Question

The demand for 3-D Printer is estimated to be Q = 1000 – 5p + 12pX – 21pZ + 0.12Y. If p = 80,
pX = 50, pZ = 150, and Y = 20,000; answer the following: Using calculus, Please show all work in order to understand where things are coming from. Thank you.

a. What is the price elasticity of demand?

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

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

d. What is the income elasticity (Income is represented by Y)?

Answer 1

a. If p= 80

Q = 1000 -400 + 600 -3150 + 2400 = 450

Price elasticity of demand = (dQ / dp ) × p/Q

= (-5) × (80/450)

= - 0.88

b. Cross price elasticity w.r.t.x = (dQ/ dPX)× Px/ Q

=12 ×( 50/450)

=1.33

X would be a substitute good like 3- D printer of another brand.

c. Cross price elasticity w.r.t.z = (dQ/ dPz) × Pz/ Q

= -21 × (150/450)

= - 7

This z commodity would be a complementary good for printer like ink .

d. Income elasticity = (dQ/dY)× Y/Q

= 0.12 × (20000/450)

= 5.33