Question

Suppose INDIVIDUAL 1 has a healthy-state income IH = $80,000, a sick-state income IS = $5,000, and probability of illness p = 0.4. INDVIDUAL 1’s utility, a function solely of income, is represented in the table and income-utility diagram below (on the following page).

a. Calculate INDIVIDUAL 1’s expected income E[I].

On the income-utility diagram provided on the next page, INDIVIDUAL 1’s healthy-state and sick-state incomes,

IH and IS, are marked along the x-axis. Please label INDIVIDUAL 1’s expected income E[I].

b. Using the provided income-utility table on the following page, calculate INDIVIDUAL 1’s expected utility E[U(I)].

c. Using both the income-utility table and the income-utility diagram determine INDIVIDUAL 1’s utility of expected

Answer 1

Individual 1's expected income E[I] is $50,000, calculated from a healthy-state income of $80,000, sick-state income of $5,000, and a 0.4 probability of illness. Expected utility E[U(I)] and utility of expected income would require specific utility values from the provided income-utility table and diagram, which are not provided in the question.

Step-by-step explanation:

To calculate Individual 1's expected income E[I], we use the formula E[I] = (p * IS) + ((1 - p) * IH), where 'p' represents the probability of illness, 'IS' is the income when sick, and 'IH' is the income when healthy. Substituting the given values: E[I] = (0.4 * $5,000) + (0.6 * $80,000) = $2,000 + $48,000 = $50,000. Thus, Individual 1's expected income is $50,000.

Next, to calculate Individual 1's expected utility E[U(I)], we would normally look at the utility values assigned to the incomes IS and IH in the income-utility table. Expected utility is then computed as E[U(I)] = (p * U(IS)) + ((1 - p) * U(IH)). However, as no specific utility values are provided, we cannot calculate the exact numerical value for expected utility.

To determine Individual 1's utility of expected income, we would find the utility corresponding to the expected income of $50,000 on the income-utility diagram. This utility reflects the individual's well-being from the expected income, but exact utility values are needed to specify this.