Question

Diogo has a utility​ function, ​U(q1, q2) = q1^.8q2^.2, where q1 is chocolate candy and q2 is slices of pie. If the price of slices of​ pie, p2​, is ​$5.00​, the price of chocolate​ candy, p1​, is ​$10.00​, and​ income, Y, is ​$100​, what is​ Diogo's optimal​ bundle? The optimal value of good q1 is?

Answer 1

U = q1^0.8q2^0.2

Budget line: 100 = 10q1 + 5q2, or 20 = 2q1 + q2

Utility is maximized when MU1 / MU2 = P1 / P2 = 10/5 = 2

MU1 = $\partial$ U / $\partial$ q1 = 0.8 x (q2 / q1)^0.2

MU2 = $\partial$ U / $\partial$ q2 = 0.2 x (q1 / q2)^0.8

MU1 / MU2 = (8/2) x (q2 / q1) = 4q2 / q1 = 2

4q2 = 2q1

2q2 = q1

Substituting in budget line,

20 = 2q1 + 2q1 = 4q1

q1 = 5

q2 = 2 x 5 = 10

Optimal value of good 1 = P1 x q1 = $10 x 5 = $50