The probability that it will rain on any given day is 0.20, and the probability is independent from day to day. You are trying to decide whether or not to make a tee time tomorrow to play golf. This requires a commitment on your part of turning down, say, movie tickets in favor of playing golf. If you accept the tickets, you also make the commitment not to go golfing. There is a weather forecast that signals whether it will rain tomorrow or not. There is a 0.80 probability that it rains when there is a "rainy" forecast and a 0.125 probability of rain when there is a "sunny' forecast. The overall probability of getting a "rainy" forecast is 0.111. Assume you are risk neutral. You place the following monetary values on the potential outcomes: a sunny day at the golf course a rainy day at the movies a rainy day at home $95 $20 -$18 a sunny day at $1 the movies a. If you have no weather forecast, evaluate the expected value of planning to golf and planning to go to the movies. What is the optimal decision? b. What is the value of perfect information about tomorrow's weather?

The probability that it will rain on any given day is 0.20, and the probability is independent from day to day. You are trying to decide whether or not to make a tee time tomorrow to play golf. This requires a commitment on your part of turning down, say, movie tickets in favor of playing golf. If you accept the tickets, you also make the commitment not to go golfing. There is a weather forecast that signals whether it will rain tomorrow or not. There is a 0.80 probability that it rains when there is a "rainy" forecast and a 0.125 probability of rain when there is a "sunny' forecast. The overall probability of getting a "rainy" forecast is 0.111. Assume you are risk neutral. You place the following monetary values on the potential outcomes: a sunny day at the golf course a rainy day at the movies a rainy day at home $95 $20 -$18 a sunny day at $1 the movies a. If you have no weather forecast, evaluate the expected value of planning to golf and planning to go to the movies. What is the optimal decision? b. What is the value of perfect information about tomorrow's weather?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The probability that it will rain on any given day is 0.20, and the probability is independent from day to day. You are trying
to decide whether or not to make a tee time tomorrow to play golf. This requires a commitment on your part of turning
down, say, movie tickets in favor of playing golf. If you accept the tickets, you also make the commitment not to go golfing.
There is a weather forecast that signals whether it will rain tomorrow or not. There is a 0.80 probability that it rains when
there is a "rainy" forecast and a 0.125 probability of rain when there is a "sunny" forecast. The overall probability of getting
a "rainy" forecast is 0.111.
Assume you are risk neutral. You place the following monetary values on the potential outcomes:
a sunny day at
the golf course
a rainy day at
the movies
a rainy day at
home
$95
$20
-$18
a sunny day at $1
the movies
a. If you have no weather forecast, evaluate the expected value of planning to golf and planning to go to the movies.
What is the optimal decision?
b. What is the value of perfect information about tomorrow's weather?

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Step 1: Calculate the probability of it raining or being sunny.

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