ARE 100A2

ARE 100A2 - 1 NOTE consider 2 Ex numeric example a Suppose...

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1. NOTE: consider 2. Ex. numeric example. a. Suppose U= x^.5Y^.5 b. Px = 10 c. Py= 5 d. I=100 e. Max U = X^.5 Y^.5 subject to 10X + 5Y = 100 f. Need: 2 things i. MRSxy = Px/PY ii. Maintain 100 budget constraint. iii. MRS= Mux/Muy iv. Mux=Du/Dx = ½ x ^-.5 Y^1/2 v. Muy = Du/Dy = 1/2X^.5Y^-.5 g. MRS= Mux/Muy= [½ x ^-.5 Y^1/2]/[ 1/2X^.5Y^-.5] h. MRSxy = Y/X 3. Px/Py = 10/5 = 2 a. Take MRSxy and Px/y and plug into budget constaint b. 10X+5Y= 100 c. from MRSxy = Px/Py d. y/x= 2 y = 2x e. 10X + 5(2x)= 100 i. x=5 ii. y= 10

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iii. Px/Py= 2, MRSxy= y/x = 2 iv. If they aren’t equal, you did it wrong 4. a. at the optimum, we have MRSxy= PX/Py (this is an equilibrium condition as opposed to a definition) i. def: MRSxy= Mux/Muy = (dTU/dx)/(dTu/dy) 1. marginal rate of sub(trade off) = marginal utilityx/marginal utility = derivative totalx/derivativetotal y ii. Mux/Muy = Px/Py iii. MUx/Px = MUy/Py b. MUX/Px = additional utility gained by spending your last dollar on x. i. Ex. when you invest your dollar you want the highest marginal return on that dollar ii. Aka how hard your money works for you. iii. Note: if we have N goods then MUX/Px = MUY/Py = MUn/Pn iv. Suppose MUx/Px< MUy/Py 1. nor maximizing utility a. which do you buy more of to maximize utility b. utility for last dollar is greater for Y, so buy more Y
c. 2. a. Sometimes he sees a brick of cheddar cheese, Ie. Someone decides that they give up the cheese to buy some M&Ms. 3. suppose- Julie likes trips to Hawaii a lot and Pencils very little. a. X= Hawaii b. Y= Pencils c. If X and Y are free, Julie will pick Hawaii yet we observe Julie buys pencils and takes only 1 tript o Hawaii. Why is this? i. No money ii. MUX/Px= MUY/Py iii. Utility of Hawaii is high/ but there is large cost = utility of pencil is low/ very low price. 5. Now on Pink sheet. 6. Summary: MRXxy = Px/Py subject to budget constraint MUx/MUy = Px/ Py MUx/Px = MUy/Py

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7. CH 3 a. Assume consumer problem b. MaxU = U(q1, q2) c. Subject to P1q1 +P2q2 =y d. MU1 =du/dq1 e. 3 methods to solve this consumer problem i. MRS1,2 =P1/P2 subject to budget constraint from last lecture ii. Substitution method (on page 83 of the text) ignore it. iii. Lagrange method (today) 1. advantage- get one more piece of info. Ie: lambda f. Lagrange book method i. Maximize U = U(q1q2) ii. Subject to p1q1 +p2q2 = Y iii. Consumers choose the values of q1 and q2 1. ex. you walk into store, the store sets the prices, you have an equation that sets consumption into satisfaction and you pick q1 and q2. iv. Lagrange 1. Max L = U(q1,q2) + (y- p1q1 - p2q2) [solve for ) Note: FOC = first order condition v. 3 FOC 1. find values of a. q1 b. q2 c. vi.
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This note was uploaded on 04/11/2009 for the course ARE 100A taught by Professor Constantine during the Spring '08 term at UC Davis.

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ARE 100A2 - 1 NOTE consider 2 Ex numeric example a Suppose...

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