Question

Suppose the utility function for Bernard is given by Z=2H₁H₂ and his income equation by Y=P₁H₁+P₂H₂

Derive the demand equation for H₁H₂

Answer 1

given utility function $Z=2H_1H_2$

income constraint $Y=P_1H_1+P_2H_2$

utility maximization condition $MRS=\frac{P_1}{P_2}$

$MRS=\frac {\delta H_1}{\delta H_2}=\frac{2H_2}{2H_2}=\frac{H_2}{H_2}$

$\frac{H_2}{H_1}=\frac{P_1}{P_2}$

$H_2-\frac{P_1}{P_2}H_1......(I)$

putting equation (i) in the income constraint

$Y=P_1H_1+P_2(\frac{P_1}{P_2}H_1)$

$Y=P_1H_1+P1H_1$

$Y=2P_1H_1$

$H_1=\frac{Y}{2P_1}$ .....(Demand equation for $H_1$ )

Putting $H_1$ in equation (I)

$H_2=\frac{P_1}{P_2}(\frac{Y}{2P_1})$

$H_2=\frac{2}{2p_2}$ ......(demand function for $H_2$ )