Download 3.1 Practice Problems 1. a. b. At a price of $3,000 (point a in the

3.1 Practice Problems
1. a.
b. At a price of $3,000 (point a in the graph), total revenue is $30 million (= $3000 × 10 000), at a price of $2,000 (point b) it is $40 million (=
$2000 × 20 000), and at a price of $10,000 (point c) it is $30 million (= $1000 × 30 000).
c. The market demand curve is elastic in the price range $3000 to $2000, since total revenue and price move in opposite directions. Total revenue
rises as price falls. In contrast, the demand curve is inelastic in the range $2000 to $1000, because total revenue and price are moving in the same
direction, with both falling.
d. Recall the formula for elasticity:
Between prices $3,000 and $2,000, the coefficient of the price elasticity of demand has a value of -1.67 {= [(20,000 - 10,000) / (15,000)] /
[($2,000 - $3,000) / ($2,500)]}, and between $2000 and $1000 it has a value of -0.60 {= [(30,000 - 20,000) / (25,000)]/[($1,000 - $2,000) /
($1,500)]}.
e. Yes, the answers are consistent. The absolute value of the price elasticity of demand between prices $3,000 and $2,000 is greater than one.
This is consistent with part c. where demand in this price range was found to be elastic. Similarly, the absolute value of the price elasticity of
demand between $2,000 and $1,000 is less than one, which is consistent with part c., where demand in this range was found to be inelastic.
Recall that price elasticity of demand always has a negative sign because the numerator and denominator necessarily have different sings but that
it is customary to use the absolute value of this calculation in further analysis.
2
a. The cross-price elasticity's value of +1.29 is found using the formula:
exy = [(750,000 - 1 million) / 875,000] / [($20,000 - $25,000) / $22,500] = 1.29. The sign of the coefficient of cross-price elasticity is positive
because the two goods are substitutes.
b. The price elasticity of demand's value of -0.69 is found using the formula:
ed = [(17,500 - 15,000) / 16,250] / [($400 - $500) / $450] = -0.69. The sign of the coefficient of demand elasticity is negative because the demand
curve is downward sloping. With a downward sloping demand curve the formula's numerator and denominator will always have different signs.
c. This income elasticity's value of -0.87 is found using the formula:
ei = [(3,000 - 2,000) / 2,500] / [($50,000 - $80,000) / $65,000] = -0.87. The sign of the coefficient of income elasticity is negative because the
product is an inferior product.
End of Chapter Problems:
1. The absolute value of the first percentage change is found by subtracting the variable's initial value from its final value, and dividing by the initial
value or:
%Δ = (final value - initial value) / initial value.
The absolute value of the second change is found by using the same formula, but reversing the initial and final values or:
%Δ = (initial value - final value) / final value.
The absolute value of the final change is found by using the average of the two values, [average value - (initial value + final value) / 2], and then
dividing the change in the two variables by the average value or
%Δ = (final value - initial value) / (initial value + final value) / 2].
a. The absolute value of the first percentage change is: 100% = ($6 - $3) / $3. The second is 50% - ($3 - $6) / $6. The third is found first by
calculating the average of the two values, $4.50 = ($3 + $6)/2, and then dividing the change in the two variables by this average value: 67% = ($3
- $6) / $4.50 = ($6 - $3) /$4.50.
b. The absolute value of the first percentage change is: 40% = (150 - 250) / 250. The second is 67% = (250 - 150) / 150. The average is 200 =
(250 + 150) / 2 and the absolute value of the third percentage change is 50% = (250 - 150) / 200 = (150 - 250) / 200.
c. The absolute value of the first percentage change is: 67% = ($4 - $12) / $12. The second is 200% = ($12 - $4) / 150. The average is $8 = ($12 +
$4) / 2 and the absolute value of the third percentage change is 100% = ($12 - $4) / $8 = ($4 - $12) / $8.
d. The absolute value of the first percentage change is: 33% = (2,000 - 1,500) / 1,500. The second is 25% = (1,500 - 2,000) / 2,000. The average
is 1,750 = (1,500 + 2,000) / 2 and the absolute value of the third percentage change is 29% = (1,500 - 2,000) / 1,750 = (2,000 - 1,500) / 1,750.
2. a. Because consumers can live without luxuries and it is easier to respond to price changes when an item has many close substitutes, demand for
this product is likely to be elastic.
b. Because buyers pay more attention to price when an item makes up a large portion of their incomes and it is easier to respond to price changes
when an item has many close substitute, demand for this product is likely to be elastic.
c. Because consumers find it difficult without necessities and a short-run time frame does not give consumers time to change their habits and
needs, demand for this product is likely to be elastic.
d. Because consumers can live without luxuries and buyers pay more attention to price when an item makes up a large portion of their incomes,
demand for this product is likely to be elastic.
