## Calculating variance, Microeconomics

Assignment Help:

Calculating Variance (σ)

The standard deviations of the 2 jobs are:

The standard deviation is used when there are several outcomes instead of only two.

* An Example

- Job 1 is a job in which income varies from \$1000 to \$2000 in increments of \$100 which are all equally likely.

- Job 2 is a job in which income varies from \$1300 to \$1700 in increments of \$100

that, are all equally likely.

* Outcome Probabilities of Two Jobs

- Job 1: bigger spread and standard deviation

- The peaked distribution: extreme payoffs are much less probable

*? Decision Making

- A risk avoider would select Job 2: same expected income as Job 1 with less risk.

- Assume that we add \$100 to each payoff in Job 1 which makes expected payoff = \$1600.

The standard deviation is square root of deviation squared.

*?  Decision making

- Job 1: the expected income is \$1,600 and a standard deviation of \$500.

- Job 2: the expected income of \$1,500 and a standard deviation of \$99.50

- Which job?

• Greater value or less risk?

*? Example

- Suppose a city wants to deter people from wrong parking.

- The alternatives ......
*  Assumptions:

1) Wrong parking saves a person \$5 in terms of time spent searching for a parking space.

2) The driver is risk neutral.

3) Cost of apprehension is zero.

*  A fine of \$5.01 would deter the driver from double parking.

- Benefit of wrong parking (\$5) is less than the cost (\$5.01) equals the average benefit which is less than 0.

*  Increasing fine can reduce the cost of enforcement:

- A \$50 fine with a .1 probability of being caught results in the expected penalty of \$5.

- A \$500 fine with a .01 probability of being caught results in the expected penalty of \$5.

*  The more risk reluctant drivers are, lower the fine is required to be in order to be effective.

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