Question

1. Suppose the consumer has Cobb-Douglas preferences U(x₁, x₂)=X₁^aX₂^b Find out Ordinary Demands

2. Suppose the consumer has a perfect complement preferences U(X₁,X₂)=min{aX₁, X₂} Find out Ordinary Demands

Answer 1

Answer 1.

Let be price of good , price be of good and represent the consumer's income. Therefore, represents consumer's budget constraint. "For maximizing utility, marginal rate of substitution must be equivalent to price ratio. "

" Marginal rate of substitution is calculated using: "

Numerator of is given by  .

and denominator of   is given by  .

  

Equating to price ratio , imply:

This can be written as :  

Put in ----------

Put in   ---------------------------

So, ordinary demand of is and of is .

Answer 2.

Let be price of good , price be of good and represent the consumer's income. Therefore, represents consumer's budget constraint.

In this case optimal demand occurs at a point where

putting in imply

Putting in to get

So, ordinary demand of is   and of is   .