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11ReducingRisk: Insurance

14.01 Principles of Microeconomics, Fall 2007ChiaHui Chen

September 28, 2007

Lecture10InsuranceandProductionFunction

Outline1.Chap 5: Reducing Risk: Insurance2.Chap 6: Outlineof Producer Theory3.Chap 6: Production Function: Short RunandLong Run

1 ReducingRisk: InsuranceReducing Risk:

Diversification

Insurance

Example (House insurance). Assume that one house has the proba-bility p to catch fire, with loss l each time, i.e. the owners wealthwill reduce from y1 to y2 = y1l. If the owner pay premium kto buyan insurance which covers the loss lwhen there is a fire, her wealthwill be y3 = y1 k, for the situations listed (see Table 1).

No Insurance InsuranceNo Fire y1 y3 = y1 kFire y2 = y1 l y3 = y1 k

Table 1: Wealth of House Owner in Different Situations.

Assuming the owner is a riskaverse, the utility function is concave.

u(y)

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21ReducingRisk: Insurance

Figure 1: The Utility Function of Risk Averse Person.

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31ReducingRisk: Insurance

The insurance premium is equal to the expected payout by the in-surance company, and we say the insurance is actuarially fair.

Since the person is riskaverse,

u(y3) >(1p) u(y1) + p u(y2).she will choose to buy insurance.If the insurance is actuarially unfair,

k > p l.Then

y3

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41ReducingRisk: Insurance

Figure 2: Distribution ofL

with Different Customer Numbers.n

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52OutlineofProducerTheory

2 OutlineofProducerTheory Production Function: Inputs to Outputs

Given Quantity Produced, Choose Inputs to Minimize the Cost

Choose Quantity to Maximize Firms Profit

The Production Function is

q= F(k, L).The two inputs:

k: Capital

L: Labor

It is easier to change labor level but not to change capital in a short time.

Shortrun. Period of time in which quantity of one or more inputs cannot bechanged. For example, capital is fixed and labor is variable in the shortrun.

Long run. Period of time need to make all production inputs variable. In thelong run, both capital and labor are variable.