## Expected utility - consumer choice involving risk, Microeconomics

Assignment Help:

Expected Utility:

Theory Assume that a utility index exists which conforms to the five axioms. The expected utility for the two-outcome lottery L = (P, A, B) is given by,

E [U (L)] = P U (A) +(1-P) U (B)

Consider the lotteries L1 = (P1, A1, A2) and L2 = (P2, A3, A4). An expected utility theorem states that if L1 is preferred to L2, E [U (L1)] > E [U (L2)]. The significance of this theorem is that uncertain situations can be analysed in terms of the maximisation of expected utility.

The proof of the theorem is straightforward. Select outcomes such that B, the best, is preferred to all other outcomes under consideration, and W, the worst, is inferior to all other outcomes. By the continuity axiom, Qi's exist such that Ai is indifferent to (Qi, B, W) (i=1,...,4). Thus L1 and L2 are equivalent to, i.e., have the same expected utility as, the lotteries (Z1, B, W) and (Z2, B, W) respectively where Z1 = P1Q1 + (1-P1)Q2 and Z2 = P2Q3 + (1-P2)Q4. By assumption, L1 is preferred to L2 and it follows from the unequal probability axiom that Z1>Z2. Since origin and unit of measure are arbitrary for utility indexes, let U (B) = 1 and U (W) = 0. Then E [U (L1)] = Z1 and E [U (L2)] = Z , establish the theorem.

#### Chamberlins model, lung run eqiulibrium

lung run eqiulibrium

#### Equilibrium price and equilibrium quantity of cassette, The compact disk pl...

The compact disk player has literally revolutionized the recording industry with its state-of-the-artclarity, sound, durability, and the fact that it costs less than cassette tape

#### Calculate wi’s cost of debt and wacc, 1.    Introduction Wood Investm...

1.    Introduction Wood Investments (WI) is a private equity fund that specialises in the leveraged acquisition of publicly-quoted companies with the intention of producing h

#### Change in consumer and producer surplus from price controls, Change in con...

Change in consumer and  producer surplus from price controls * Observations: - The loss is equal to area B + C. - The change in surplus = (A - B) + (-A - C) = -B - C -

#### Total cost function, TC = Q3 – 8Q2 + 68Q + 4, get the median and mode

TC = Q3 – 8Q2 + 68Q + 4, get the median and mode

#### Homework, Which of the following has not occurred over time in the past sev...

Which of the following has not occurred over time in the past several decades in the physician services market? A. The level of competition has increased. B. Economies of scale ha

#### Mr, implications of varios market structure for price determination

implications of varios market structure for price determination

#### Technical economies, Technical Economies: They are economies that acc...

Technical Economies: They are economies that accrue from the use of large machines with emphasis on full utilization and efficiency in production. First, there are some equip

#### Describe the poverty cycle, Describe the poverty cycle and suggest how a de...

Describe the poverty cycle and suggest how a developing country can break the cycle. The poverty cycle is explained as the trap developing countries can land in; low incomes →

#### Elasticities of demamnd, The demand for soft drinks has been estimated asQx...

The demand for soft drinks has been estimated asQx 20PX 0.25PY0.45M 2 Determine the own, cross and income price elasticities of demand. Interpret your results.  