Alvin the Chipmunk consumes only two things: tree nuts and berries. His utility

function is:

u(n,b) = 4n + b

(a) The bundle(25, 0) gives Alvin a utility of 20. What are other points that would

give him the same utility (Hint: stick in quantities of n that are perfect squares)?

Plot these points on a graph and draw the indifference curve that connects

them.

(b) What is Alvin's marginal utility of nuts? Of berries? When will the utility he

gets from an extra nut be higher than the utility he gets from an extra berry?

Give some intuition for your answer.

(c) Suppose that Alvin faces prices Pn and Pb and has income 'I' to spend. Use Method 2 (the Lagrangian) to find the optimal bundle that Alvin will consume (leave the prices and income in your answer).

(d) Your answer for the optimal bundle will look different from the Cobb-Douglas versions we saw on Problem 1 above. Can you explain what is going on in words?

Now suppose that the price of nuts is Pn = $1 and the price of berries is Pb = $2 and Alvin has an income of $24, with nuts on the x-axis.

(e) Draw Alvin's budget constraint based on these prices.

(f) How much money in total will Alvin spend on nuts?

(g) How much will be spent on berries?

(h) What share (fraction) of Alvin's income is he spending on nuts?