Question 1 (27 marks total) Napoleon consumes only two goods: left shoes (good x) and right shoes (good y). His utility function is given by U(x, y) = min{x, y}. (Napoleon is very proud of the fact that he only needs two shoes. After all, four legs good, two legs better.) Napoleon has an income of $6. The price of right shoes (good y) is normalised to $1 throughout this question.

(a) (4 marks) Suppose the price of left shoes (good x) is $1. Find Napoleon's utility maximising consumption bundle and calculate the utility he achieves at the bundle you have found. (Hint: Don't try to calculate the MRS or do the Lagrangian. How does the indifference curves look like?)

(b) (3 marks) In a graph with the quantity of right shoes on the x-axis and the quantity of left shoes on the y-axis, draw Napoleon budget line, clearly marking the intercepts and the utility maximising bundle you have solved in part (a) (call it bundle A). Also sketch an indifference curve passing through bundle A.

(c) (4 marks) The cunning humans raises the price of left shoes to $2 (but the price of right shoes remains unchanged). Find Napoleon's new utility maximising consumption bundle.

(d) (3 marks) On the diagram you have drawn for part (b), draw Napoleon's new budget line, clearly marking the intercepts and the new utility maximising bundle you have solved in part (c) (call it bundle B). Also sketch an indifference curve passing through bundle B.

(e) (4 marks) Calculate the amount of income required for Napoleon to just afford his old bundle (bundle A) under the new prices. Solve for Napolean's utilitymaximising consumption bundle given the new prices and the income you have just calculated. (Hint: Again don't attempt to use the MRS or the Lagrangian. Instead, think of how the diagram would look like.)

(f) (3 marks) On the diagram you have drawn for parts (b) and (d), draw the budget line associated with the new prices and income you have solved in part (e), clearly marking the intercepts and the utility-maximising bundle you have solved in part (e) (call this bundle H).

(g) (4 marks) Using your answers above, compute the changes in the quantity of left shoes and right shoes due to the substitution effect, and the changes in quantities due to the income effect, both associated with the increase in the price of left shoes from $1 to $2.

(h) (2 marks) What is the substitution effect on either good? Why?