5. The demand for good X is estimated to be QXd = 10,000 - 4PX + 5PY + 2M + AX where PX is the price of X, PY is the price of good Y, M is income and AX is the amount of advertising on X. Suppose the present price of good X is $50, PY = $100, M = $25,000, and AX = 1,000 units. Determine 1. a. Own price elasticity of demand b. Cross price elasticity of demand c. Income elasticity of demand d. Is good y a complement or a substitute e. Is good is normal or inferior

We need to calculate quantity demanded of good X

Qxd = 10,000 − 4PX + 5PY + 2M +
AX

Qxd = 10,000 − 4(50) + 5(100) + 2(25000) + 1000  

Qxd  = 10,000 - 200 + 500 + 50000 + 1000

Qxd  = 61,300

a. E(P) = ∆Qx/∆Px * (Px / Qx)

E(P) = - 4 * (50 / 61,300)

{where, ∆Qx/∆Px is the price coefficient = -4}

E(P) = = - 0.003    (The absolute value is 0.003)

Demand is inelastic, because price elasticity is less than 1.

b. CPED = ∆Qx/∆Py * (Py / Qx)

CPED = 5 * (100 / 61,300)

[where, ∆Qx/∆Py is the price coefficient of good Y = 5]

CPED = 0.008

c. IED = ∆Qx/∆M * (M / Qx)

= 2 * (25,000 / 61,300)

[where, ∆Qx/∆M is the income coefficient = 2]

= 0.816

d. Good Y and X is subtitles because  CPED is positive.

e. Good X is a normal good because income elasticity is positive.