4. a.
b. The equilibrium price and quantity are at $250 and 80,000 jackets (point a in the graph), since at a price of $250 the quantities demanded and
supplied are identical.
c. Because of the supply increase, quantity supplied becomes 160.000 jackets at a $300 price, 140,000 at $250, 120,000 at $200, 100,000 at $150
and 80,000 at $100. The new equilibrium price and quantity are $150 and 100,000 jackets (point b in the graph) because at this new price the
quantities demanded and supplied are again identical.
d. See graph above.
e. The initial total revenue of producers is $20 million (= $250 × 80,000), as shown by area A + B in the graph, while the new total revenue is
$15 million (= $150 × 100,000), as shown by area B + C in the graph. Price and total revenue move in the same direction, so that demand is
inelastic between the two equilibrium points.
6. Recall the price elasticity of demand is found using the formula whose numerator is the change in quantity demanded divided by average quantity
demanded and whose denominator is the change in price divided by average price:
a. Given the change in price from $10 to $12 and the change in quantity demanded from 4 to 3, average price is $11 = ($10 + $12) / 2 and
average quantity demanded is 3.5 = (4 + 3) / 2. The coefficient of the price elasticity of demand, e d, is: (-)1.57 = [(3 - 4) / 3.5] / [($12 - $10) /
$11].
b. Given the change in price from $1 to $0.80 and the change in quantity demanded from 1.2 million to 1.3 million, average price is $0.90 = ($1
+ $0.80) / 2 and average quantity demanded is 1.25 million = (1.2 million + 1.3 million) / 2. The coefficient of the price elasticity of demand, e d,
is: (-)0.36 = [(1.3 million - 1.2 million) / 1.25 million] / [($0.80 - $1) / $0.90].
c. Given the change in price from $25 to $30 and the change in quantity demanded from 85,000 to 80,000, average price is $27.50 = ($25 + $30)
/ 2 and average quantity demanded is 82,500 = (80,000 + 85,000) / 2. The coefficient of the price elasticity of demand, e d, is: (-)0.33 = [(80,000 85,000) / 82,500] / [($30 - $25) / $27.50].
d. Given the change in price from $700 to $600 and the change in quantity demanded from 200,000 to 300,000, average price is $650 = ($700 +
$600) / 2 and average quantity demanded is 250,000 = (200,000 + 300,000) / 2. The coefficient of the price elasticity of demand, ed, is: (-)2.60 =
[(300,000 - 200,000) / 250,000] / [($600 - $700) / $650].
3.2 Practice Problem
1. Recall the formula for the elasticity of supply:
a. es is 0 = [(80,000 - 80,000) / (80,000)] / [($1.20 - $1) / ($1.10)].
b. es is 1 = [(1.2 million - 1 million) / (1.1 million)] / [($1.20 - $1) / ($1.10)].
c. es is undefined = [(final quantity - initial quantity) / (average quantity)] / [($1 - $1) / ($1)] = [quantity / 0] because division by zero is always
undefined.
d. This is a constant-cost industry, since its long-run supply curve is perfectly elastic. This means the industry is not a major user of any single
resource, so price is always driven back to its original level in the long run after a change in production.
e.
End of Chapter Problems:
3. The initial and final values for sellers' total revenue are found by multiplying the relevant price and quantity demanded for both the initial value
of total revenue and for the final value of total revenue. If the change in total revenue is in the same direction as the change in price then demand
is inelastic. If the change in total revenue is in the opposite direction to the change in price then demand is elastic. Should total revenue not
change when price changes then demand is unit-elastic.
a. The initial value of total revenue is $80,000 = ($4 × 20,000). The final value for total revenue is $75,000 = ($5 × 15,000). Because the change
in total revenue from $80,000 to $75,000 is in the opposite direction to the change in price from $4 to $5, demand is elastic.
b. Initial total revenue is $80,000 = ($4 × 20,000). The final value of total revenue is $75,000 = ($3 × 25,000). Because the change in total
revenue from $80,000 to $75,000 is in the same direction as the change in price from $4 to $3, demand is inelastic.
c. The initial value of total revenue is $350,000 = ($10 × 35,000). The final value of total revenue is $360,000 = ($9 × 40,000). Because the
change in total revenue from $350,000 to $360,000 is in the opposite direction to the change in price from $10 to $9, demand is elastic.
d. The initial value of total revenue is $300,000 = ($60 × 5,000). The final value for total revenue is $300,000 = ($50 × 6,000). Because the
change in total revenue from $300,000 to $300,000 is constant, demand is unit-elastic.
