Question

Find a measure of inflation that's appropiate for a consumer with the utility fuction of U(q1, q2) = (q1)^(1/3) + (q2)^(1/3)

Answer 1

From the utility function U(q1, q2) = (q1)^(1/3) + (q2)^(1/3), we see that MRS is given by MUq1/MUq2 = (1/3)q1^(-2/3)/(1/3)q2^(-2/3) or MRS = (q2/q1)^(2/3)

The optimal choice has |MRS| = price ratio or MUq1/MUq2 = Pq1/Pq2. Now see that in this case where q1 and q2 are perfect substitutes, we must have MUq1/MUq2 = Pq1/Pq2

If MUq1/MUq2 > Pq1/Pq2, only q1 is purchased and if MUq1/MUq2 < Pq1/Pq2 only q2 is purchased.

This implies that if the consumer is consuming only Q1, we can infer that MUq1/MUq2 > Pq1/Pq2 and that Pq1 < Pq2. Similarly, if the consumer is consuming only Q2, we can infer that MUq1/MUq2 < Pq1/Pq2 and that Pq1 > Pq2. This gives us a meausre of inflation in Pq1 and Pq2.