Suppose the demand for inkjet printers is estimated to be Q

Suppose the demand for inkjet printers is estimated to be Q = 1000 - 5p + 10p_X - 2p_Z + 0.1Y. If p = 80, p_X= 50, p_Z= 150, and Y = 20,000, answer the following sub-questions: [5 pts. each]

What is the price elasticity of demand?

What is the cross-price elasticity with respect to commodity X? Give an example of what commodity X might be.

What is the cross-price elasticity with respect to commodity Z? Give an example of what commodity Z might be.

What is the income elasticity?

(If you could show your work that would be great!)

Solution

Q = 1000 - 5p + 10p_X - 2p_Z + 0.1Y

With given values,

Q = 1000 - 5p + (10 x 50) - (2 x 150) + (0.1 x 20,000)

Q = 1,000 - 5p + 500 - 300 + 2,000

Q = 3,200 - 5p

(a)

Price elasticity = (dQ/dp) x (p/Q)

When p = 80, Q = 3,200 - (5 x 80) = 3,200 - 400 = 2,800

Price elasticity = - 5 x (80 / 2,800) = - 0.14

(b)

Cross price elasticity = (dQ/dpX) x (pX / Q) = 10 x (50 / 2,800) = 0.18

Since cross-elasticity is positive, inkjet printers & good X are substitutes. So X can be laser-jet printer.

(c)

Cross price elasticity = (dQ/dpZ) x (pZ / Q) = - 2 x (150 / 2,800) = - 0.11

Since cross elasticity is negative, inkjet printer and good Z are complements, used in conjunction. So good Z may be printer cartridge.

(d)

Income elasticity = (dQ/dY) x (Y / Q) = 0.1 x (20,000 / 2,800) = 0.71