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 Napoleons utility

maximising consumption bundle and calculate the utility he achieves at the bundle

you have found. (Hint: Dont try to calculate the MRS or do the Lagrangian. How

does the indifffference 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 indifffference 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 Napoleons new utility maximising con

sumption bundle.

(d) (3 marks) On the diagram you have drawn for part (b), draw Napoleons 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 indifffference curve

passing through bundle B.

(e) (4 marks) Calculate the amount of income required for Napoleon to just afffford

his old bundle (bundle A) under the new prices. Solve for Napoleans utility

maximising consumption bundle given the new prices and the income you have

just calculated. (Hint: Again dont 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 bud

get 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 effffect, and the changes in quantities

due to the income effffect, both associated with the increase in the price of left

shoes from $1 to $2.

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

Please pay attention to answering question g& (h)

Please pay attention to answering question g& (h)

Please pay attention to answering question g& (h)