Question

Cleopatra spends all her money on bags (B) and shoes (S). Her utility function is U(B, S) = 2B0.5S 0.5 . Her income is $150. Price of shoes is pS = 2. Price of bags depends on the number of bags purchased. Bags cost $5 each if she purchases between 1 and 8 bags. If she purchases more than 8 bags, the price falls to $2 for all subsequent books.

(a) Draw Kleopatra's budget constraint where bag is on the horizontal axis. (10 Points)

(b) Solve for Cleopatra's optimal bundle. (15 Points)

(c) Suppose Cleopatra's utility function is U(B, S) = 0.5ln(B) + 0.5ln(S). What is her optimal bundle? (10 Points) (Hint: Compare the MRS for both utility functions.)

Answer 1

a) The budget constraint consists of two equations

When x<=8: 5x + 2y = 150

When x>8: (x-8)2 + (8×5) + 2y = 150

=> x+y = 63

Plotting this, we'll get a graph like this.

b)

c)

If we observe, the MRS of the new utility function is same as the old one. Hence we get the same bundle of x=y= 31.5

Hope this helps. Cheers!