Question

Question 1. Suppose a person has the following utility function over food (F) and shelter (S): U=F^2/3 S^1/3 They have income y, the price of food is pf, and price of shelter is ps. Find the demand functions for food and shelter. Use the lagrangian method and show your work

Answer 1

Answer 1

Maximize: F2/3S1/3

Subject to: F*pf + S*ps = y -----------------(1)

Legrange is given by:

L = F2/3S1/3 + u(y - F*pf + S*ps), where u = Legrange multiplier

First Order condition:

Dividing above conditions we get :

2S/F = pf/ps => F*pf = 2S*ps

Putting this in (1) we get:

2S*ps + S*ps = y

=> S = (1/3)(y/ps) ------Demand for Shelter

=> F = (2ps/pf)(1/3)(y/ps)

=> F = (2/3)(y/pf)------Demand for Food

answered by: anonymous