Question

Given utility function U= where PX = 12 Birr, Birr, PY = 4 Birr and the income of the consumer is, M= 240 Birr. 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

$MUx​=0.5\frac{x0.5}{y0.5​}$

$MU_y=0.5 \frac {x^{0.5}}{y^{0.5}}$

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

$x \times p_x+ y \times p_y=M$

y= 3x

12* x+4*y=240

x=10, y=30

D)

$\frac {\partial U}{\partial x \partial y} =\frac {0.25} {(xy)^{0.5}}$​

$MRS x.y = \frac {\partial U} {\partial x \partial y} = \frac {0.25}{(10 \times 30)^{0.5}}=0.015$

 

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