{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# eco331h2 - Northwestern University Fall 2009 HOMEWORK 2 DUE...

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

Northwestern University Marciano Siniscalchi Fall 2009 Econ 331-0 HOMEWORK 2 DUE MONDAY, OCTOBER 19, IN CLASS. 1. Forecasting and Random Variables Consider a finite state space S , a probability P on S , and a random variable X : S R . Suppose that the following penalty scheme is offered to a decision-maker: she is asked to report a number ξ , and then she will be subject to the penalty [ X ( s ) - ξ ] 2 in each state s S . Show that, if the individual minimizes her expected loss from this penalty scheme, using the probability P , then her optimal forecast is ξ = E[ X ] = s X ( s ) P ( { s } ), the expectation of X with respect to the probability P . Observe that the simple penalty scheme for a single event we talked about in class as a prelude to our theorem about admissible forecasts is actually a special case of this result: just take X = 1 E , the indicator function of E . 2. Forecasting and Expected Utility This question asks you to verify something we claimed to be true in class: expected-utility decision-makers provide admissible forecasts, even though the forecast systems they provide will not, in general, correspond to the subjective probability they use to evaluate bets. Consider a finite state space S , and consider an individual who must provide a forecast system π : P ( S ) R , under the penalty scheme we described in class: that is, if the realized state is s , the individual must pay E ∈P ( S ) [1 E ( s ) - π ( E )] 2 . As we did in class, denote the latter quantity by

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

eco331h2 - Northwestern University Fall 2009 HOMEWORK 2 DUE...

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

View Full Document
Ask a homework question - tutors are online