Problem
1. A consumer has the utility function U = 20X0.5Y 0.4 and buys good X at £10 a unit and good Y at £2 a unit. If their budget constraint is £450, what combination of X and Y will maximize utility? Check that second-order conditions are satisfied by using the bordered Hessian.
2. A consumer has the utility function U = 4X0.75Y 0.25 and can buy good X at £12 a unit and good Y at £2 a unit. Find the combination of X and Y that they should purchase to minimize the cost of achieving a utility level of 580 and check that second-order conditions are met using the bordered Hessian matrix.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.