An agent consumer quantity (X1, X2) of goods 1 and 2. She has utility U(X1, X2)=X½,X½.
a) Derive the MRS
of the consumer.
The MRS (Marginal Rate of Substitution) of the consumer is the rate at which the consumer is willing to substitute one good for another while maintaining the same level of utility.
MRS = ∆U/∆X1/∆X2
Substituting the given utility function, we get:
MRS = (1/2X-1/2)/(X1-X2)
Therefore, the MRS of the consumer is 1/2X-1/2 divided by the difference between X1 and X2.