ak_ps03_micro_s08

ak_ps03_micro_s08 - Answer Keys for Problem Set 3...

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

View Full Document Right Arrow Icon
Answer Keys for Problem Set 3 Microeconomics Spring 2008 1. A household consumes only apples ( X ) and bananas ( Y ). We denote a consumption bundle consisting of x bags of apples and y bags of bananas is denoted by ( x, y ) . The preferences of the household are given by the utility function U ( x, y )= Ax α y 1 α where A> 0 and 0 <α< 1 . Suppose that prices for apples and bananas are P X and P Y and let I denote the income of the household. (a) Determine the marginal rate of substitution (MRS) for any consumption bundle ( x, y ) . MRS = MU x y = ∂U ∂x ∂y = Aαx α 1 y 1 α A (1 α ) x α y α = α 1 α y x (b) Describe the consumer’s utility maximaiztion problem using the information provided. max ( x,y ) Ax α y 1 α s.t. P X x + P Y y = I (c) Illustrate graphically where the optimal consumption bundle will lie with appropriately drawn indi f erence curve and budget line. X Y I/P X I/P Y x * y * 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
(d) Write out the Lagrangian function for the consumer’s maximization problem. L = Ax α y 1 α + λ ( I P X x P Y y ) (e) What are the f rst order conditions ?(Hint: There are three.) ∂L ∂x = Aαx α 1 y 1 α P X λ =0 ∂y = A (1 α ) x α y α P Y λ ∂λ = I P X x P Y y (f) Use the f rst order conditions to solve for the optimal quantity of x and y. X ( P X ,P Y ,I )= αI P X Y ( P X Y (1 α ) I P Y (g) If α . 25 , I = 100 , and both prices are equal to 2 , f nd the optimal consumption bundle of apples and bananas. x = 0 . 25 (100) 2 =12 . 5 y = 0 . 75 (100) 2 =37 . 5 (h) Now assume that the income of the household is $80 and the prices for apples and bananas stay the same. What’s the new demand (utility maximizing amount) for apples and bananas?
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.

Page1 / 11

ak_ps03_micro_s08 - Answer Keys for Problem Set 3...

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