Consider a consumer with utility function U(x) =2√x1+x2. Draw her two Engel curves. Find the Demand...

Consider a consumer with utility function U(x) =2√x1+x2.

Draw her two Engel curves.

Find the Demand Function.

Solutions

Expert Solution

Solution: Let us find the demand function first :

1. Find MRS first.

= 2 . 1 / 2X1^(1/2) = 1/X1^(!/2)

= 1

MRS = = 1/X1^(1/2)

2. Equate MRS with the price ratio:

1/X1^(1/2) = Px1/ Px2

X1 =( Px2)^2/(Px1)^2

3. Put the value of X1 in the budget line :

M = Px1 *X1 + Px2 *X2

M = Px1 * ( Px2)^2/(Px1)^2 + Px2 *X2

Solve for X2 ,

X2 = (MPx1 -Px2^2) /Px1*Px2

If you see the demand function X1 and X2 you will come to know that X1 is not dependent on Price but X2 is dependent on price.

We can say that X1 is a good like Salt. If the income of a consumer increases he will be purchasing salt but the demand will not change due to increase in the salt .So its engel curve will look like this.

While the demand of X2 is positively related to income ,if you increase the level of income you can see that the demand for X2 will also increase so the engel curve will look like :

Rahul Sunny answered 1 year ago

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