Question

Given the utility function U =10Q₁Q₂ and relative prices of P₁= ₦20, P₂ = ₦10 and consumer money income of ₦400. You are required to determine the units of each commodity to consume at the equilibrium point.

   

Answer 1

$U= 10Q_1Q_2$

$P_1= 20, P_2= 10, I= 400$

Budget line= $20Q_1+10Q_2= 400$

At equilibrium,

$\frac{Mu_1}{MU_2}= \frac{P_1}{P_2}$

$Mu_1= \frac{\delta U}{\delta Q_1}= 10Q_2$

$Mu_2= \frac{\delta U}{\delta Q_2}= 10Q_1$

$\frac{10Q_2}{10Q_1}= \frac{20}{10}$

$Q_1= 0.5Q_2$

$Q_2= 2Q_1$

Plug the these values in the budget Equation

$20(0.5Q_2)+10Q_2= 400$

$20Q_2= 400$

$Q_2^*= 20$

$20Q_1+10(2Q_1)= 400$

$40 Q_1= 400$

$Q_1^*= 10$