Answer:
1. a) Price elasticity at income $20000 = -1
b) Price elasticity at income $24000 = -0.47
2. a) Income elasticity at price $12 = 1.25
b) income elasticity at price $16 = 2.5
Explanation:
Price Elasticity of demand = change is quantity / change in price
Where
Change in quantity = (quantity current – quantity previous)/ ((quantity current+ quantity previous)/2)
Change in Price = (Price current – Price previous)/ (Price current+ Price previous)/2)
Putting in values for income $20,000
Price elasticity income $20000 = {(32-40)/((32+40)/2)} / {(10-8)/((10+8)/2)}
= -1
Similary
Price elasticity income $24000 = {(32-40)/((32+40)/2)} / {(10-8)/((10+8)/2)}
= -0.47
2) For income elasticity of demand, change in quantity demand is divided by change in income. Putting in the values
Income elasticity of deman @ $12 = {(30-24)/24}/{(24000-20000)/20000} = 1.25
Income elasticity of deman @ $16 = {(12-8)/8}/{(24000-20000)/20000} = 2.5
The elasticity of demand is the change in quantity due to economic factors such as price, salary, etc.
The price elasticity of demand, when price increases from $14 to $16 and
The income elasticity of demand when income increases from $20000 to $24000 and
(a): Price elasticity of demand
Price elasticity of demand is calculated as follows:
[tex]E_p = \frac{\Delta Q}{\Delta P}[/tex]
Where:
[tex]\Delta P = (P_2 - P_1) \div (P_2 + P_1)/2[/tex] --- change in price
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex] --- change in quantity
When price increases from $14 to $16 and income is $20,000;
We have:
[tex]Q_1 = 16\\Q_2 = 8[/tex]
So, we have:
[tex]\Delta P = (P_2 - P_1) \div (P_2 + P_1)/2[/tex]
[tex]\Delta P = (16 - 14) \div (16 + 14)/2[/tex]
[tex]\Delta P = 2 \div 15[/tex]
[tex]\Delta P = \frac 2{15}[/tex]
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex]
[tex]\Delta Q = (8 - 16) \div (8+16 )/2[/tex]
[tex]\Delta Q = -8 \div 12[/tex]
[tex]\Delta Q = -\frac 23[/tex]
So, we have:
[tex]E_p = \frac{\Delta Q}{\Delta P}[/tex]
[tex]E_p = -\frac{2}{3} \div \frac{2}{15}[/tex]
[tex]E_p = -\frac{2}{3} \times \frac{15}{2}[/tex]
[tex]E_p = -5[/tex]
When price increases from $14 to $16 and income is $24,000
We have:
[tex]Q_1 = 20\\Q_2 = 12[/tex]
So, we have
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex]
[tex]\Delta Q = (12 - 20) \div (12+20 )/2[/tex]
[tex]\Delta Q = -8 \div 16[/tex]
[tex]\Delta Q = -\frac 12[/tex]
So, we have:
[tex]E_p = \frac{\Delta Q}{\Delta P}[/tex]
[tex]E_p = -\frac{1}{2} \div \frac{2}{15}[/tex]
[tex]E_p = -\frac{1}{2} \times \frac{15}{2}[/tex]
[tex]\Delta Q = -\frac{15}{4}[/tex]
[tex]\Delta Q = -3.7 5[/tex]
Hence, the price elasticity of demand, when price increases from $14 to $16 and
Solving (b): Income elasticity of demand
Income elasticity of demand is calculated as follows:
[tex]E_I = \frac{\Delta Q}{\Delta I}[/tex]
Where:
[tex]\Delta I = (I_2 - I_1) \div (I_2 + I_1)/2[/tex] --- change in income
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex] --- change in quantity
When income increases from $20000 to $24000 and price is $12
We have:
[tex]Q_1 = 24\\Q_2 = 30[/tex]
So, we have:
[tex]\Delta I = (24000 - 20000) \div (24000 + 20000)/2[/tex]
[tex]\Delta I = 4000\div 22000[/tex]
[tex]\Delta I = \frac 2{11}[/tex]
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex]
[tex]\Delta Q = (30 - 24) \div (30+24 )/2[/tex]
[tex]\Delta Q = 6 \div 27[/tex]
[tex]\Delta Q = \frac 29[/tex]
So, we have:
[tex]E_I = \frac{\Delta Q}{\Delta I}[/tex]
[tex]E_I = \frac 29 \div \frac 2{11}[/tex]
[tex]E_I = \frac 29 \times \frac {11}2[/tex]
[tex]E_I = \frac {11}9[/tex]
[tex]E_I = 1.22[/tex]
When income increases from $20000 to $24000 and price is $16
We have:
[tex]Q_1 = 8\\Q_2 = 12[/tex]
[tex]\Delta Q = (Q_2 - Q_1) \div (Q_2 + Q_1)/2[/tex]
[tex]\Delta Q = (12 - 8) \div (12 + 8)/2[/tex]
[tex]\Delta Q = 4 \div 10[/tex]
[tex]\Delta Q = \frac 25[/tex]
So, we have:
[tex]E_I = \frac{\Delta Q}{\Delta I}[/tex]
[tex]E_I = \frac 25 \div \frac 2{11}[/tex]
[tex]E_I = \frac 25 \times \frac {11}2[/tex]
[tex]E_I = \frac {11}5[/tex]
[tex]E_I = 2.2[/tex]
Hence, the income elasticity of demand when income increases from $20000 to $24000 and
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