Question

Suppose demand for inkjet printers is estimated to be Q = 500 – 0.6 p -5 px + 4 pz + 0.2 Y. where p is the price of inkjet printers, Y is income, and px and pz are the prices of related goods, X and Z. Suppose that p = 40, px = 25 , pz = 100 , and Y = $50, 000. Answer the following questions: 

a. What is the price elasticity of demand? Interpret and explain your results.

b. What is the cross price elasticity with respect to commodity X? Interpret and explain your result and give an example of what commodity X might be.

c. What is the coss price elasticity with respect to commodity Z? Interpret and explain your result and give an example of what commodity Z might be.

d. What is the income elasticity? Interpret and explain your result.

Answer 1

a.

$Q=500-0.6\times 40-5\times 25+4\times 100+0.2\times 50,000\\Q_d=10751 \space units$

$e_d=\frac{\delta Q}{\delta p}\times\frac{p}{Q}=-0.6\times\frac{40}{10751}=0.02.$ < 1 therefore the demand is inelastic.

b.

$e_c=\frac{\delta Q_d}{\delta p_x}\times\frac{p_x}{Q}=-5\times\frac{25}{10751}=-0.011$ <0

Therefore good x is a substitute of good z. The good can be laser printers.

c.

$e_c=\frac{\delta Q_d}{\delta p_z}\times\frac{p_z}{Q}=4\times\frac{100}{10751}=0.03$

since e_c is greater than zero, the good is a complement of inkjet printer and cartridges is an example.

d.

$e_m=\frac{\delta Q_d}{\delta y}\times\frac{y}{Q}=0.2\times\frac{5900}{10751}=0.93$ >0

The good is a normal good