{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm1_f09solutions2

midterm1_f09solutions2 - Economics 105 Midterm 1 Solutions...

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

View Full Document Right Arrow Icon
Economics 105 Midterm 1 Solutions 1. Lady Gaga values outlandish clothes ( x 1 ) and special effects ( x 2 ). Here utility function is given by: u ( x 1 , x 2 ) = x α 1 + βx α 2 where 0 < α < 1 and 0 < β . (a) Calculate Lady Gaga’s marginal rate of substitution (2 pts) MRS = - ∂U/∂x 1 ∂U/∂x 2 = - αx α - 1 1 βαx α - 1 2 = - 1 β parenleftbigg x 1 x 2 parenrightbigg α - 1 (b) Calculate Lady Gaga’s elasticity of substitution (6 pts) MRS = - 1 β parenleftbigg x 1 x 2 parenrightbigg α - 1 = - 1 β parenleftbigg x 2 x 1 parenrightbigg 1 - α ln ( | MRS | ) = ln parenleftBigg 1 β parenleftbigg x 2 x 1 parenrightbigg 1 - α parenrightBigg = ln parenleftbigg 1 β parenrightbigg + (1 - α ) ln parenleftbigg x 2 x 1 parenrightbigg dln ( | MRS | ) = (1 - α ) dln parenleftbigg x 2 x 1 parenrightbigg dln parenleftBig x 2 x 1 parenrightBig dln ( | MRS | ) = σ = 1 1 - α (c) How does Lady Gaga’s elasticity of substitution depend upon α and β ? (2 pts) ∂σ/∂α = - 1 / (1 - α ) 2 < 0. It does not depend on β (d) Suppose Lady Gaga’s elasticity of substitution was greater than 1. What would this tell you about how an increase in p 1 affected demand for x 2 ? Explain your answer. (2 pts) If σ > 1 then, then the substitution effect dominates the income effect and ∂x 2 /∂p 1 > 0 1
Background image of page 1

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

View Full Document Right Arrow Icon
2. Stunned by Kanye’s appearance, Taylor forgets her preferences. All she can remember is that her expenditure function is ( p 1 + 4 p 2 ) u . (a) Find Taylor’s indirect utility function. Verify that it is homogeneous of degree in (3 pts) The indirect utility function is the inverse of the expenditure function. So: v ( p 1 , p 2 , I ) = I p 1 + 4 p 2 Indirect utility functions are homogeneous of degree zero in income and prices v ( τp 1 , τp 2 , τI ) = τI τp 1 + 4 τp 2 = I p 1 + 4 p 2 = v ( p 1 , p 2 , I ) (b) Find Taylor’s hicksian demands. Verify that h 1
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.

{[ snackBarMessage ]}