Frist mid term review

Frist mid term review - 1. Drawing the demand functions and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1. Drawing the demand functions and supply functions and &ning the equi- librium price and quantity by solving the two equations together Q D = a bP;Q S = c + dP: 2. Finding the price elasticity of demand and supply dQ D dP P Q D = bP Q D ; dQ S dP P Q S = dP Q S 3. Fitting linear equations to demand data: demand elasticity (at equilibrium): & 0 : 5 equilibrium price: P = $2 equilibrium quantity: Q = 12 million metric tons per year demand curve: Q = a bP Finding a;b & 0 : 5 = b ± P Q = b ± 2 12 ; hence b = 3 : Substitute this value and values of P ;Q into the demand equation Q = a bP ; we get the value for a = 18 : Therefore demand is given by Q = 18 3 P 4. Drawing indi/erence curves for di/erent utility functions through a point ( x 0 ;y 0 ) u ( x;y ) = ax + by;u ( x;y ) = x a y b ;u ( x;y ) = a ln x + b ln y;u ( x;y ) = min( ax;by ) ;u ( x;y ) = ln x + y 5. Drawing a budget constraint p x x + p y y = I: 6. Finding optimal consumption by solving MRS = p x p y ;p x x + p y y = I: (This applies to Cobb-Douglas, logarithm and quasi-linear case with interior solutions) (a) Cobb-Douglas case: u ( x;y ) = x 2 y MRS = 2 xy x 2 = 2 y x and more generally when u ( x;y ) = x a y b MRS = ax a ± 1 y b bx a y b ± 1 = ay bx 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Therefore, this MRS depends only on the ratio y x : This makes the Cobb-Douglas functions popular with economists. A useful formula to remember x = a a + b I p x ;y = b a + b I p y : Examples: (a1) suppose u ( x;y ) = xy; and p x = 2 ;p y = 3 ;I = 10 : optimal consumption choice. Set y x = 2 3 Combine with the budget equation 2 x + 3 y = 10 The two equations are solved simultaneously, and we get a unique solution. For instance, substitute y = 2 3 x into the budget equation, we get 2 x + 3 2 3 x = 10 and we get x = 2 : 5 ;y = 5 3 : Therefore the optimal consumption choice is the bundle (2 : 5 ; 5 3 ) : (a2) Finding the Engel curve: Suppose u ( x;y ) = xy; and p x = 2 ;p y = 3 ; let income be denoted by I: From the optimal consumption, we get the two equations y x = 2 3 ; 2 x + 3 y = I Substitute y = 2 3 x into the budget equation, we have 2 x + 2 x = I hence x = I 4 ;y = I 6 : In other words, half of the income is spent on X to purchase I 4 quantities of the good, and half of the income is spent on Y to purchase I 6 quantities of the good. The two solutions
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/03/2011 for the course ECON 303 taught by Professor Cheng during the Spring '07 term at USC.

Page1 / 7

Frist mid term review - 1. Drawing the demand functions and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online