Question

4. Chrissy spends her income on fishing lures (L) and guitar picks (G). Lures are priced at $2, while a
package of guitar picks cost $1. Assume that Chrissy has $30 to spend and her utility function can be
represented as U(L, G) = L0.5G0.5.
a. For this utility function, find the MUL and MUG.
b. What is the optimal number of lures and guitar picks for Chrissy to purchase? How much utility
does this combination bring her? (Put fishing Lures [L] on the horizontal axis).
c. If the price of guitar picks doubles to $2, how much income must Chrissy have to maintain the same
level of utility?

Answer 1

Solutiion::

a) PL=2, PG=1 I=30

$$U(L;G)=\sqrt{LG}$$

$$MUL=\frac{\delta U}{\delta L}=\frac{\sqrt {G}}{2\times \sqrt {L}}=\frac{1}{2}\times \sqrt{\frac{G}{L}}$$

$$MUG=\frac{\delta U}{\delta G}=\frac{\sqrt{L}}{2\times \sqrt{G}}=\frac{1}{2}\times\sqrt\frac{L}{G}$$

b) I=2L+G

if L=0 then G=30,

if G=0 then L=15.

c) If G=2? then we will have I=2L+2G, so

$$I=2\times30=60$$