Suppose that your demand schedule for dvds is as follows: price quantity demanded (income = $10,000) quantity demanded (income = $12,000) $8 40 dvds 50 dvds 10 32 45 12 24 30 14 16 20 16 8 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. b. calculate your income elasticity of demand as your income increases from $10,000 to $12,000 if (i) the price is $12 and (ii) the price is $16.

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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