ECMB02-PS2A.pdf

10 Pages
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Department
Financial Accounting
Course Code
MGAB03H3
Professor
Kwan Fung

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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 =
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