Information, Insurance, and Financial Markets

This is Unit Fifteen of Principles of Microeconomics: what happens when one side of a trade knows more, the market built on not knowing, and the price that links money across dates. Unit fourteen ended on a distribution of income. This unit takes up two markets the exam groups together. The first is any market where a seller, a worker or a borrower knows something the other side cannot see, and the devices that make hiding it costly; insurance is that problem at its sharpest. The second is the market for capital, where one interest rate prices every claim on the future. By the end you will be able to distinguish the two kinds of not knowing and match a mechanism to the problem. To compute pooled and fair premiums and define moral hazard. To run the adverse-selection spiral and describe the third-party payer. To name how firms raise capital. And to compute present value, price a bond, apply the investment rule, and carry one rate through three assets.

Four entries on not knowing: the two kinds, price as a signal, the devices that close the gap, and matching device to problem.

Two kinds of not knowing.

MIC 1401 Imperfect and Asymmetric Information

Imperfect information means a party is unsure what is traded; asymmetric means one side knows more. Either can block trades that benefit both, since a buyer who cannot tell a sound car from a lemon will not pay for one; the seller knows the car's history, the buyer sees the paint. The witness has no chapter on this, and these entries rest on the anchor.

What price tells a buyer.

MIC 1402 Price as a Signal of Quality

When quality cannot be seen, buyers read it from price: a cut can lower sales and a rise raise them, against the law of demand, within limits, and markets with few traders are thin. The cheapest used car carries the most risk. Reputable dealers charge more and fix hidden faults to keep repeat buyers, and the premium buys information.

The devices that close the gap.

MIC 1403 Bridging the Gap

Sellers bridge information gaps with reputation, guarantees, warranties and service contracts; a warranty is a seller betting its own money on quality. Employers screen with degrees and references and read signals such as grades, and licenses and probation do the same. Lenders use credit checks, cosigners and collateral. A license certifies quality and bars entry at once, and the course states both edges.

Matching device to problem.

MIC 1404 Which Mechanism Fits

Given an information problem, name who knows more, what they could hide, and the mechanism that makes hiding costly or reveals the truth. A seller who knows the flaws is answered by a guarantee or warranty; a worker who knows their own reliability by verifiable screens and a probation; a borrower who knows their intent by a credit check, a cosigner or collateral. Four cases. A used car sold by a stranger: a dealer's warranty or a reputation for repeat business makes hiding faults expensive. A new hire: transcripts and references screen, a work sample signals, and probation reveals. A small loan to a first-time borrower: a cosigner who knows them, or collateral the lender can seize. A mail-order purchase: a money-back guarantee lets the buyer inspect after paying. Every mechanism costs something, so thin markets do not become thick for free, and a signal works only if it is harder to fake than to earn; a credential anyone can buy signals nothing.

Three entries on insurance: pools and risk groups, the premiums in numbers, and what insurance does to behavior.

The market built on not knowing.

MIC 1405 Insurance, Pools and Risk Groups

Insurance pools premiums priced on group loss probability and pays those who suffer loss; over time premiums must cover claims, costs and profit. A risk group shares one risk, and a premium equal to its expected claim is actuarially fair, so a pooled premium makes safe drivers pay for risky ones. Nobody can predict who will crash, and any group mixes safer and riskier.

The premiums in numbers.

MIC 1406 Pooled and Fair Premiums

From a table of how many in a pool suffer each size of loss, compute total expected claims and divide by the number insured: that is the pooled premium when nobody can be told apart. Then compute each risk group's actuarially fair premium, its own expected loss per member, and compare; members below the pooled premium subsidize those above it, and the gap is what classification would remove. One hundred drivers: seventy will have two hundred dollars of damage, twenty two thousand, and ten twelve thousand, one hundred seventy-four thousand in all, so the pooled premium is one thousand seven hundred forty. Fair premiums by group are two hundred, two thousand and twelve thousand. The seventy safe drivers each pay fifteen hundred forty more than their risk, and the ten worst each pay ten thousand two hundred sixty less. The pooled premium is fair to the pool, not to any member, and whether the safe should subsidize the risky is an equity question the arithmetic does not settle; the insurer's costs and profit sit on top.

