Reference no: EM13238647
Suppose a consumer has wealth w and is considering investing some amount,x,in risky asset.This asset can earn a return of Rg(which is positive return and therefore a good outcome or Rb (a negative return that ultimately reduces initial wealth per dollar invested in the asset).Thus wealth in the good and bad states will be:
Wg=(w-x)+x(1+Rg)=w+wRg where Rg>0
Wb=(w-x)+x(1+Rb)=w+wRb where Rb<0
the probability of the good state is π and the probability of the bad state is 1-π.
a)Find the general expression for the consumer's expected utility maximization problem for investing x dollars in the risky asst.Let u(w) represent the general utility function.Characterize the solution to this problem by finding the first order condition and check to see if (or when ) the second order condition ( or will be)satisfied.
b)Let the individual's utility function be given by u(w)=ln w .Using this,solve the consumer's expected utility maximization problem.(Assume that the amount invested is positive)
c)suppose the individual has to pay a (positive)tax,t,on the return of the asset,whether it is positive or negative.Thus the after tax returns will be (1-t)Rg and (1-t)Rb.Wealth in each state is no:
Wg=w+x(1-t)Rg where Rg>0
Wb=w+x(1-t)Rb where Rb<0
Given the specific utility function in (2b),find the optimal amount of investment when t>0.
d)What is the relationship between investment when the tax rate is zero versus when it is strictly positive?Does your make sense?Explain.
|
How construction cost index has increased an average rate
: if an ammonia plant that produces 500,000 pounds per year cost $2,500,000 to construct eight years ago, what would a 1,500,000 pound per year plant cost now Suppose that the construction cost index has increased an average rate of 125
|
|
Compute the concentration of ha
: If .050 moles of HA were dissolved in 1L of water, calculate the concentration of [HA], [H30+], and [A-] in the solution at equilibrium. What is the pH? Ka=7.94 x 10^-7, equivalence point ~ 9 mL, pH at equivalence ~ 9]
|
|
What is the probability that the sample mean is 20 or higher
: The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean of 18.6 and a standard deviation of 5.9. A simple random sample of 60 students who took the exam is selected for study
|
|
Define the oxidation reduction behind the reaction
: Explain the oxidation reduction happening behind the reaction: 2 NH4NO3 (s) -> 2N2 (g) + O2 (g) + 4H2O (l)
|
|
Find the general expression for consumers expected utility
: Find the general expression for the consumer's expected utility maximization problem for investing x dollars in the risky asst.Let u(w) represent the general utility function.Characterize the solution to this problem by finding the first order con..
|
|
What is the net work done on the plane
: The model airplane in figure below is flying at a speed of 19 m/s on a horizontal circle of radius 17 m, What is the net work done on the plane
|
|
Demonstrate that utility function that is monotonic utility
: To demonstrate that a utility function that is a monotonic transformation of another utility function gives that same first-order conditions and hence the same demand functions, multiply the utility function U = U(X,Y) by a constant
|
|
What are the frequency and wavelength of the wave
: A wave on a string is described by the equation y = (4.2 mm)cos(3000t 0.45x) where t is measured in s and x is measured in mm
|
|
What is the intensity of light emerging from p1
: A beam of unpolarized light of intensity 12.o w/m^2 is incident on an ideal linear polarizer, P1, whose transmission axis is in the vertical (y) direction, What is the intensity of light emerging from P1
|