Answer to Question #297664 in Microeconomics for BAi

Question

Suppose a consumer having a disposable income of 300 birr consumers only two commodities X and Y and his utility function is given as U(X,Y)=50X-X2+25Y given further that price of X and Y are 1 birr and 2.5 birrr respectively, determine:

A. The consumer's optimal bundles

B. His Marginal utility of income and its interpretation

Answer 1

$U_(x,y)=50X-2X+25Y$

Budget line:

$300=X+2.5Y$

At optimal bundle, slope of the budget line is equal to the slope of Indifference curve.

Slope of BL$=\frac{-y}{x}=\frac{-2.5}{1}=-2.5$

Slope of IC$=\frac{-MU_x}{MU_y}$

$MU_x=48+25Y$

$MU_y=48X+25$

Therefore slope of IC$=\frac{-(48+25Y)}{48X+25}$

Equating slope of BL and IC:

$\frac{-(48+25Y)}{48X+25}=\frac{-2.5}{1}$

$-48-25Y=120X-62.5$

$25Y=120X+14.5$

$Y=4.8X+0.58$

Replacing Y in the budget line:

$300=X+2.5×(4.8X+0.58)$

$300=13X+1.45$

$13X=298.55$

$X=22.97$

$Y=4.8X+0.58$

$Y=4.8×22.97+0.58=110.84$

B)

$U_{x,y}=48X+25Y$

$=48×22.97-2×22.97+25×110.84$

$=3873.56$