What insurance does to behavior.

MIC 1407 Moral Hazard

Moral hazard is insured people taking more risk, since the insurer pays. It is reduced, not removed, by fraud investigation, monitoring and cost sharing: a deductible, copayment or coinsurance, so a three-thousand claim with a five-hundred deductible and twenty percent coinsurance leaves the patient paying one thousand. The cause is imperfect information, and paying providers per service invites more services than a fixed fee per patient.

Three entries on who buys: adverse selection, the spiral in numbers, and the third party in the gap.

Who buys.

MIC 1408 Adverse Selection

Adverse selection: buyers know their own risk better than the insurer, so at a pooled price the high-risk buy, the low-risk leave, and the premium spirals. The ways out are to classify buyers by risk, or require the low-risk to buy; auto liability is a mandate, Medicare direct provision. Below-fair premiums for one group are paid by others, and insurance's law cannot be repealed.

The spiral in numbers.

MIC 1409 The Adverse-Selection Spiral

From the risk table, offer the pooled premium; groups paying more than their expected loss leave. Recompute the pool from those remaining, claims against premiums, and raise the premium to cover it, asking who leaves next, until only the worst risks remain at their own fair premium. Then show what a mandate does. At the pooled premium of one thousand seven hundred forty, the seventy drivers whose expected loss is two hundred leave. Thirty remain, with claims of one hundred sixty thousand against premiums of fifty-two thousand two hundred, a loss of one hundred seven thousand eight hundred. The premium must rise to five thousand three hundred thirty-three, and now the twenty with two-thousand-dollar risk leave, until ten remain at twelve thousand each, insuring only those certain to claim. A mandate keeps all one hundred in at one thousand seven hundred forty, and the seventy safe drivers pay one hundred seven thousand eight hundred toward the others' claims. The spiral turns on buyers knowing their own group; if the insurer could classify, the safe would stay. And the mandate does not make coverage cheap; it decides who pays for the risky, which is why it is contested.

Insurance in the market for care.

MIC 1410 Third-Party Payers

When an insurer pays most of a bill, patients face a low price and demand more visits; supplying them takes a higher price, which the insurer pays, so quantity, the providers' price and spending all rise. A fifteen-dollar copay raises visits from eight hundred thousand to twelve hundred thousand. Equilibrium is not where demand meets supply, since a third party sits in the gap.

Two entries on financial capital: how firms raise money, and debt against equity.

The other financial market.

MIC 1411 How Firms Raise Financial Capital

Firms raise capital four ways: early investors, reinvested profits, borrowing by bank loan or bond, and stock. A bond is an amount borrowed, an interest rate and a repayment date. A firm is paid for stock only when it issues it, and later trades pass between investors; shareholders earn dividends and capital gains and elect the board. A share bought from another investor pays the firm nothing.

Choosing between them.

MIC 1412 Debt, Equity, and the Three Characteristics

Debt commits the firm to fixed interest but keeps control; equity brings money with no repayment but sells ownership. Every investment has expected return, risk and liquidity, and an interest rate pays for waiting, inflation and risk: the Treasury pays the least, risky firms the most. Founders' own money invested is a signal, and higher return is the compensation for higher risk.

Four entries on the price that links dates: present value, a bond when rates move, the investment rule, and the unit's capstone, one rate through three assets.

The price that links dates.

MIC 1413 Interest and Present Value

Interest pays for postponing wealth's use. Present value is the sum needed now to equal a future sum: divide by one plus the rate, raised to the years, date by date, so at ten percent one ten next year is worth one hundred now. Present value falls as the rate rises or the wait lengthens, which is why bond prices move opposite to rates.

Pricing a bond.

