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 u(r, 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 $1, and the price of an ounce of quinoa is $2. Arlo has $180 to spend this week on these two goods. Suppose that the price of quinoa suddenly falls to $1. v 25th attempt Part 1 (2 points) See Hint Before the price change, Arlo consumed 120 packs of rice cakes and 30 ounces of quinoa per week.
I just need help with the number answers of part 5 of this question.

Answer 1

Solution:

We are given the utility function as: u(r, q) = r²q

Initial prices: pr = $1, pq = $2

Final prices: pr' = $1, pq' = $1

Given this information, the optimal consumption bundle before price change is: (r*, q*) = (120, 30) following the optimality condition r* = 4q* (using ratio of marginal utility of goods should equal ratio prices)

So, the compensated income (the income required to buy the old optimal bundle at new prices) = 1*120 + 1*30 = $150

So, income effect is equivalent to an increase in income by (180 - 150) = $30 per week.

Further, at new prices, optimality condition is:

2q/r = 1/1

r = 2q

Optimal bundle at this new income and new prices is:

2q + q = 150

q = 150/3 = 50 units

r = 2*50 = 100 units

The optimal bundle at original income level and new price:

2q + q = 180

q = 180/3 = 60 units

And r = 2*60 = 120 units

So, income effect increases consumption of quinoa by (fin bundle - substitution bundle) 50 - 40 = 10 units