Respuesta :
a. use the midpoint method to calculate your price elasticity of demand as the price of dvds increases from $8 to $10 if (i) your income is $10,000 and (ii) your income is $12,000 : -1
Explanation:
Suppose that your demand schedule for DVDs is as follows:
price
$8
10
12
14
16
quantity demanded (income = $10,000)
40 pizza
32
24
16
8
quantity demanded (income = $12,000)
50 pizza
45
30
20
12
a. use the midpoint method to calculate your price elasticity of demand as the price of dvds increases from $8 to $10 if (i) your income is $10,000 and (ii) your income is $12,000.
Price elasticity of demand (Income $10,000) = Quantity present - quantity previous / (quantity present + quantity previous /2) divide with (Price present - price previous / (price present + price previous /2))
quantity present - quantity previous / (quantity present + quantity previous/2) = 32-40 / ((32+40)/2) = 9/36 = -0.2222
(Price present - price previous / (price present + price previous /2))
= 10-8 / ((10+8)/2) = 2/9 = 0.2222
Price elasticity of demand (Income $10,000) = Quantity present - quantity previous / (quantity present + quantity previous /2) divide with (Price present - price previous / (price present + price previous /2)) = -0.2222 / 0.2222 = -1
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The demand schedule is first rearranged as in the attached photo.
The questions can be answered using the following midpoint method formulae:
Price elasticity of demand = Change is quantity / Change in price …………… (1)
Income elasticity of demand = Change is quantity / Change in income …………(2)
Where:
Change in quantity = (New quantity - Old quantity) / ((New quantity + Old quantity)/2)
Change in Price = (New price - Old price)/ ((New price + Old price)/2)
Change in income = (New income - Old income)/ ((New income + Old income)/2) =
Using the formulae, we have:
a(i) Price elasticity of demand when income is $10,000
We have:
Change in quantity = (New quantity - Old quantity) / ((New quantity + Old quantity)/2) = (32-40) / ((32+40)/2) = -0.222222222222222
Change in Price = (New price - Old price) / (New price + Old price)/2) = (10-8) / ((10+8)/2) = 0.222222222222222
Price elasticity of demand when income is $10,000 = Change is quantity / Change in price = -0.222222222222222 / 0.222222222222222 = -1
a(ii) Price elasticity of demand when income is $12,000
We have:
Change in quantity = (New quantity - Old quantity) / ((New quantity + Old quantity)/2) = (45-50) / ((45+50)/2) = -0.105263157894737
Change in Price = (New price - Old price) / (New price + Old price)/2) = (10-8) / ((10+8)/2) = 0.222222222222222
Price elasticity of demand when income is $12,000 = Change is quantity / Change in price = -0.105263157894737 / 0.222222222222222 = -0.473684210526316, or -0.47 approximately
b(i) Income elasticity of demand as income increases from $10,000 to $12,000 if the price is $12
Change in quantity = (New quantity - Old quantity) / ((New quantity + Old quantity)/2) = (30 - 24) / ((30 + 24)/2) = 0.222222222222222
Change in income = (New income - Old income)/ (New income + Old income)/2) = (12,000 – 10,000)/ ((12,000 + 10,000)/2) = 0.181818181818182
Income elasticity of demand = Change is quantity / Change in income = 0.222222222222222 / 0.181818181818182 = 0.81818181818182, or 0.82 approximately
b(ii) Income elasticity of demand as income increases from $10,000 to $12,000 if the price is $16
Change in quantity = (New quantity - Old quantity) / ((New quantity + Old quantity)/2) = (12 - 8) / ((12 + 8)/2) = 0.40
Change in income = (New income - Old income)/ (New income + Old income)/2) = (12,000 – 10,000)/ ((12,000 + 10,000)/2) = 0.181818181818182
Income elasticity of demand = Change is quantity / Change in income = 0.40 / 0.181818181818182 = 2.20
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