Answer to Question #218048 in Microeconomics for thuy

Question

suppose that your demand schedule for pizza is follows

pice: $8,$10,$12,$14,$16

quantity demanded ( income $16.000): 40,32,24,16,8

quantity demanded (income $20.000): 50,45,30,20,12

a. use the midpoint method t calculate your price elasticity of demand as the price of pizza increases from $8 to $10 if (i) your income is $16,000 and (ii) your income is $20,000.

b. calculate your income elasticity of demand as your income increases from $16,000 to $20,000 if (i) the price is $12 and (ii) the price is $16

Answer 1

Solution:

a.). Price elasticity of demand using the midpoint method.

i.). When income (Y) = 16,000:

Price elasticity of demand using the midpoint method (PED) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

PED =$=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

P₁ = 8     Q₁ = 40

P₂ = 10    Q₂ = 32

PED = $\frac{32 -40}{(32+40)/2 } \div \frac{10 -8}{(10+8)/2 } = \frac{-8}{36 } \div\frac{2}{9 } = \frac{-0.22}{0.22 } = -1$

PED = -1

ii.). When income (Y) = 20,000:

Price elasticity of demand using the midpoint method (PED) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

PED =$=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

P₁ = 8     Q₁ = 50

P₂ = 10    Q₂ = 45

PED = $\frac{45 -50}{(45+50)/2 } \div \frac{10 -8}{(10+8)/2 } = \frac{-5}{47.5 } \div\frac{2}{9 } = \frac{-0.11}{0.22 } = -0.5$

PED = -0.5

b.). Income elasticity of demand:

i.). When the price is 12:

Income elasticity of demand (YEd) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; income}$

Income elasticity of demand (YEd) = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{Y_{2} -Y_{1}}{(Y_{2}+Y_{1})/2 }$

Q₁ = 24      Y₁ = 16,000

Q₂ = 30      Y₂ = 20,000

Income elasticity of demand (YEd) =$\frac{30 -24}{(30+24)/2 } \div \frac{20,000 -16,000}{(20,000+16,000)/2 } = \frac{6}{27 } \div\frac{4,000}{18,000 } = \frac{0.22}{0.22 } = 1$

YED = 1

ii.). When the price is 16:

Income elasticity of demand (YEd) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; income}$

Income elasticity of demand (YEd) = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{Y_{2} -Y_{1}}{(Y_{2}+Y_{1})/2 }$

Q₁ = 8       Y₁ = 16,000

Q₂ = 12      Y₂ = 20,000

Income elasticity of demand (YEd) =$\frac{12 -8}{(12+8)/2 } \div \frac{20,000 -16,000}{(20,000+16,000)/2 } = \frac{4}{10 } \div\frac{4,000}{18,000 } = \frac{0.4}{0.4 } = 1$

YED = 1