Answer to Question #85642 in Microeconomics for AVENUE HEALTHCARE

Question

The utility function for a consumer utility is U=30Q11/2Q21/2 .If the price per unit of Q1 is Ksh 10 and Ksh 5per unit of Q2, determine quantities Q1 and Q2 that the consumer should have to maximize utility if the consumer Ksh 350budgeted

Answer 1

The condition of optimal consumer choice is:

〖MU〗_1/〖MU〗_2 =P_1/P_2

〖MU〗_1=〖U'〗_1=30×1/2×Q_1^(-1/2)×Q_2^(1/2)

〖MU〗_2=〖U'〗_2=30×1/2×Q_2^(-1/2)×Q_1^(1/2)

〖MU〗_1/〖MU〗_2 =(30×1/2×Q_1^(-1/2)×Q_2^(1/2))/(30×1/2×Q_2^(-1/2)×Q_1^(1/2) )=Q_2/Q_1

Q_2/Q_1 =10/5=2

So, Q2=2Q1

And the budget constraint is 10Q1+5Q2=350

So,

10Q_1+5×2×Q_1=350

20Q_1=350,

Q1=17.5

Q2=35