Q: Suppose you are offered a lottery that pays $$90 with probability $$\frac{2}{3}$$ and 30 $$with probability $$\frac{1}{3}. $$What is the expected value of this lottery?

$$EV = 90 \times \frac{2}{3} + 30 \times \frac{1}{3} = 70$$

Question 1

Which of the following best describes 'risk' in the context of microeconomics?

Accepted Answer

Uncertainty that can be quantified by assigning probabilities to outcomes.

Question 2

Suppose you are offered a lottery that pays $$90 with probability $$\frac{2}{3}$$ and 30 $$with probability $$\frac{1}{3}. $$What is the expected value of this lottery?

Accepted Answer

$$EV = 90 	imes \frac{2}{3} + 30 	imes \frac{1}{3} = 70$$

Question 3

If a consumer's utility function is $$u(x) = x$$, how does their expected utility compare to the expected value of a lottery?

Accepted Answer

Expected utility is equal to expected value.

Question 4

Which of the following utility functions represents risk aversion?

Accepted Answer

$$u(x) = \sqrt{x}$$

Question 5

A risk-averse individual is offered a fair bet. What is their likely response?

Accepted Answer

They will refuse the bet.

Question 6

The certainty equivalent $$x_{ce} of a $$lottery $$(x_1$, x_2$, p_1$, p_2$) is $$defined by which equation?

Accepted Answer

$$u(x_{ce}) = p_1$ u(x_1$) + p_2$ u(x_2$)$$

Question 7

If an insurance policy is 'actuarially fair', what condition must it satisfy?

Accepted Answer

$$pP + p(P - C) = 0$$

Question 8

Consider a consumer with initial wealth $$w$$ who faces a potential loss $$L in $$state 2. If they buy insurance with premium $$P$$ and claim $$C$$, what is their consumption in state 2?

Accepted Answer

$$w - L - P + C$$

Question 9

Why does risk pooling reduce risk for insurers?

Accepted Answer

Because the average outcome becomes more predictable as the number of independent risks increases.

Question 10

Suppose an individual can invest $$z in a $$risky asset with returns $$r_1$$ \u003e 0$$ in state 1 (probability p_1$) and r_2$ \u003c 0 in $$state 2 (probability $$p_2). $$For a risk-averse agent, what is the optimal investment $$z^* if $$the net expected return $$p_1$$ $$r_1$$ + $$p_2$$ $$r_2 = 0$?

Accepted Answer

$$z^* = 0$$

Question 11

Which of the following statements about risk pooling is FALSE?

Accepted Answer

Risk pooling is always effective, even if all risks are perfectly correlated.

Question 12

If a consumer faces two possible states with probabilities $$p_1$$ and $$p_2$$, and state-contingent consumptions $$x_1$$ and $$x_2$$, what is their expected utility?

Accepted Answer

$$EU = p_1$ u(x_1$) + p_2$ u(x_2$)$$

Question 13

A risk-loving individual's utility function is characterized by which property?

Accepted Answer

Convexity: $$u''(x) \u003e 0$$

Question 14

In the context of insurance, what does 'full insurance' mean for the consumer's consumption?

Accepted Answer

Consumption is independent of the state of the world.

Question 15

If an insurance policy is 'actuarially unfair', what is true about the premium $$P$$ and expected claim $$pC$$?

Accepted Answer

$$P \u003e pC$$

Question 16

Which of the following is a real-world example where risk pooling failed due to perfect correlation?

Accepted Answer

Flood insurance in a region where all properties are affected simultaneously.

Question 17

Suppose a consumer is risk neutral. Which of the following is true about their utility function?

Accepted Answer

$$u(x) is $$linear in $$x$$

Question 18

If a consumer's utility function is $$u(x) = \ln(x)$$, and they face a lottery with $$x_1 = 100$ (probability 0.5$) and x_2$ = 200 ($$probability $$0.5$$), what is their expected utility?

Accepted Answer

$$EU = 0.5 \ln(100) + 0.5 \ln(200)$$

Question 19

A consumer with initial wealth $$w$$ faces a potential loss $$L$$ and can buy insurance with premium $$P$$ and claim $$C. If $$the insurance is actuarially fair, what is the relationship between $$P$$ and $$C$$?

Accepted Answer

$$P = pC$$

Uncertainty in Microeconomic Decision-Making: Risk, Insurance, and Risk Pooling

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