ECO - The demand curve is given by QD = 500 - 5PX + 0.5I + 10PY - 2PZ

The demand curve is given by
QD = 500 - 5PX + 0.5I + 10PY - 2PZ
where
QD = quantity demanded of good X
PX = price of good X
I = consumer income, in thousands
PY = price of good Y
PZ = price of good Z 

a. Based on the demand curve above, is X a normal or an inferior good?

b. Based on the demand curve above, what is the relationship between good X and good Y?

c. Based on the demand curve above, what is the relationship between good X and good Z?

d. What is the equation of the demand curve if consumer incomes are $30,000, the price of
good Y is $10, and the price of good Z is $20?

e. Graph the demand curve that you found in (d), showing intercepts and slope.

f. If the price of good X is $15, what is the quantity demanded? Show this point on your
demand curve.

g. Now suppose the price of good Y rises to $15.
Graph the new demand curve.