Download Report

Chapter 1: Supply, Demand and Elasticity
Section 1: Supply and Demand
(Source: http://www.sophia.org/tutorials/economic-basics-supply-and-demand)
In the context of supply and demand discussions, demand refers to the quantity of a good that is desired by
buyers. An important distinction to make is the difference between demand and the quantitiy demanded. The
quantity demanded refers to the specific amount of that product that buyers are willing to buy at a given price.
This relationship between price and the quantity of product demanded at that price is defined as the demand
relationship.
Supply is defined as the total quantity of a product or service that the marketplace can offer. The quantity
supplied is the amount of a product/service that suppliers are willing to supply at a given price. This
relationship between price and the amount of a good/service supplied is known as the supply relationship.
When thinking about demand and supply together, the supply relationship and demand relationship basically
mirror each other at equilibrium. At equilibrium, the quantity supplied and quantity demanded intersect and are
equal.
In the diagram below, supply is illustrated by the upward sloping blue line and demand is illustrated by the
downward sloping green line. At a price of P* and a quantity of Q*, the quantity demanded and the supply
demanded intersect at the Equilibirum Price. At equilibrium price, suppliers are selling all the goods that
they have produced and consumers are getting all the goods that they are demanding. This is the optimal
economic condition, where both consumers and producers of goods and services are satisfied.
The Law Of Demand
Very simply, the law of demand states that if all other factors remain constant, if a good's price is higher, fewer
people will demand it. As the price of that good goes down, the quantity of that good that the market will
demand will increase. In the diagram below, you see this relationship. At price P1, the quanity of that good
demanded is Q1. If the price of this good were to be decreased to P2, the quantity of that good demanded would
increase to Q2. The same is true for P3 and Q3. When prices move up or down (assuming all else is constant),
the quantity demanded will move up or down the demand curve and define the new quantity demanded.
The Law Of Supply
After understanding the law of demand, the law of supply is simple, it's effectively the inverse of the law of
demand. The law of supply states that as the price rises for a given product/service, suppliers are willing to
supply more. Selling more goods/services at a higher price means more revenue. In the diagram below, you can
see that as the price shifts from P1 to P2, the quantity supplied of that good shifts from Q1 to Q2. The
movement in price (up or down) causes movement along the supply curve and the quantity demanded will
change accordingly.
Section 2: Computations with Supply and Demand Curves
Example 1: Suppose the demand function for pumpkins is D(q) = 700 – 0.8q , and the supply function for
pumpkins is S(q) = 100 + 0.5q. D(q) and S(q) are the prices, in dollars per ton, and q is the amount of pumpkins,
in tons.
a) Sketch a graph of D(q) and S(q) on the same grid
b) Calculate D(300) and S(300) and explain what they mean, and place these points on the graph
Solution:
a) the two functions are shown below. Notice the demand function is downward-sloping, and the supply curve is
upward-sloping.
700
600
D(q)
500
S(q)
400
300
200
100
100
200
300
400
500
600
700
800
900
b) To calculate D(300) and S(300), replace q with 300 and compute:
The demand:
D(300)
= 700 – 0.8(300)
= 460.
This means, when there are 300 tons of pumpkins available, the price is $460 per ton. (or, at $460, 300 tons of
pumpkins will be sold)
The supply:
S(300)
= 100 + 0.5(300)
= 250.
This means, when quantity is 300, the price is $250 per ton. This means when the price is $250, the farmers (the
suppliers in this case) are willing and/or able to produce 300 tons of pumpkins.
These points are shown on the graph below:
Notice that, at the same quantity, the prices are different. The point (300, 460) represents the buyer’s perspective.
In other words, at $460, buyers are willing to buy 300 tons. The other point, (300, 250), represents the seller’s
perspective. In other words, at $250, sellers are willing to produce 300 units.
Example 2: A politician complains about the high price of pumpkins and the “greedy pumpkin farmers”. He
proposes a new law: “Henceforth, the maximum price for pumpkins shall be $200 per ton”. The population
cheers… but what happens as a result?
Solution:
Let’s start with the demand curve: if price is set at $200 per ton, what will be the quantity demanded? Solve the
equation:
Set the demand equation equal to 200:
Subtract 700 from each side:
Divide by -0.8:
700 – 0.8q = 200
-0.8q = -500
q = 200
If the price is set at $200, then customers will demand 625 tons of pumpkins.
Now, let’s look at the supply equation:
Set the supply equation equal to 200:
100 + 0.5q = 200
Subtract 100 from each side:
Divide by 0.5:
0.5q = 100
q = 200
At $200, producers are only willing or able to produce 200 tons of pumpkins.
These points are shown on the graph below:
Notice that we have a small problem: People want 625 tons of pumpkins, but the farmers only produced 200
tons… we have a shortage! How did this happen? When the price is artificially set too low, then producers are
unable or unwilling to produce. Only the most efficient farmers could produce pumpkins cheaply enough to
make a profit at $200 per ton, so not many pumpkins were grown. This is a natural consequence of the supply
curve.
How to fix this problem? Remove the price control, and allow the price to increase. Then more farmers are
willing and/or able to produce more pumpkins at the higher price.
