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301lec7

# 301lec7 - Intermediate Microeconomics 301 UBC Sergei...

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Intermediate Microeconomics 301 UBC Sergei Severinov Lecture notes Uncertainty, Risk Decision-Making and Choice under Uncer- tainty 1

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Topics: Risk and Uncertainty Attitude Towards Risk and Uncerainty The Demand for Insurance and Risky Assets 2
Choice under uncertainty Uncertainty in a pervasive feature of the economic life. Many events and out- comes of actions are random: may or may not occur (good or bad weather for the agriculture), or may take different values (prices, incomes). Main questions: (1) How to describe uncertainty? (2) How the economic actors i.e. firms and individuals take the decisions under uncer- tainty? (3) How to describe preferences over ran- dom events? (4) What is the effect of uncertainty on the individuals, on their utility (welfare) and their choices? (5) What is the effect of risk? 3

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Probability and Probability Distribu- tion. States of the World First task: develop a common lan- guage to deal with different types of un- certainty and describe them in a universal way. The most convenient description of the random events can be given by using the following concepts: (i) random variable (ii) the state of the world (iii) probability distribution random variable is a common name for the thing that we are studying (weather, price, income) and the value of which is random (uncertain) and will be realized in the future. A random variable is synony- mous with uncertainty. 4
Definition. A possible realization (out- come) of a random variable is called a “state of the world .” For example, if prices tomorrow can take integer values from 1 to 10, then there are 10 possible states of the world tomor- row each corresponding to a different price. When price turns out to be equal to p i , we say that the state of the world correspond- ing to p = p i has occurred. 5

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Suppose that the variable x which we are studying (next year’s crop, your starting salary after graduation, the loss or win in the casino) is uncertain can take n possible values x i i = 1 , ..., n . Let π i be the probability that out- come x i occurs. Note that π i 0 and i = n i =1 π i = 1. Then { π 1 , π 2 , .., π n } is called the probability distribution. It describes how the probabilities with which possible values of x are distributed. Often, we will write π ( . ) as a function of the realization of x . Interpretation: the probability that the variable x takes value x i is given by π ( x i ) = π i 6
Consider some random variable x . Sup- pose that we know that it has possible re- alizations x i , i = 1 , ..., n , and corresponding probabilities π i . (i.e. we know its probabil- ity distribution). Main characteristics of a random vari- able are expected value and variance. Expected value (synonymous with av- erage value): E ( x ) = i = n X i =1 π i x i Variance of the random variable: V ar. ( x ) = i = n X i =1 π i ( x i - E ( x )) 2 7

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Variance and Standard Deviations Standard deviation and variance are measures of risk – Measure how variable the outcome will be – More variability means more risk – Individuals generally prefer less variability – less risk
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301lec7 - Intermediate Microeconomics 301 UBC Sergei...

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