midterm2_f09solutions

midterm2_f09solutions - Economics 105 Midterm 2 SOLUTIONS...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 105 Midterm 2 SOLUTIONS Oct. 30, 2009 1. Mark whether the statement is True or False (a) Third degree price discrimination is Pareto efficient (2 pts) FALSE: Third degree price discrimination still has monopolies charging prices higher than marginal cost, which means some consumers are not getting the good who would be willing to pay more than marginal cost. (b) The supply function can be found by substituting conditional input demands into the production function (2 pts) FALSE: the supply function is found by substituting unconditional input demands into the production function (c) Hotellings Lemma allows us to go from profit functions to supply functions and input demands (2 pts) TRUE: w =- l ( p,w,r ), r =- k ( p,w,r ), and p = x ( p,w,r ) (d) The production function min { 2 L 2 , 3 K 2 } is quasi-concave but not concave (2 pts) TRUE: Since the production function is increasing returns to scale, f ( L,K ) = min { 2( L ) 2 , 3( K ) 2 } = 2 min { 2 L 2 , 3 K 2 } = 2 f ( L,K ) the production function is convex (not concave). Also, since the isoquants are Leotieff (L- shaped), the production function has a convex upper contour set, so it is also quasi-concave. 1 2. A firms production function is given by x = l 1 / 2 k 1 / 2 . (a) Find the firms conditional input demands. Verify that they are homogeneous of degree in (5 pts) To find the conditional inputs we need to do expenditure minimization. min wl + rk s.t. x = l 1 / 2 k 1 / 2 L = wl + rk + ( x- l 1 / 2 k 1 / 2 ) L w = w- (1 / 2) l- 1 / 2 k 1 / 2 = 0 L r = r- (1 / 2) l 1 / 2 k- 1 / 2 = 0 L = x- l 1 / 2 k 1 / 2 = 0 Solving for the conditional inputs demands gives k ( x,w,r ) = x w r 1 / 2 l ( x,w,r ) = x r w 1 / 2 Conditional input demands are homogeneous of degree 0 in prices. l ( x,w,r ) = x r w 1 / 2 = x r w 1 / 2 = l ( x,w,r ) k ( x,w,r ) = x w r 1 / 2 = x w r 1 / 2 = k ( x,w,r ) (b) Find the firms cost function. Verify that it is homogeneous of degree in (2 pts) The cost function is: C ( x,w,r ) = wx r w 1 / 2 + rx w r 1 / 2 = 2 x ( rw ) 1 / 2 Cost function are homogeneous of degree 1 in prices....
View Full Document

This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.

Page1 / 10

midterm2_f09solutions - Economics 105 Midterm 2 SOLUTIONS...

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