Question

Find the demand functions for the individuals below, the budget constraint is pxx+pyy=m

23

Bill:U(x ,x )=x y 12

2/5 3/5 Buster: U(x, y)=x y

23 Ben: U(x, y) = (x+1) (y+2)

Barbara: U(x ,x ) =3x +2y 12

Beth: U(x, y)=min{x , y}

Answer 1

Bill:

$$U(x,y)=x^2y^3$$

$$m=12$$

$$MU_x=\frac { \delta U}{ \delta x}=2xy^3$$

$$MU_y=\frac { \delta U}{ \delta y}=3x^2y^2$$

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

$$xp_x=\frac {2}{3}yp_y$$

$$xp_x+yp_y=12$$

$$yp_y=9.2$$

$$xp_x=4.8$$

Buster:

$$U(x,y)=x^{\frac{2}{3}}y^{\frac {3}{5}}$$

$$m=23$$

$$MU_x=\frac { \delta U}{ \delta x}= (\frac {x}{y})^{\frac {2}{5}}$$

$$MU_y=\frac { \delta U}{ \delta y}=(\frac {y}{x})^{\frac {3}{5}}$$

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

$$yp_x=xp_y$$