Each individual consumer takes the prices as given and chooses her consumption bundle, (x1, x2) ∈ R 2 +, by maximizing the utility function U(x1, x2) = ln(x1 · x2), subject to the budget constraint p1 · x1 + p2 · x2 = 1000.
(a) (3 points) Write out the Lagrangian function for the consumer's problem.
(b) (6 points) Write out the system of first-order conditions for the consumer's problem.
(c) (6 points) Solve the system of first-order conditions to find the optimal values of x1 and x2. Your answer might depend on p1 and p2.
(d) (Voluntary, 0 points) Check that the critical point satisfies the second-order condition.
Recently Asked Questions
- I work for a telecommunications company and there a too many shadow IT projects that have been established. I need to identify the main functions of a new
- I checked to see if this was conservative or not and it wasn't, how do I solve this problem? Thank you
- Describe and the six (6) forces of change Describe one of the six forces that act as stimulants to change. Describe one of the sources of resistance to