Question

QD= 8000-2PX+0.4I+2PY-4PZ

A - What are the intercepts and slope of your demand curve? price intercept and the quantity intercept and the slope

B - the price of good X is $100, what is the quantity demanded?

C - Now suppose the price of good Y rises to $150. What would happen to your demand curve? What are the price intercept, quantity intercept and slope?

Answer 1

a)

QD = 8000 - 2PX + 0.4I + 2PY - 4PZ  

For price intercept put QD = 0

0 = 8000 - 2PX + 0.4I + 2PY - 4PZ  

2PX  = 8000 + 0.4I + 2PY - 4PZ  

PX = 4000 + 0.2I + PY - 2PZ

So price intercept for good X is  PX = 4000 + 0.2I + PY - 2PZ

put Px = 0 to get quantity intercept  

QD =   8000 - 2PX + 0.4I + 2PY - 4PZ  

= 8000 - 2(0) + 0.4I + 2PY - 4PZ  

QD  = 8000 + 0.4I + 2PY - 4PZ  

So quantity intercept for good X is QD  = 8000 + 0.4I + 2PY - 4PZ  

QD = 8000 - 2PX + 0.4I + 2PY - 4PZ  

dQD/dPx = - 2

dPx/dQD = - 1/2

slope of demand curve = dPx/dQD = -1/2 and

in terms of absolute value slope =  |dPx/dQD | = |−1/2| = 1/2

b)

QD = 8000 - 2PX + 0.4I + 2PY - 4PZ

Px = 100

QD = 8000 - 2(100)  + 0.4I + 2PY - 4PZ  

QD = 8000 - 200 + 0.4I + 2PY - 4PZ

QD = 7800 + 0.4I + 2PY - 4PZ  

c)

QD = 8000 - 2PX + 0.4I + 2PY - 4PZ  

PY rises to 150

QD = 8000 - 2PX + 0.4I + 2(150) - 4PZ  

QD = 8000 - 2PX + 0.4I + 300 - 4PZ  

QD = 8300 - 2PX + 0.4I - 4PZ  

put Px = 0 to get quantity intercept

QD = 8300 - 2(0)  + 0.4I - 4PZ  

QD = 8300 + 0.4I - 4PZ  

therefore quantity intercept is QD = 8300 + 0.4I - 4PZ  

price intercept put QD = 0

QD = QD = 8300 - 2PX + 0.4I - 4PZ  

0 =    8300 - 2PX + 0.4I - 4PZ  

2Px = 8300 + 0.4I - 4Pz

Px = 4150 + 0.4I - 4Pz

price intercept is Px = 4150 + 0.4I - 4Pz

Demand function when PY rises to 150 is given as

QD = 8300 - 2PX + 0.4I - 4PZ  

dQD/dPx = - 2

dPx/dQD = - 1/2

slope of demand curve = dPx/dQD = -1/2 and

in terms of absolute value slope =  |dPx/dQD | = |−1/2| = 1/2