Investors have utility U Expected income 10 Variance of in

Investors have utility U = Expected income - 10* Variance of income. Stock in the TransUkraine Pipeline Company has return F + epsilon, epsilon ~N (0, 0.16), where 0.16 is the variance in dollars squared. X shares of stock are outstanding. Investors can either invest in the TransUkraine Pipeline Company, or the riskless asset (money). There are 500 investors available. Each believes (rationally) that F = 1. Compute the price of the TransUkraine Pipeline Company stock for X = 100.

Solution

given e is normally distributed with N(0,0.16)

e=(1/standard deviation(2pi))*exp^(-((x-mean)^2)/2*variance)

given mean =0

variance=0.16

standard deviation =root of variance

when x=100, substitute all given alues in the formula for e

we get e=0

given return =f+e

return=1*500=500

so price of 1 stock =500/100

=5