A consumer chooses x1 and x2 to maximize U(x1,x2) = log x1 + log x2, subject to the budget
constraint: px1 + x2 = y (note that the price of x2 has been normalized to equal one).
Solve the budget constraint for x2 as a function of x1. Using the substitution method, convert the consumer's optimization problem into a one-dimensional maximization problem, and find the consumer's optimal level of x1 as a function of p and y. Do the same for x2. After, solve the consumer's optimization problem using the Lagrange multiplier method. Interpret the first-order conditions in terms of the slope of budget constraint and indifference curves.