Question

The demand curve is given by: Qdx=500-1.5Px-0.2I-2Py+Pz

Where Qdx= quantity demanded of good X

Px= Price of good X

I= income (in thosands)

Py= Price of good Y

Pz= Price of good Z

A. Is good X a normal or inferior good? Why?

B. What is the relationship between goods X & Y? Why?

C. What is the relationship between goods X & Z? Why?

D. What is the equation of this demand curve if income is $40,000, the price of good y is $80 and the price of good Z is $25? Note, the income variable is in thousands.

E. If the price of good Z rises to $30, what would happen to the demand curve for good X?

Answer 1

The demand curve is given by: Qdx=500-1.5Px-0.2I-2Py+Pz

A. Good X is an inferior good because income coefficient (-0.2) is negative which indicates that if income rises, quantity demanded of X will decrease.

B. There is a complementary relationship between goods X & Y because the price coefficient of good Y (-2) is negative. This indicates that if price of good Y declines, quantity demanded of X will increase.

C.  X & Z are substitutes because the price coefficient of good Z (+1) is positive. This indicates that if price of good Z declines, quantity demanded of X will decrease.

D. Equation of this demand curve if I = 40, Py = $80 and Pz = $25 is

Qdx = 500 - 1.5*Px - 0.2*40 - 2*80 + 25

= 357 - 1.5Px

E. If the price of good Z rises to $30, The demand curve for X will shift to the right. The new demand equation will be Qdx = 500 - 1.5*Px - 0.2*40 - 2*80 + 30 or Qdx = 362 - 1.5Px