QD=8000-2PX+0.4I-2PY+5PZ 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 $75,000, the price of good Y is $80, and the price of good Z is $105? e. What are the intercepts and slope of your demand curve? You do not need to draw the demand curve. Just indicate the price intercept and the quantity intercept and the slope. f. If the price of good X is $100, what is the quantity demanded? g. Now suppose the price of good Z rises to $150. What would happen to your demand curve? What are the price intercept, quantity intercept and slope?

a. Normal b. Complementary c. Substitutes d. Qd= 38365-3Px e. X axis intercept 38365, Y axis intercept 19182.5 f. 38,165 units g. Demand shifts to left; X axis intercept 38065, Y axis intercept 19032.5

Explanation:

a. X is a normal good,as we see from the demand equation there is a negative relationship between quantity demanded and price of X.

b. Y and X are complementary goods as price of Y is inversely related to demand for X.

c. X and Z are substitutes as in the demand equation we see, there is a positive relationship between quantity demanded of X and price of Z.

d. Qd= 8000-2Px-0.4I-2Py+2 Pz

Now, Income=75,000, Price of Y=$80, Price of Z= $105

Qd

= 8000-2Px+0.4*75000-2*80+5*105

=8000-2Px+30000-160+525

=38365-2Px

e. On X axis, Px=0 then,

Qd

=38365-2*0

=38365

On Y axis, Qd=0 then,

0=38365-2Px

2Px=38365

Px= 19182.5

f. If price of X is $100,

Qd

= 38365-2*100

=38365-200

=38165

g. If price of X rises to $150 then,

Qd

=38365-2*150

=38365-300

=383065

The demand curve shifts leftwards.

The X axis intercept will be

Qd

=383065-2*0

=383065

The Y axis intercept will be

0=383065-2Px

Px=383065/2

Px=19032.5