7. Recall that the coefficient of the cross-price elasticity, exy, is found using the formula whose numerator is the change in the quantity demanded of
one product divided by that product's average quantity demanded and whose denominator is the change in price of the other product divided by
that product's average price:
a. Given the change in price of access to the internet from $20 to $10 and the change in quantity demanded of emagazines from 3 to 5, average
price is $15 = ($20 + $10) / 2 and average quantity demanded is 4 = (3 + 5) / 2. The coefficient of the cross-price elasticity, exy, is then found
using the formula whose numerator is the change in the quantity demanded of emagazines divided by average quantity demanded and whose
denominator is the change in price of access to the internet divided by average price: (-)0.75 = [(5 - 3) / 4)] / [($10 - $20) / $15]. Because the
cross price elasticity is negative, the two products are complementary.
b. Given the change in price of a hairstylist's cut from $40 to $60 and the change in quantity demanded of do-it-yourself haircutting sets from
5,000 to 10,000, average price is $50 = ($40 + $60) / 2 and average quantity demanded is 7,500 = (5,000 + 10,000) / 2. The coefficient of the
cross-price elasticity, exy, is then found using the formula whose numerator is the change in the quantity demanded of do-it-yourself haircutting
sets divided by average quantity demanded and whose denominator is the change in price of a hairstylist's cut divided by average price: (+)1.67 =
[(10,000 - 5000) / 7,500] / [($60 - $40) / $50]. Because the cross price elasticity is positive, the two products are substitutes.
c. Given the change in price of smartphones from $300 to $200 and the change in quantity demanded of smartphone apps from 1 million to 3
million, average price is $250 = ($300 + $200) / 2 and average quantity demanded is 2 million = (1 million + 3 million) / 2. The coefficient of the
cross-price elasticity, exy, is then found using the formula whose numerator is the change in the quantity demanded of smartphone apps divided
by average quantity demanded and whose denominator is the change in price of smartphones divided by average price: (-)2.50 = [(3 million - 1
million) / 2 million] / [($200 - $300) / $250]. Because the cross price elasticity is negative, the two products are complements.
8. Recall that income elasticity is found using the formula whose numerator is the change in quantity demanded divided by average quantity
demanded and whose denominator is the change in income divided by average income:
a. Given the change in income from $50,000 to $70,000 and the change in quantity demanded from 2 million to 3 million, average income is
$60,000 = ($50,000 + $70,000) / 2 and average quantity demanded is 2.5 million = (2 million + 3 million) / 2. The coefficient of income
elasticity, ei, is: (+)1.20 = [(3 million - 2 million) / 2.5 million] / [($70,000 - $50,000) / $60,000]. Because the income elasticity is positive the
product is normal.
b. Given the change in income from $30,000 to $40,000 and the change in quantity demanded from 100,000 to 50,000, average income is
$35,000 = ($30,000 + $40,000) / 2 and average quantity demanded is 75,000 = (100,000 + 50,000) / 2. The coefficient of income elasticity, e i, is:
(-)2.33 = [(50,000 - 100,000) / 75,000] / [($40,000 - $30,000) / $35,000]. Because the income elasticity is negative the product is inferior.
c. Given the change in income from $3,000 to $2,800 and the change in quantity demanded from 120,000 to 100,000, average income is $2,900
= ($3,000 + $2,800) / 2 and average quantity demanded is 110,000 = (120,000 + 100,000) / 2. The coefficient of income elasticity, ei, is: (+)2.64
= [(100,000 - 120,000) / 110,000] / [($2,800 - $3,000) / $2,900]. Because the income elasticity is positive the product is normal.
9. Recall that the price elasticity of supply is found using the formula whose numerator is the change in quantity supplied divided by average
quantity supplied and whose denominator is the change in price divided by average price:
a. With a price change from $300 to $350 and the change in quantity supplied from 8 million to 9 million, average price is $325 = ($300 + $350)
/ 2 and average quantity supplied is 8.5 million = (8 million + 9 million) / 2. The coefficient of the price elasticity of supply, e s, is found
employing the formula whose numerator is the change in quantity supplied divided by average quantity supplied and whose denominator is the
change in price divided by average price: 0.76 = [(9 million - 8 million) / 8.5 million] / [($350 - $300) / $325].
