Question

Tastego comsumes only whale meat (W) and port (P). His utility function is ? = √2? + √4?. The price of whale meat is $10 per pound, and port is $5 per bottle. Tashtego has a weekly income of $400 to spend on these goods. You may assume that it is possible to consume fractional amounts of either good. a. Draw and label Tashtego’s budget constraint. You may assume whale meat is on the horizontal axis, because this will match the answer key. (Again, this doesn’t really matter to find the optimal consumption bundle solution.) b. Using the tangency condition method, calculate Tashtego’s optimal quantities of whale meat and port, and label this consumption bundle on the diagram above with the letter A. Sketch the indifference curve through point A on your diagram.

Answer 1

U = (2W)^0.5 + (4P)^0.5 = 2^0.5W^0.5 + 2P^0.5

(a) Budget line: 400 = 10W + 5P, or 80 = 2W + P

When W = 0, P = 80 (Vertical intercept) & when P = 0, W = 80/2 = 40 (Horizontal intercept).

In following graph, XY is budget line.

(b) Utility is maximized when MUW/MUP = PW/PP = 10/5 = 2

MUW = U/W = (0.5 x 2^0.5) / W^0.5

MUP = U/P = (2 x 0.5) / P^0.5

MUW/MUP = (P/W)^0.5 x (2^0.5/2) = 2

Squaring,

(P/W) x (2/4) = 4

P/W = 8

P = 8W

Substituting in budget line,

80 = 2W + 8W = 10W

W = 8

P = 8 x 8 = 64

This is shown as point A.

(c) Indifference curve IC0 is tangent to budget line at point A as shown.