Lectures in Microeconomics-Charles W. Upton Buying Insurance.

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Presentation transcript:

Lectures in Microeconomics-Charles W. Upton Buying Insurance

Some Cases The Case for Insurance How much for Insurance Does it always pay to buy insurance How much are you willing to pay to gamble?

Buying Insurance The Case for Insurance U(Y) For most people, the marginal utility of income is decreasing

Buying Insurance The Consequences of a Fire U(Y) No FireFire

Buying Insurance The Consequences of a Fire U(Y) No FireFire p fire = 0.01 I no fire = 250,000 I fire = 150,000

Buying Insurance Expected Utility U(Y) No FireFire E(U) Naked Draw the red line and the green dot.

Buying Insurance Expected Utility U(Y) No FireFire E(U) Naked This is your situation if you are “naked” (uninsured).

Buying Insurance The Case for Insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked Suppose you can buy insurance at your expected loss.

Buying Insurance The Case for Insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked With a 1% chance of a $100,000 loss, the insurance company would charge $1,000.

Buying Insurance The Case for Insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked Higher E(U)

Buying Insurance The Case for Insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked If people were risk takers, then buying insurance would mean lower E(U)

Buying Insurance The Case for Insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked Most people buy insurance; that is why we think most people are risk averters.

Buying Insurance How much for insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked This is an ideal case: the insurance company only charges its actuarial loss, no administrative selling, etc.

Buying Insurance How much for insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked Common sense says if the company charged enough (say ) $50,000 for this policy, even a risk averter would not buy.

Buying Insurance How much for insurance U(Y) No FireFire Loss E(U) Insurance E(U) Naked But how much?

Buying Insurance How much for insurance U(Y) No FireFire E(U) Insurance E(U) Naked Suppose they charge this much

Buying Insurance How much for insurance U(Y) No FireFire E(U) Insurance E(U) Naked Your utility is equal to going naked

Buying Insurance How much for insurance U(Y) No FireFire E(U) Insurance E(U) Naked Your utility is equal to going naked This is the maximum amount you will be willing to pay.

Buying Insurance Does it always make sense to buy insurance? U(Y)

Buying Insurance Does it always make sense to buy insurance? U(Y)

Buying Insurance Does it always make sense to buy insurance? U(Y) Let’s take a section and expand it

Buying Insurance Does it always make sense to buy insurance? U(Y) If we blow the scale up, we get something that looks like a straight line. That is, we are essentially risk-neutral.

Buying Insurance Does it always make sense to buy insurance? U(Y) For small bets, that is essentially the case.

Buying Insurance Does it always make sense to buy insurance? U(Y) If we are risk neutral we don’t care about insurance even if the insurance costs us our expected losses.

Buying Insurance Does it always make sense to buy insurance? U(Y) And if it costs more, it makes sense not to buy.

Buying Insurance Does it always make sense to buy insurance? U(Y) Should I insure against loss of a quarter in a vending machine.

Buying Insurance Does it always make sense to buy insurance? U(Y) Should I insure against loss of a quarter in a vending machine. Theoretically possible, but when transaction costs are considered, a foolish idea.

Buying Insurance Does it always make sense to buy insurance? U(Y) Should I insure against a $500 loss on my car?

Buying Insurance Does it always make sense to buy insurance? U(Y) Should I insure against a $500 loss on my car? Theoretically possible, but when transaction costs are considered, a foolish idea.

Buying Insurance Wagering Suppose you are a risk taker You are willing to gamble, but like a risk averter who is unwilling to pay too much for insurance, there is a limit to how much you are willing to lose. How much?

Buying Insurance Wagering Find the red line Find the green dot

Buying Insurance Gambling If you want to gamble you must be a risk taker.

Buying Insurance Gambling If you want to gamble you must be a risk taker. Your utility function looks something like this.

Buying Insurance If you gamble Win Lose Stay home Utility from staying home

Buying Insurance If you gamble Win Lose Stay home Utility from staying home

Buying Insurance If you gamble Win Lose Stay home Utility from staying home Utility from gambling

Buying Insurance Casinos as Charitable Institutions They are not. The house always has an edge. You should expect to lose. But how big an edge?

Buying Insurance This Big an Edge Win Lose Stay home Utility from gambling Utility from staying home

Buying Insurance End ©2003 Charles W. Upton