Question

a. The utility function for a consumer utility is U=30Q1 1/2 Q2 1/2 .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

a. U = $30Q1^{0.5}*Q2^{0.5},$ P1 = Ksh 10, P2 = Ksh 5, I = Ksh 350.

Utility is maximized, when:

$MU1/P1 = MU2/P2$

and

$P1*Q1 + P2*Q2 = I$

MU1 = U'(Q1) = $15Q2^{0.5}/Q1^{0.5}$

MU2 = U'(Q2) = $15Q1^{0.5}/Q2^{0.5}$, so:

$15Q2^{0.5}/10Q1^{0.5} = 15Q1^{0.5}/5Q2^{0.5},$

$1.5Q2 = 3Q1, Q2 = 2Q1,$

10Q1 + 5*2Q1 = 350,

20Q1 = 350, Q1 = 17.5 units,

Q2 = 35 units.