MIC 1414 Pricing a Bond When Rates Move

A bond has a face value, a coupon rate and a maturity. List its payments, the coupon each year and the face value plus the last coupon at maturity, discount each at the market rate, and add: that is the price. At a market rate equal to the coupon the price equals face value; when the market rate rises above the coupon the price falls below face, and when it falls the price rises above. A two-thousand-dollar two-year bond with a five percent coupon pays one hundred after year one and two thousand one hundred after year two. At five percent, ninety-five twenty-four plus one thousand nine hundred four seventy-six is two thousand, the face value. Rates rise to eight percent: ninety-two fifty-nine plus one thousand eight hundred forty-one, about one thousand eight hundred ninety-three. The payments did not change; their present value did. Discount the second payment by one plus the rate squared, not doubled, and remember the coupon rate is fixed at issue while the yield moves with the market.

The same arithmetic on a machine.

MIC 1415 The Investment Rule and the Demand for Capital

A firm buying a machine compares its cost now with the present value of its net returns: discount each year's return at the interest rate, add, subtract the cost, and invest if the net present value is positive. Raise the rate and every present value falls, some projects turn negative, and the firm buys less capital, so capital demanded falls as the rate rises, and the rate is set where borrowers' demand for funds meets savers' supply. A machine costs ten thousand dollars and returns six thousand at the end of each of two years. At five percent the returns are worth eleven thousand one hundred fifty-six, a net present value of plus one thousand one hundred fifty-six: buy it. At fifteen percent they are worth nine thousand seven hundred fifty-four, minus two hundred forty-six: do not. The interest rate is the opportunity cost of the firm's own money too, so a firm that pays cash still discounts, and the rule is the input rule of unit six across time: capital's marginal revenue product, in present value, against its cost.

One rate through three assets.

MIC 1416 The Interest Rate as a Price

The rate is payment for waiting, plus inflation, plus a risk premium, and every asset is a claim on future payments whose price is their present value at a rate that fits its risk. The bond's payments are fixed by contract, so a higher market rate lowers its price and nothing else. A share's payments are the firm's expected profits, forecasts, so its price moves both when the rate changes and when expectations change. A machine's returns are the firm's own forecast; it buys while their present value exceeds the cost, and a higher rate turns marginal projects negative. Add these up across the economy and the demand for capital slopes down in the rate, which clears the market for loanable funds: households supply saving, more at higher rates, and firms demand funds for positive-value projects. A rise in the demand for capital raises the rate, a fall in saving raises it too, and the higher rate cuts the quantity demanded. At five percent and then fifteen. The two-thousand-dollar bond: worth two thousand, then about one thousand six hundred seventy-five. A share in a firm expected to earn four, five and six million now, in one year and in two, with one hundred thousand shares: one hundred forty-two dollars a share at five percent, one hundred twenty-nine at fifteen. The machine: plus one thousand one hundred fifty-six, then minus two hundred forty-six. One rate change lowered the bond, lowered the share, and cancelled the machine. Three cautions. The rate that prices a share carries the risk premium, and choosing it is a judgment, which is why share prices disagree while bond prices do not. Compound interest is the same arithmetic run forward, so small differences in rate or time compound into large ones. And the demand for capital, like the demand for labor, is derived: it shifts with expectations, technology and the demand for what capital produces, not only with the rate.

Look at what you can now do. You can separate imperfect from asymmetric information, say why a buyer reads quality from price, and match a warranty, a screen or collateral to the side that knows more. You can compute a pooled premium from a loss table, compute each group's fair premium, and say who subsidizes whom; and you can define moral hazard and the cost sharing that limits it. You can run the adverse-selection spiral from the pooled premium to the last risk group, show what a mandate does, and say why a third-party payer raises quantity, price and spending. You can name the four sources of financial capital, say that a share trades between investors without paying the firm, and set debt against equity. And you can discount a future sum date by date, price a bond as rates move, apply the net present value rule to a machine, and carry one rate through a bond, a share and a machine. Unit sixteen turns to trade between countries.