Clara has preferences represented by utility function U (x1; x2) = x1 + 400 ln (x2): The consumer has an income level of m = 20; 000 dollars. The price of good 1 is p1 = 5 and the price of good 2 is p2 = 5. (Note that ln is natural logarithm.) (a) Compute the Marginal Utility of good 2. (10 Points) (b) Compute the Marginal Rate of Substitution (in absolute value). (10 Points) (c) Find the optimal levels of consumption for Clara (x

1 and x

2 ). (Hint: You can use Lagrange.)

(10 Points) (d) Suppose the government imposes a per-unit sales tax of $1 on good 1. Find the new budget restriction. (10 Points)