Question

Julia likes to consume two brands of jeans: jeans from the Gap (G) and jeans from J. Crew (J). She considers these goods to be substitutes and her utility function is:?(?,?)=?+4?. Julia’s birthday is this weekend and her (very generous) parents have given her $3000 to spend on jeans at the mall. In addition, Julia’s (very generous) Aunt Sally has sent her a birthday card with a gift certificate to the Gap worth $600.The price of jeans at the Gap is $30 and the price of jeans at J. Crew is $60.What is Julia’s optimal bundle? Show this solution graphically, putting G on the horizontal axis. As before, label the optimal consumption levels ?∗and ?∗, draw the indifference curve at the optimum (does not need to be exact but please make sure that you get the correct shape and the correct tangency), the budget line, and all axes and other relevant points).

Answer 1

The two goods are perfect substitutes

Max U(G,J)= G+4J subject to 30G+60J = 3600

60J= 3600-30G

or J= (3600/60) - (30/60)G

J= 60- 0.5J

Similarly, 30G= 3600-60J

G= 120-2J

Now, U= G+4J

4J= U-G

or J= U/4 - G/4

Therefore, Slope of the budget line is negative 1/4