Question

A consumer's utility function is given by the

expression: U = (0.6X" + 0.4Y^°'1².

·    Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases?

·    Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate?

·    Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing the consumer's equilibrium condition.

·    Obtain the equilibrium values of X and Y.

·    Find the expressions for change in MU₎, due to increase in Y and change in MU, due to increase in X.

Answer 1

$$U=12x^{0.6}y^{0.4}$$

$$MU_x=7.2(\frac {y}{x})^{0.4}$$

$$MU_y=4.8(\frac {x}{y})^{0.6}$$

$$p_x=15$$

$$p_y=6$$

$$15x+6y=240$$

$$y=-2,5x+75$$

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

$$x=0.6y$$

$$y=-2.5\times0.6y+75$$

$$y=30$$

$$x=18$$

$$\frac {MU_y}{MU_x}=\frac {2}{3}\times(\frac {18}{30})=0.4$$