the budget line; the rate at which the market allows people to exchange goods
if good 2 is a composite good, then the MRS may be thought of as
the marginal utility of good 1 measured in dollars or the marginal willingness to pay for good 1
Marginal rate of substitution
the slope of the indifference curve; how many units of good 2 are you WILLING to give up to get another unit of good 1.
if two goods are complements, the POC slopes
upwards; when the price of one good changes you either buy more of both or less of both.
well behaved optimality
utility function is smooth (mrs not defined piecewise), strictly convex (dMRS/dX1 <= 0 and dMRS/dX2 >= 0 with at least 1 strict), and strictly monotonic (MU1 > 0 and MU2>0 for any X1, X2). The indifference curves don't cross the axes (lim of MRS as x1 approaches 0 is infinity, lim of MRS as x2 approaches 0 is 0). BL is a simple straight line
endogenous variable
variable result that comes out of the model; dependent
convexity
variety is better; averages are preferred to extremes; diminishing MRS; C>=X and C>= Y if on cord connecting bundles X and Y when consumer is indifferent between them.