Utility theory

Question 1

If f(x,y)=X^0.5 + Y^0.5 and the price of x is p1 and the price of y is p2, and income is m. What is the demand function( Optimal choice for x and y)

Answer 1

X=(mp2)/(p1^2 + p1p2) Y=(mp1)/(p2^2 +p1p2)

Question 2

If U’(w)= 7.5-2w. (W>0). What is the range that this utility function can be applied.

Answer 2

0

Question 3

What is theformula for arrow pratt absolute and relative wealth.

Answer 3

A(w)= -U''(w)/U'(w)
R(w)= -wU''(w)/U'(w)

Question 4

What is the certainty equivalent Cx of a gamble.

Answer 4

E(U(w+x))= U(w+Cx)

Question 5

If Fa(X)=X and Fb(X)=X^0.5 show that Fa(X) exhibits stochastic dominance

Answer 5

A is preferred to B on the basis of first-order stochastic dominance if:
Fa(x) ≤  Fb(x)
for all 0 ≤ x ≤ 1 and
Fa(x) <  Fb(x)
for some value of x in this range

i.e. if x ≤ x^0.5 this means x-x^0.5 ≤ 0 which means x^0.5(x^0.5-1) ≤ 0

This clearly holds for all 0 ≤ x ≤ 1 the equality being strict for 0 < x < 1.
Hence A first-order dominates B.