Bruno’s stock should return 14 percent in a boom, 11 percent in a normal economy, and 4 percent in a recession. the probabilities of a boom, normal economy, and recession are 8 percent, 90 percent, and 2 percent, respectively. what is the variance of the returns on this stock?
a. 0.011387
b. 0.000169
c. 0.001506
d. 0.001538
e. 0.011561

option (b)  variance of the returns is 0.000169

Explanation:

Given data

boom return = 14% = 0.14

normal economy = 11% = 0.11

recession = 4% = 0.04

boom probability = 8% = 0.08

normal economy  probability = 90 %  = 0.90

recession  probability = 2 % = 0.02

to find out

the variance of the returns on this stock

solution

we know variance of the returns is sum of standard deviation

expected return = boom return × boom probability

expected return boom = 0.14 × 0.08 = 0.0112

expected return = economy × economy probability

expected return economy  = 0.11 × 0.9 = 0.099

expected return = recession × recession probability

expected return recession = 0.04 × 0.02 = 0.0008

total expected return = 0.0112 + 0.099 + 0.0008 = 0.111

for boom

standard deviation = probability × (return - 0.111)²

standard deviation = 0.08 × (0.14 - 0.111)²   = 0.00006728    1

for normal economy

standard deviation = probability × (economy - 0.111)²

standard deviation = 0.90 × (0.11 - 0.111)²   = 0.00000090    2

for recession

standard deviation = probability × (recession - 0.111)²

standard deviation = 0.02 × (0.04 - 0.111)²   = 0.00010082    3

variance of the returns is sum of standard deviation

variance of the returns = 0.00006728 + 0.00000090 + 0.00010082

variance of the returns is 0.000169

answer; blank(1); /rises; blank(2); //increases;

answer: in the short-run firms will respond by raising the price of turkey.

explanation: initially the long-run equilibrium is at a price of $5 per pound of turkey and a quantity of 50 million pounds per year. now, when webmd claims that a protein found in turkey will increase your expected lifespan by 4 years. the consumers demand for turkey will increase at every price shifting the demand curve to the right from d1 to d2. while, there will be no change in the supply curve in the short-run as it is not possible for producers to adjust supply so quickly. as a result the new equilibrium will occur at a higher price and a higher quantity of turkey.

thus, in the short run firms will respond by increasing the price of turkey, selling more quantity at a higher price and earning economic profits.