Question

Graph a typical isoquant curve for the following production functions and determine whether they have convex indifference curves. Also calculate MRTS for each of the following functions
Q(x,y)=3x+y
Q(x,y)=√(x.y)
Q(x,y)=√x+ y

Answer 1

a)

$$Q(x,y)=3x+y$$

$$\frac {\delta Q}{\delta x}=3$$

$$\frac {\delta Q}{\delta y}=1$$

$$MRTS=\frac {3}{1}=3$$

b)

$$Q(x,y)=\sqrt {xy}$$

$$\frac {\delta Q}{\delta x}=\frac {y}{2 \sqrt {xy}}$$

$$\frac {\delta Q}{\delta y}=\frac {x}{2 \sqrt {xy}}$$

$$MRTS=\frac {y}{x}$$

c)

$$Q(x,y)=\sqrt {x+y}$$

$$\frac {\delta Q}{\delta x}=\frac {1}{2 \sqrt{x+y}}$$

$$\frac {\delta Q}{\delta y}=\frac {1}{2 \sqrt{x+y}}$$

$$MRTS=1$$