Answer to Question #134031 in Microeconomics for shadrick

Question

Joan’s gross monthly income is 3000 kwacha. She consumes two goods only, food and clothing. Her utility function is given by . The price of clothing has been at k50 per unit, and the price of food has been at k100 per unit.

(a)  Derive Joan’s demand functions for food and clothing

(b)  Mathematically derive and graphically present Joan’s budget line.

(c)  Derive and graphically present Joan’s optimal choice of clothing and food, as well as her optimal level of utility. 

Answer 1

a) Let $y$ to represent food and $x$ to represent clothing.

Demand function=$Qy=\frac{M} {Py} - \frac{Px} {Py} Qx$

$Y=\frac{3,000}{50}-\frac{100}{50}x$

y=60$-$2x

b) Q=$\frac{Income} {Pricey} =\frac{3,000} {50}$ =60

Q=$\frac{Income} {Price x} =\frac{3,000} {100}$ =30

Hence to get the budget line we plot 30 on the x-axis against 60 on the y-axis.

The optimal choice for food is 60 and the optimal level of clothing is 30.