Basic Economic Theory of Risk. Expected Utility Function, Risk Premium and Risk Aversion Measures. Основы экономической теории риска. Функция ожидаемой полезности. Премия риска и избегание риска.
A random variable is a variable with an uncertain future value. The expected value of a random variable is the weighted average of all possible values, where the weights on each possible value correspond to the probability of that value occurring. EV = (P1 x S1) + (P2 x S2) + ... + (Pn x Sn). Expected utility is the expected value of an individual’s total utility given uncertainty about future outcomes. A premium is a payment to an insurance company in return for the promise to pay in certain states of the world. A fair insurance policy is an insurance policy for which the premium is equal to the expected value of the claims.
Risk-averse individuals will choose to reduce the risk they face when that reduction leaves the expected value of their income or wealth unchanged. Individuals differ in risk aversion for two main reasons: differences in preferences and differences in income or wealth. So just as markets for goods and services typically produce an efficient allocation of resources, markets for risk also typically lead to an efficient allocation of risk—an allocation of risk in which those who are most willing to bear risk are those who end up bearing it. A risk-neutral person is completely insensitive to risk.
Two possible events are independent events if each of them is neither more nor less likely to happen if the other one happens. An individual can engage in diversification by investing in several different things, so that the possible losses are independent events. Pooling is a strong form of diversification in which an individual takes a small share in many independent events. This produces a payoff with very little uncertainty.
When an event is more likely to occur if some other event occurs, these two events are said to be positively correlated. Positively correlated financial risks: 1) Severe weather. 2) Political events. 3) Business cycles.
Markets do very well at dealing with risk due to uncertainty: situations in which nobody knows what is going to happen, whose house will be flooded, or who will get sick. However, markets have much more trouble with situations in which some people know things that other people don’t know—situations of private information. Adverse selection occurs when an individual knows more about the way things are than other people do.
private information. Moral hazard occurs when an individual knows more about his or her own actions than other people do.
A deductible in an insurance policy is a sum that the insured individual must pay before being compensated for a claim. In addition to reducing moral hazard, deductibles provide a partial solution to the problem of adverse selection.
Profit Maximization and Theory of Firm and Industry Supply. Максимизация прибыли и теория предложения фирмы и отрасли.
N
B!
The question may demand an expended answer with other market
structures rather than perfect competition!
TR=P*Q Profit = TR – TC
Total profit can be expressed in terms of profit per unit: Profit=TR−TC=(TR/Q−TC/Q)*Q
Profit=(P−ATC)*Q
If TR > TC, the firm is profitable. If TR = TC, the firm breaks even. If TR < TC, the firm incurs a loss. The break-even price of a price-taking firm is the market price at which it earns zero profits. At P=min ATC – breaks even and no entry/exit in long-run. At P=min AVC – shout-down price and indifference to producing in short-run.
T
here
is short-run
market equilibrium when
the quantity supplied equals the quantity demanded, taking the number
of producers as given. Market is in long-run
market equilibrium when
the quantity supplied equals the quantity demanded, given that
sufficient time has elapsed for entry into and exit from the industry
to occur.
The price-taking firm’s optimal output rule says that a price-taking firm’s profit is maximized by producing the quantity of output at which the marginal cost of the last unit produced is equal to the market price. P = MC
The marginal cost curve has a “swoosh” shape—falling at first before rising— the short-run average variable cost curve is U-shaped: the initial fall in marginal cost causes average variable cost to fall as well, before rising marginal cost eventually pulls it up again.
The short-run individual supply curve shows how an individual producer’s optimal output quantity depends on the market price, taking fixed cost as given. A market is in long-run market equilibrium when the quantity supplied equals the quantity demanded, given that sufficient time has elapsed for entry into and exit from the industry to occur.