Answer to Question #287311 in Economics for Israel

Question

Solve this question: Supposed a consumer utility function is written as U=(2q1,q2) where q1 and q2 are commodities 1 and 2 respectively. Let their respective price be given as p1=#2,p2=#8 and income be given as: B=#240. Use the above data to:

A. Find the maximum values of q1 and q2 that the consumer will consumed.

B. Show that the budget constraint is satisfied in the sense that all the income will be spent.

C. Show that the equal marginal principle is fulfilled.

Answer 1

A. The maximum values of q1 and q2 are consumed at:

MU1/MU2 = p1/p2 = 2/8 = 1/4.

MU1 = U'(q1) = 2q2,

MU2 = U'(q2) = 2q1,

$\frac{2q2}{2q1} = \frac{1} {4},$

q1 = 4q2.

B. The budget constraint is satisfied in the sense that all the income will be spent, so:

2×4q2 + 8q2 = 240,

16q2 = 240,

q2 = 15 units,

q1 = 4×15 = 60 units.

C. The equal marginal principle is fulfilled, because:

MU1/MU2 = p1/p2.