b. With a price change from $8 to $7.50 and the change in quantity supplied from 2 million to 1 million, average price is $7.75 = ($8 + $7.50) / 2
and average quantity supplied is 1.5 million = (2 million + 1 million) / 2. The coefficient of the price elasticity of supply, es, is found employing
the formula whose numerator is the change in quantity supplied divided by average quantity supplied and whose denominator is the change in
price divided by average price: 10.33 = [(1 million - 2 million) / 1.5 million] / [($7.50 - $8) / $7.75].
c. With a price change from $2 to $3 and the change in quantity supplied from 2 million to 4 million, average price is $2.50 = ($2 + $3) / 2 and
average quantity supplied is 3 million = (2 million + 4 million) / 2. The coefficient of the price elasticity of supply, e s, is found employing the
formula whose numerator is the change in quantity supplied divided by average quantity supplied and whose denominator is the change in price
divided by average price: 1.67 = [(4 million - 2 million) / 3 million] / [($3 - $2) / $2.50].
10 a. In the immediate run, quantity supplied is still 1 million ounces at the new $8 price, since silver producers are unable to vary the amount they
produce. This is shown by the immediate-run supply curve, a vertical line, whose horizontal intercept is 1 million.
b. In the short run, silver producers respond to the new $8 price by raising quantity supplied above what it would be at $6. This means that the
short-run supply curve is upward-sloping.
c. If the industry exhibits constant costs, the high revenues available at an $8 price attract new silver producers in the long run, which pushes
down price until it returns to its initial level of $6. The industry's long-run supply curve is therefore a horizontal line (with a vertical intercept of
$6). If the industry exhibits increasing costs, the high revenues available at the $8 price again attract new silver producers, pushing down price.
Price stops falling at a value between $8 and $6 because an increasing-cost industry is a significant user of a certain resource such as mining
machinery, whose price rises when the quantity supplied of silver increases. Higher quantities supplied therefore push up each producer's per-unit
costs, forcing price to remain above $6. This means the long-run supply curve is a gently upward-sloping line.
7.4 Practice Problems
1. a.
b. The initial equilibrium price and quantity of $0.80 and 60 million kilograms are found at the intersection of D and S (point a in the graph).
Consumers' total expenditure and producers' total revenue are both equal to the area of the rectangle (C + D) in the graph whose height is $0.80 and
width is 60 million litres. This amount is $48 million (= $0.80 x 60 million).
c. The $0.90 price support creates an annual surplus of 20 million (= 70 million - 50 million) litres. This is the distance between points b and c in the
graph.
d. Consumers are made worse off by the program because they buy less of the product at a higher price. Their total expenditure is the area of the
rectangle (A + C) in the graph. This rectangle's height is $0.90 and its width is 50 million litres so the new consumer expenditure is $45 million (=
$0.90 x 50 million). Producers benefit through selling a higher quantity at a higher price. Their total revenue becomes the area of the rectangle (A +
B + C + D + E). This rectangle's height is $0.90 and its width is 70 million litres so the new total revenue for producers is $63 million (= $0.90 x 70
million).
e. The cost of the program to taxpayers is the government's total expenditure to purchase the surplus. This is the area of the rectangle (B + D + E) in
the graph. This rectangle's height is $0.90 and its width is 20 million (= 70 million - 50 million) litres so the total cost to taxpayers is $18 million (=
$0.90 x 20 million).
2. a.
b. The initial equilibrium rent and quantity of $1,200 and 40,000 units are found at the intersection of D and S (point a in the graph).
c. The $800 price ceiling creates a shortage of 20,000 (= 30,000 - 50,000) units, as shown by the distance between points b and c in the graph.
Tenants who are able to find units at the ceiling price are made better off because they pay less than the original $1,200 price. Landlords are made
worse off because of this reduction in rent.
d. Total revenue before controls is $48 million. It is found by multiplying the initial rent of $1,200 by the initial quantity of 40,000 units. Total
revenue after controls are imposed becomes $24 million. This is found by multiplying the new rent of $800 by the new quantity of 30,000 units.
7.2 Practice Problems
1. a. The disturbance created by the club for nearby residents is a spillover cost.
b. The subway's reduction of traffic congestion is a spillover benefit.
c. Because the existence of the species is a public good poaching that leads to its extinction is a tragedy of the commons.
d. The addition to soil pollution caused by throw-away batteries is a spillover cost.
e. The reduction in electricity use and carbon emissions stemming from use of the new bulb is a spillover benefit.
f. The higher energy use and carbon emissions associated with the new jet is a spillover cost.
g. Given that email is a public good its declining usefulness as a result of proliferating spam messages is a tragedy of the commons.