Question

05 Question (17 points) @ See page 149 Arlo is very health-conscious and consumes only two goods, rice cakes and quinoa. His utility function is ulr, q) = r2q, wherer is the number of packs of rice cakes he consumes and q is ounces of quinoa. The price of a pack of rice cakes is $5, and the price of an ounce of quinoa is $10.Arlo has $900 to spend this week on these two goods. Suppose that the price of quinoa suddenly falls to $5. 1st attempt Part 1 (2 points) See Hint Before the price change, Arlo consumed packs of rice cakes and ounces of quinoa per week. Part 2 (3 points) See Hint If, after the price change, Arlo's income had changed so that he could exactly afford his old consumption bundle, his new income would have been $ . With this income and the new prices, Arlo would consume packs of rice cakes and ounces of quinoa. Part 3 (2 points) See Hint How many Does the substitution effect of the fall in the price of quinoa make Arlo buy more quinoa or less quinoa? ounces more quinoa or less quinoa?

Answer 1

1. The consumer's problem is:
$\dpi{80} \fn_phv \small max \ r^2q \ s.t. \ 5r+10q=900$
At equilibrium, marginal rate of substitution is equal to the price ratio:
$\dpi{80} \fn_phv \small \frac{2rq}{r^2}=\frac{2q}{r}=\frac{1}{2}\rightarrow r=4q$
a. b. Substituting this into the consumer's budget equation:
$\dpi{80} \fn_phv \small 4q*5+10q=900\rightarrow q=30,r=120$

2. c. In order to purchase the original bundle, income required by the consumer is: $\dpi{80} \fn_phv \small 120*5+30*5=750$

d. The consumer's problem with the new prices and this income is:
$\dpi{80} \fn_phv \small max \ r^2q \ s.t. \ 5r+5q=750$
At equilibrium, marginal rate of substitution is equal to the price ratio:
$\dpi{80} \fn_phv \small \frac{2q}{r}=1\rightarrow 2q=r$
Substituting this into the consumer's budget equation:
$\dpi{80} \fn_phv \small 2q*5+5q=750 \rightarrow q=50,r=100$