Question

5. The utility function of a consumer is u(x, y) =x²y

i. Find the demand functions x(p_1,p₂,m) and y(p₁,p₂,m).

ii. What is the consumers indirect utility?

Answer 1

Answer 5

(i)

Maximize: x²y

Subject to: xp₁ + yp₂ = m -----------------(1)

Legrange is given by:

L = x²y + u(m - xp₁ + yp₂), where u = Legrange multiplier

First Order condition:

=> (2xy)/x² = (p₁u)/(p₂u)

=> 2y/x =  p₁/p₂

=> xp₁ = 2yp₂

Putting this in (1) we get:

2yp₂ + yp₂ = m => y = (1/3)(m/p₂)

=> x = 2yp₂/p₁ => x = (2/3)(m/p₁)

(ii)

Thus, Indirect utility(v) = ((2/3)(m/p₁))²(1/3)(m/p₂)

=> Indirect utility(v) is given by :