Question

Q1) Given the utility function:
U = X3/4 .Y1/4
Find out the optimal quantities of the two commodities using Lagrange method and simplified procedure, if it is given that price of X is Rs.6 and price of Y is Rs.3 and income is equal to Rs.120.

Answer 1

$$MU_x=\frac {3}{4}(\frac {y}{x})^{\frac {1}{4}}$$

$$MU_y=\frac {1}{4}(\frac {x}{y})^{\frac {3}{4}}$$

$$\frac {MU_x}{p_x}=\frac {MU_y}{p_y}$$

$$y=1.5x$$

$$2x+1.5x=40$$

$$x=11.4$$

$$y=17.1$$