Georgina consumes only pasta (good x) and wine (good y). Her utility function is given by U (x, y) = 3 ln x + ln y.

(a) Consider only bundles with both x > 0 and y > 0. Are Georgina's preferences monotone? Are they strictly monotone? Does this utility function satisfy diminishing MRS?

(b) Find the expenditure-minimizing bundle (x,y) as a function of the prices px and py, and the target utility U.

(c)(c.1) Find the expenditure necessary to attain the utility U as a function of the prices px and py, and the target utility U itself. If the prices are px = 1, py = 1, obtain the expenditure necessary to attain the utility U = ln 16.

(c.2) What is Georgina's utility-maximizing bundle if her income is M = 16 and prices are px = 3 and py = 1? What utility does she attain?

(d) The owner of the store where Georgina buys her groceries has a special oer: any customer that buys more than 2 units of pasta is charged only p0x = 1 per unit for any quantity in excess of 2 units (but for the first two units of x customers still have to pay px = 3 per unit). Recall that Georgina's income is M = 16 and py = 1

(d.1) What is (are) the equation(s) describing Georgina's budget line under this special offer?

(d.2) What is Georgina's optimal consumption with this special offer?