Study Guides (248,645)
MGAB03H3 (30)
Kwan Fung (1)

# ECMB02-PS2A.pdf

10 Pages
58 Views

Department
Financial Accounting
Course Code
MGAB03H3
Professor
Kwan Fung

This preview shows pages 1,2 and half of page 3. Sign up to view the full 10 pages of the document.
Description
UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT ECMB02: Price Theory: A Mathematical Approach (Intermediate Microeconomics I) Problem Set-2 (Solutions) 1.a) C U2 U1 U0 M b) B U2 U1 U0 M c) F F U0 U 1 U 2 1 2. a) That is only true if both individuals are characterized by a convex indifference curve. If either one is characterized by “perfect substitute” or “perfect complement” indifference curve then the statement will not be true. Therefore, uncertain. b) FALSE: SinceMRS = 3, the corner solution will be either all X or all Y depending on whether the relative price is less than 3 or more than 3: Indifference Curves Budget Lines Slope<3 Slope>3 2 3. a) Equation for the budget line is: I= P1 1 + p2x 2=> 50x 1 +20x 2 = 500 p1 50 = − = − = −2.5 p2 20 b) x2 25 x1 10 c) This will create a kink on the budget line. There will be a new line parallel to th1 x axis for a length of 5 units: x2 x2 5 15 x1 d) x2 27 25 x1 5 15 3 4. Lagrange Method Utility Function U (x,y) = xy Budget Constraint I = x x + y y with I=100, px=20, py=25 20x + 25y=100 a) Transform Budget Constraint 0 = 20x + 25y -100 b) Build the Lagrangian L(x,y,λ) = xy - λ(20x + 25y -100) c) Calculate partial derivatives for x, y, and λ and set them equal to zero 1. ∂L = y − 20λ = 0 ∂x 2. ∂L = x −25λ = 0 ∂y 3. ∂L = −(20x +25y −100) = 20x +25y −100 = 0 ∂λ d) Solve for x and y From (1) & (2) y 20 4 x = 25 => y = 5x plug into 3: 4 20x+25( )5−100 = 0 |Solve for x and y => x = 2.5,y = 2 U = 2×2.5=5 y U=5 5 2 x 2.5 4 4 5. a) U = 40 = 2XY 2 2 Y = 4 => 40 = 2X4 => X = 40/32 =1.25 Y 1.25, 4 U=40 X 1.25 1.25 b) 500 10 10X +15Y = 500=> Y = − X 15 15 Slope: −PX = −10 = − 2 P 15 3 Y Y 33.3 X 50 5 c) MRS = MU X = PX MU P Y Y 2Y 2 10 Y => = = 4XY 15 2X => X = 0.75Y 10X +15Y = 500 =
More Less

Only pages 1,2 and half of page 3 are available for preview. Some parts have been intentionally blurred.

Unlock Document

Unlock to view full version

Unlock Document
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.