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Ecns 300: Fall 2016
Midterm 3: November 14, 2016
Question 1-4 are to be answered in class; question 5 is due at the beginning of class on
Wednesday, Nov. 16, 2016.
1. Give the numerical range of possible values and critical values for (a) the price elasticity of
demand, (b) the cross price elasticity of demand, and (c) the income elasticity of demand.
Specifically,
a. For price elasticity of demand, indicate the numerical range of possible values, the
range for which the elasticity of demand is considered to be “elastic,” and the range for
which elasticity of demand is considered to be “inelastic.” Also indicate how price
elasticity relates an increase in the price of a good to the change in Total Revenue.
Range: -∞ < ε < 0 (OK if you used absolute values)
“Elastic” when absolute value > 1; “Inelastic” when absolute value < 1.
If elastic, an increase in P causes TR to fall; if inelastic, an increase in P
causes TR to increase.
b. For cross price elasticity of demand indicate the numerical range of possible values, the
range of numerical values for goods that are “substitutes” in consumption and the range
of numerical values for goods that are “complementary” in consumption. What is the
numerical value if the goods are neither substitutes nor complements?
Range: from -∞ to +∞
Substitutes when cross price elasticity > 0
Complements when cross price elasticity < 0
Neither substitutes nor complements when cross price elasticity = 0
c. For income elasticity of demand, indicate the numerical range of possible values, and
the ranges for both “inferior” and “normal–superior” goods. What would be the range of
values for “luxury” goods?
Range: from -∞ to +∞
Inferior if income elasticity < 0
Normal-Superior if income elasticity >0
Luxury good if income elasticity > 1
2. If there are only two goods, and the income elasticity of demand for one of them is negative,
must the other good be a “luxury” good? Explain.
Yes. See p. 285 of textbook: the weight average of income elasticities is = 1 where the
weights are the expenditure shares. Therefore if one of the terms in the weighted average
is negative because the income elasticity is negative, the other term must be greater than 1.
That other term is the product of the expenditure share for that good (which must be ≤ 1)
multiplied by that good’s income elasticity. This means that the income
elasticity must be greater than 1, which is the definition of a luxury good.
(There are other ways to explain this as well).
3. Is the following statement true or false? “If the price elasticity of demand is ‘inelastic,’
marginal revenue must be negative.” Explain your answer.
True. If price elasticity is “inelastic” then as price falls, quantity increases by a lesser
proportion than the decrease in price. This means that TR will decrease as price falls to
increase quantity demanded. Marginal Revenue is the change is TR for a one-unit increase
in quantity. Since TR is falling, the change in TR is negative, so MR is negative. (Note:
This is true for single prices, but may not be true if multipart pricing is used…but that is not a
caveat that you are expected to know right now.)
4. If the cross price elasticity of demand between two goods increases from 0 to 3, do you
think that the (own) price elasticity of demand for each of these goods will become more or
less “elastic”? Or can you tell? Explain.
If the cross price elasticity increases as stated, this means that consumers suddenly feel
that the two goods are strong substitutes (whereas before they were considered unrelated),
If a good suddenly has a strong substitute available, a price change in that good will elicit a
stronger response by consumers than if there were no substitute. For example, if the price
of a good goes up, the change in quantity demanded will be greater if there is a close
substitute to which consumers can switch than if there is no such substitute. Therefore, we
would expect the own price elasticity of demand to increase as close substitutes become
available.
5. Suppose a good is being bought and sold at the equilibrium price where there are several
demanders and 4 producers. The market demand is given by D(p) = 700 – 20p while each
of the 4 individual suppliers has a supply given by S(p) = -5 + p for p ≥ $5 and S(p) = 0 if p
<$5
a. Calculate and show the equilibrium price and quantity on a well-labeled supply and
demand diagram.
P* = 30 Q* = 100
b. Now, suppose that a 5th producer—whose supply is identical to that of each of the other
4 producers—enters the market. Show what will happen to the equilibrium price and
quantity if the original producers stay in the market and the market demand doesn’t
change. Calculate the new equilibrium price and quantity and show it on your supply and
demand diagram.
P* = 29 Q* = 120
c. Comparing part (a) and (b), carefully label areas and identify “before” and “after” areas to
demonstrate your answers to the following:
i.
Calculate the numerical value and show on your diagram what happens to consumer
surplus when the 5th producer enters the market.
CS before = 250 ; CS after = 360 (includes transfer of 98 from original 4 producers
because price fell to 29 + 12 in new surplus due to being able to buy 120 rather than
100)
ii.
Calculate the numerical value and show on your diagram what happens to the
producer surplus for the original 4 producers when the 5th producer enters the
market.
PS before (4) = 1250 ; PS after (4) = 1152
iii.
Is there any dead weight loss caused by the entry of the 5th producer? Is there a
social gain? If your answer is “yes” to either question, calculate the amount and
explain who loses (if there is a dead weight loss) or who gains (if there is a social
gain).
Social gain = 300 (increase in CS of 12 that was not transferred from the 4 original
producers + new PS of 288 for the 5th producer)
iv.
Are the quantities Pareto Efficient both before and after the 5th producer enters the
market? Explain.
Yes, in each case ( first case given 4 producers and the second case given 5
producers), you cannot move away from the equilibria without making someone
worse off…and lowering the size of the CS +PS amount.
One could argue that the transition from the first to the second equilibrium (due to the
entry of the 5th producer) was not Pareto Efficient because the original 4 producers
were made worse off (their producers’ surplus went from 1250 to 1152.) However,
that is the difference of 98 that was transferred to CS. That could have been given
back to the producers (by taxing the consumers) who would have still been better off
by 12 even after fully compensating the producers.