eco331h4 - Northwestern University Fall 2009 Marciano...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Northwestern University Marciano Siniscalchi Fall 2009 Econ 331-0 HOMEWORK 4 DUE MONDAY, NOVEMBER 16, 2009, IN CLASS. PLUS ONE PRACTICE PROBLEM 1 Consider an economy with one risk-free asset, with return r f = 1 . 01, and two risky returns ˜ r 1 , ˜ r 2 . The latter are jointly normally distributed, with means μ 1 = 1 . 02 and μ 2 = 1 . 05, standard deviations σ 1 = 0 . 02 and σ 2 = 0 . 05, and covariance σ 12 = - 0 . 0003. (a) Why is it OK to use the mean-variance approach in this setting? (b) Construct the efficient frontier. You need to find an expression for the minimum amount of σ required to achieve any target level μ of expected return; the expression will be of the form “constant plus μ times another constant,” and you must specify what these constants are. If you wish, you can also plot the efficient frontier (using Excel, Matlab etc.: remember σ goes on the horizontal axis); however, you do need to find an explicit expression for the efficient frontier. 2 Consider the following variant of the monopoly example we discussed in class. Demand is given by Q ( p,s ) = e - sp , the marginal cost is zero, and the possible values of s (i.e. the states) are S = [1 , 9]. Beliefs over S are uniform, as in the lecture notes. The information partition is I = { [1 , 5] , [5 , 9] } ; in other words, the firm learns whether s [1 , 5] or s [5 , 9]. Assume that the firm is risk-neutral, as in the lecture notes. Calculate the optimal prices the firm should set without any additional information, and conditional upon receiving each of the signals [1 , 5] and [5 , 9]. Finally, compute the value of the information partition I . 3 A mine is offered for sale at 2 million dollars. If the mine is rich in ore, it is worth 3 million dollars; otherwise, it is only worth 1 million dollars. A test balloon can be lowered into a well; if the balloon encounters a solid object, it breaks; otherwise the balloon is retrieved, and can be
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

eco331h4 - Northwestern University Fall 2009 Marciano...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online