Answer to Question #215100 in Microeconomics for Dani1221

Question

4.​Suppose the demand for inject printers is estimated to be 

   Q= 1000-2p+5Px-3Py+0.1Y

  P=80   Px= 20     Py= 150       Y= 1000

A.​Calculate price elasticity of demand? (2 pt) 

B.​Calculate cross price elasticity of x and y (Exy)? And state the nature of good 

C.​Calculate income elasticity of demand and what we can say about the goods

Answer 1

A.​Calculate the price elasticity of demand? (2 pt) 

Point method for elasticity= [{Q2​−Q1} /​​​​​Q1] ÷ [{P2​−P1}/P1]]

Q1 (when P1 is 80) =1000 – 2(80) + 5 (20) – 3(150) + 0.1 (1000) =590

Q2 (when P2 is 90) =1000 – 2(90) + 5 (20) – 3(150) + 0.1 (1000) =570

Therefore Price Elasticity= [570​−590 /​​​​​590] ÷ [90-80/ 80]​]

=[-20/590] ÷ [10/80]

=-0.0339÷0.125=-0.271

Since the change is less than one (0.271), the price elasticity for inject-printers is inelastic.

https://www.khanacademy.org/economics-finance-domain/microeconomics/elasticity-tutorial/price-elasticity-tutorial/a/price-elasticity-of-demand-and-price-elasticity-of-supply-cnx

 

B.​Calculate cross-price elasticity of x and y (Exy)? And state the nature of good 

 

Cross price elasticity= change of Quantity of X/ change of Price Y

= [{QX2​−QX1} /​​​​​ 0.5(QX2​+QX1)] ÷ [PY2​−PY1/ 0.5(PY2​+PY1)]

QX1 (when PY1 is 150) =1000 – 2(80) + 5 (20) – 3(150) + 0.1 (1000) =590

QX2 (when PY2 is 160) =1000 – 2(80) + 5 (20) – 3(160) + 0.1 (1000) =560

Therefore Cross price elasticity= [560​−590 /​​​​​ 0.5 of (560+590)] ÷ [160-150/ 0.5 of (160+150​​)]

= [-30/575] ÷ [10/155]

=-0.0522÷0.0645=-0.809

The figure is less than 1 (0.809), meaning the cross elasticity is inelastic. The negative sign means the two products (X and Y) are complementary goods.

https://courses.lumenlearning.com/macroeconomics/chapter/worked-example-cross-price-elasticity-of-demand/

 

C.​Calculate income elasticity demand and what we can say about the goods

Income elasticity of demand= Change in Quantity Demanded/Change in income.

= [{Q2​−Q1} /​​​​​ 0.5(Q2​+QX)] ÷ [(Y2​−Y1)/ 0.5(Y2​+Y1)]

Q1 (when Y1 is 1000) =1000 – 2(80) + 5 (20) – 3(150) + 0.1 (1000) =590

Q2 (when Y2 is 1500) =1000 – 2(80) + 5 (20) – 3(150) + 0.1 (1500) =640

Therefore Income elasticity of demand= [640−590 /​​​​​ 0.5 of (640 +590

= [50/615] ÷ [500/1250]

=-0.0813÷0.4=0.2032

Since the income elasticity of demand is has a positive value, it means this is a normal good.

https://www.educba.com/income-elasticity-of-demand-formula/