Question

The utility function for a consumer utility is U=30Q1^½Q2^½. if the price per unit of Q1 is ksh 10 and ksh 5 per unit of Q2, determine quantities Q1 and Q2 that the consumer should have ti maximize utility if the consumer budgeted kdh 350

Answer 1

Solution:

Max $U=30Q_{1}Q_{2}$

S.t $10Q_{1} +5Q_{2} = 350$

$Q1, Q2 ≥0$

At equilibrium:

$MU_{1}/MU_{2}=P_{1}/P_{2}$

${15(Q_{2}/Q_{1})^1/2/15(Q_{1}/Q_{2})^1/2}= 10/15$

$Q_{2}/Q_{1}=2$

$Q_{2}= 2Q_{1}$

From the budget:

$10Q_{1} +5Q_{2} = 350$

$10Q_{1} + 2Q_{1} = 350$

$20Q_{1}= 350$

$Q_{1}= 17.5$

$Q_{2}= 35$