Question

GIVEN THE DEMAND FUNCTION DERIVING FROM A COUBBL-DOUGLAS WITH COEFFICIENT 0,5 AND 0,5 COMPUTE THE ELASTICITY OF DEMAND WITH RESPECT TO PRICES

Answer 1

With co-efficient 0.5 and 0.5.

U= x^.5y^.5

Now,

By multyplying both sides with x^.5 , we get,

I=P_xx+P_yy

Now, from the value of y, i.e calculated:

This is demand function of good x

The same process can be followed to calculate the demand function of good y,i.e

Now,if we compute the elasticity of demand of good x, with respect to its price, the result will be

Same way, the elasticity of demand of good y, with respect to its price will be:

Therefore,