Qd=500-5Px+0.5I+10Py-2Pz?

Question

based on demand curve above, what is the relationship between good X & Y?

Answer 1

1) As price for good X increases quantity demanded falls.

2) As price for good X falls quantity demanded increases.

3) As price for good Y increases quantity demanded increases too.

4) As price for good Y falls quantity demanded falls too.

This shows that good X for demand is complementary good

and good Y is substitute good for this demand.

Conclusion: relationship between goods Y and X is positive (as concerns prices or quantities).

Another way to proof mathematically:

Qd=500-5Px+0.5I+10Py-2Pz

5Px=500-Qd+0.5I+10Py-2Pz

Px=100-Qd/2+0.1I+2Py-0.4Pz

So rise in one price will be compensated by increase in another price - so change price for good X will cause the increase effect on price for good Y. This shows the same relationship (positive)