Quiz 3

Q:  u(x,y)=min(2x,3y), I=80 and Py=6.  Find the equation of the demand for good x. 

A:  Given the utility function the optimal bundle is where 2x=3y or y=2x/3.  Plugging this into the BC which is 80=PxX+6Y gives 80=PxX+4X.  Solving for x we find that demand is X=80/(4+Px).

Q:  If Py falls to Py=3, what will happen to demand for good x?  What is the sign of the cross price elasticity of demand?

A:  Again, we have y=2x/3.  The BC is now 80=PxX+3Y.  Through substitution and simplification we get X=80/(2+Px).  Comparing this to the demand curve we found above, we see that the dominator is smaller and thus X is larger for any Px.  So demand has shifted out as Py fell and these two goods are complements.  Hence the cross price elasticity is negative.