Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function is u(x1, x2) = x1x2. Her income is m = $200. The prices for the two goods are p1 = $20 and p2 = $10 respectively.

a. Find Anna's optimal consumption bundle. Show the complete calculations, and illustrate your answer graphically (draw the indifference curve and the budget constraint).

b. How would your answer change to part (a) if Annas utility function were given by v(x1, x2) = 4. x1^2 . x2^2 Explain.

c. Compute Anna's marginal rate of substitution (MRS) at the optimal consumption bundle and give an interpretation.

d. Now suppose the government levies a 25% tax on each bottle of wine purchased. Find Annas optimal consumption bundle and illustrate it in the same graph that you drew in part (a).

e. Would Anna prefer a $20 income tax (i.e., lump-sum tax) to the 25% value tax on wine? Which scenario would the government prefer? Justify your answers.