1) An individual has a utility function: V(c) = c²/³, for 0 ≤ c≤ 1000. There are two possible states of the world, S1 and S2, with probabilities 1/4 and 3/4, respectively. Her optimal consumption in state S1 is 8, and it is 27 in state S2. Using P₁ = 1 as numeraire. Find P2.

(d) Suppose that new copies cost $150 and used copies cost $80. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 15 copies purchased? [Hint: Let h(X) = the revenue when X of the 15 purchasers want new copies. Express this as a linear function.] $

I would appreciate your help greatly, thanks!

Direction: Solve the following problems in the space provided. (F1-F2)-do √0²/m₁ + 0²/m₂" 01 and 2 known H1-H2= do A random sample of size n₁ = 25, taken from a normal population with a standard deviation a₁ = 5, has a mean x = 80. A second random sample of size 1₂ = 36, taken from a different normal population with a standard deviation o₂ = 3, has a mean = 75. Using 5% level of significance, check whether ₁> H2 Reject Ho: > ₂ 2= (71-7₂)-do 5p1/n1+1/₂ v=1+0₂-2. ad but unknown, (n-1)+(₂-1) 7₁+n₂-2 The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections: n X s² 1-₂ do Medication 1 14 17 1.5 Medication 2 16 19 1.8 Using 0.01 level of significance, determine if medication 1 is more effective in treating the infection than medication 2, assuming normal populations with equal variances Reject Ho: Medication 1 is more effective than Medication 2. H1-H₂ do #1-2 do z Za 2 ²a/2: Two…