3. Basic economic theory of risk. Expected utility function, risk premium and risk aversion measures.

Origins of Expected Utility Theory: The concept of probability was developed in the 17^th century by Pascal, Fermat. This led immediately to the first mathematically formulated theory about the choice between risky alternatives, namely the expected value (or mean value). The expected value of a lottery A having outcomes x, with the probability p, is given by

For that reason, it makes no sense compute the expected value in terms of monetary units. Instead, we have to use units which reflect the usefulness of a given wealth. This concept leads o the utility theory. The determination of the value of an item must not be based on the price, but rather on the utility (“moral value”) it yields. In other words, every level of wealth corresponds to a certain numerical value for the person’s utility. A utility function u assigns to every wealth level (in monetary units) the corresponding utility.

Utility Function: A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function. Continuity means that small changes to a consumption bundle cause only small changes to the preference level.

A

utility

utility function U(x) represents a preference relation ≥ if and only if: x’> x” U(x’) > U(x”) x’< x” U(x’) < U(x”) x’~ x” U(x’) = U(x”).

money

A utility function

In order to maximize expected value of utility Expected Utility Theory (EUT) was introduced.

EUT was first introduced in 18^th century by Bernoulli, but has only been accepted in the middle of the 20^th century. It is used in economics to explain choice under uncertainty.

- EUT, where u – utility, x –outcomes, p – probability.

EUT implies that rational individuals act as though they were maximizing expected utility, and allows for the fact that many individuals are risk averse, meaning that the individuals would refuse a fair gamble (a fair gamble has an expected value zero). In the presence of risky outcomes, a decision maker could use the expected criterion as a rule: higher expected value investments are simply the preferred ones.

Risk aversion implies that their utility functions are concave and show diminishing marginal wealth utility. The risk attitude is directly related to the curvature of the utility function: risk neutral individuals have linear utility functions, while risk seeking individuals have convex (выпуклая) utility functions and risk averse individuals have concave (вогнутая) utility function. The degree of risk aversion can be measured by the curvature of the utility function. We call a person risk-averse if he prefers the expected value of every lottery over the lottery itself. We call a person risk-seeking if he prefers every lottery over its expected value.

4. Technology, profit maximization and theory of firm and industry supply

The theory of the firm consists of a number of economic theories that describe the nature of the firm, company, or corporation, including its existence, behavior, structure, and relationship to the market.In simplified terms, the theory of the firm aims to answer these questions:Existence – why do firms emerge, why are not all transactions in the economy mediated over the market?

1. Boundaries – why is the boundary between firms and the market located exactly there as to size and output variety? Which transactions are performed internally and which are negotiated on the market?

2. Organization – why are firms structured in such a specific way, for example as to hierarchy or decentralization? What is the interplay of formal and informal relationships?

3. Heterogeneity of firm actions/performances – what drives different actions and performances of firms?

Firms exist as an alternative system to the market-price mechanism when it is more efficient to produce in a non-market environment. For example, in a labor market, it might be very difficult or costly for firms or organizations to engage in production when they have to hire and fire their workers depending on demand/supply conditions. It might also be costly for employees to shift companies every day looking for better alternatives. Thus, firms engage in a long-term contract with their employees to minimize the cost.

In economics, profit maximization is the (short run) process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to this problem. The total revenue–total cost method relies on the fact that profit equals revenue minus cost, and the marginal revenue–marginal cost method is based on the fact that total profit in a perfectly competitive market reaches its maximum point where marginal revenue equals marginal cost. Total revenue - total cost method: To obtain the profit maximising output quantity, profit is equal to total revenue (TR) minus total cost (TC). Marginal revenue-marginal cost method: An alternative argument says that for each unit sold, marginal profit (Mπ) equals marginal revenue (MR) minus marginal cost (MC). Then, if marginal revenue is greater than marginal cost, marginal profit is positive, and if marginal revenue is less than marginal cost, marginal profit is negative. When marginal revenue equals marginal cost, marginal profit is zero.

(industry?)An export supply curve is the difference between the quantity that foreign producers supply minus the quantity that foreign consumers demand, at each price. In equilibrium, import demand = export supply, domestic demand – domestic supply =foreign supply – foreign demand. In equilibrium, world demand = world supply