Question

(This is part b of a multipart question. You may wish to make note of any calculations for subsequent parts) Assume consumer preferences satisfy A1-A4 and consider a generic consumer utility maximization problem: max u(x,y) X,у S.t Pxx Pyy x2 0, y 2 0 b. To account for the budget constraint we need to add a term called a In this course, we will denote this with the Greek lowercase letter "Lambda," A We can interpret this term in two ways: 1. Mathematically, it is aterm for violating the constraint. 2. Economically, it is the extra utility a consumer would get from a dollar increase in income, which we call the

Answer 1

Here the maximization problem is given by.

=> Max U(X, Y) subject to “Px*X+Py*Y < = I”

Now, to account for the budget constraint we need to add a term called “Lagrange Multiplier”. Mathematically it is a “shadow price” term for violating the constraint.

Economically it is the extra utility a consumer would get from a dollar increase in income which we call the “marginal utility of income”.