Question

given utility function U= where PX = $12, $, py = $4 and the income of the consumer is, M = $240.
A, Find the utility maximizing combinations of X and Y.
B, calculate marginal rate of substitution of X for Y (MRSX,Y) at equilibrium and interpret your result.

Answer 1

Since the utility function should be a function of two variables, then

$$MU_x=\frac {\delta U}{\delta x}$$ $$MU_y=\frac {\delta U}{\delta y}$$

$$12x+4y=240$$

$$\frac {MU_x}{12}=\frac {MU_y}{4}$$

$$MU_x=3MU_y$$