(a) A consumer buys 20 pounds of good X when her income is $29,000 per year and
ID: 1160502 • Letter: #
Question
(a) A consumer buys 20 pounds of good X when her income is $29,000 per year and she buys 28 pounds when her income increases to $34,000. Using the midpoint formula, what is the income elasticity of demand for good X? Is good X an inferior or a normal good for the consumer? Explain.
(b) Suppose that when the price of good X increases from $0.45 to $0.65, the quantity demanded for good Y decreases from 12,000 to 10,000. Using the midpoint formula, what is the cross-price elasticity between goods X and Y? What does the sign imply about the relationship between the two goods?
(c) Suppose when the price of good Z is $8.00, the quantity supplied is 20,000 while when the price is $10.00, the quantity supplied is 24,000. Using the midpoint formula, calculate the price elasticity of supply.
Explanation / Answer
a) Income Ed = % change in quantity demanded / % change in income
% change in income = (34000 - 29000)/29000 x 100 = 17.24
% change in quantity demnaded of X = (28 - 20)/20 x 100 = 40
Income Ed = 40/17.24 = 2.32
Good X is normal good because income Ed is positive which means increase in income increases demand of good X.
b) Cross price Ed = % change in quantity demanded of good Y / % change in price of good X
% change in quantity demanded of good Y = (10000 - 12000)/12000 x 100 = - 16.67
% change in price of good X = (0.65 - 0.45)/0.45 x 100 = 44.4
Cross price Ed = - 16.67/44.4 = - 0.375
Good X and Y are substitute goods.
c) Price Es = % change in Qs / % change in Price
% change in Qs = (24000 - 20000)/20000 x 100 = 20
% change in price (10 - 8)/8 x 100 = 25
Price Es = 20/25 = 0.8
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