An agent consumer quantity (X1, X2) of goods 1 and 2. She has utility U(X1, X2)=X½,X½.
a) Derive the MRS and show your work clearly.
MRS = Marginal Rate of Substitution
MRS = ∂U/∂X1 / ∂U/∂X2
MRS = (1/2)*(∂X1/∂X2) / (1/2)*(∂X2/∂X1)
MRS = (∂X1/∂X2) / (∂X2/∂X1)
MRS = 1
b) What is the optimal bundle of goods 1 and 2?
The optimal bundle of goods 1 and 2 is X1 = X2. This is because the MRS is equal to 1, which means that the consumer is indifferent between consuming more of one good and less of the other. Therefore, the optimal bundle is the one where the consumer consumes equal amounts of both goods.