Section 3: Equilibrium
As we saw from the pumpkin example, when prices are too low, then the supply is too low. On the other hand, if
prices are too high, then the number of pumpkins sold decreases. Is there a point where supply and price
balance out? The answer is yes, and it is called the equilibrium point.
Definition: the Equilibrium Point is the point where the demand and supply functions intersect. It occurs where
D(q) = S(q)
Example 3: Suppose the demand and supply functions for pumpkins is D(q) = 700 – 0.8q and S(q) = 100 +
0.5q. D(q) and S(q) are the prices, in dollars per ton, and q is the amount of pumpkins, in tons. Find the
equilibrium point.
Solution: The equilibrium point can be visually estimated where q is a little bit higher than 450 tons, and the
price is little higher than 300 dollars per ton.
700
600
D(q)
500
S(q)
400
Equilibrium Point
300
200
100
100
200
300
400
500
600
700
800
900
To find a more precise solution,
set the demand and supply equations equal to each other:
D(q) = S(q)
700 – 0.8q = 100 + 0.5q
Subtract 100 from each side, and 0.8 to each side:
Divide by 1.3 and round off:
600 = 1.3q
461.538 = q
What is the price? Just plug 461.538 into either the supply or demand function:
D(461.538)
= 700 – 0.8(461.538)
= 330.77
Answer: the equilibrium point is at (461.538, 330.77), which means when quantity is 461.538 tons, the price
will be $330.77 per ton.
Section 4: Price elasticity of demand (PED)
From Wikipedia, the free encyclopedia
Definition
PED is a measure of responsiveness of the quantity of a good or service demanded to changes in its price. The
formula for the coefficient of price elasticity of demand for a good is:
The above formula usually yields a negative value, due to the inverse nature of the relationship between price
and quantity demanded, as described by the "law of demand". For example, if the price increases by 5% and
quantity demanded decreases by 5%, then the elasticity at the initial price and quantity = −5%/5% = −1.
Determinants
The overriding factor in determining PED is the willingness and ability of consumers after a price change to
postpone immediate consumption decisions concerning the good and to search for substitutes ("wait and look").
A number of factors can thus affect the elasticity of demand for a good:
 Availability of substitute goods: the more and closer the substitutes available, the higher the elasticity is
likely to be, as people can easily switch from one good to another if an even minor price change is made;
There is a strong substitution effect. If no close substitutes are available the substitution of effect will be
small and the demand inelastic.
 Percentage of income: the higher the percentage of the consumer's income that the product's price
represents, the higher the elasticity tends to be, as people will pay more attention when purchasing the
good because of its cost; The income effect is substantial. When the goods represent only a negligible
portion of the budget the income effect will be insignificant and demand inelastic
 Necessity: the more necessary a good is, the lower the elasticity, as people will attempt to buy it no
matter the price, such as the case of insulin for those that need it.
 Duration: for most goods, the longer a price change holds, the higher the elasticity is likely to be, as
more and more consumers find they have the time and inclination to search for substitutes. When fuel
prices increase suddenly, for instance, consumers may still fill up their empty tanks in the short run, but
when prices remain high over several years, more consumers will reduce their demand for fuel by
switching to carpooling or public transportation, investing in vehicles with greater fuel economy or
taking other measures. This does not hold for consumer durables such as the cars themselves, however;
eventually, it may become necessary for consumers to replace their present cars, so one would expect
demand to be less elastic.
 Breadth of definition of a good: the broader the definition of a good (or service), the lower the
elasticity. For example, Company X's fish and chips would tend to have a relatively high elasticity of
demand if a significant number of substitutes are available, whereas food in general would have an
extremely low elasticity of demand because no substitutes exist.
 Brand loyalty: an attachment to a certain brand—either out of tradition or because of proprietary
barriers—can override sensitivity to price changes, resulting in more inelastic demand.
 Who pays: where the purchaser does not directly pay for the good they consume, such as with corporate
expense accounts, demand is likely to be more inelastic.
Elasticities of demand are interpreted as follows:
Value
Ed = 0
Descriptive Terms
Perfectly inelastic demand
- 1 < Ed < 0
Inelastic or relatively inelastic demand
Ed = - 1
Unit elastic, unit elasticity, unitary elasticity, or unitarily elastic demand
- ∞ < Ed < - 1 Elastic or relatively elastic demand
Ed = - ∞
Perfectly elastic demand
A decrease in the price of a good normally results in an increase in the quantity demanded by consumers because
of the law of demand, and conversely, quantity demanded decreases when price rises. As summarized in the table
above, the PED for a good or service is referred to by different descriptive terms depending on whether the
elasticity coefficient is greater than, equal to, or less than −1. That is, the demand for a good is called:
 relatively inelastic when the percentage change in quantity demanded is less than the percentage change
in price (so that Ed > - 1);
 unit elastic, unit elasticity, unitary elasticity, or unitarily elastic demand when the percentage change in
quantity demanded is equal to the percentage change in price (so that Ed = - 1); and
 relatively elastic when the percentage change in quantity demanded is greater than the percentage
change in price (so that Ed < - 1).
Selected price elasticities
Various research methods are used to calculate price elasticities in real life, including analysis of historic sales
data, both public and private, and use of present-day surveys of customers' preferences to build up test markets
capable of modeling such changes. Alternatively, conjoint analysis (a ranking of users' preferences which can
then be statistically analysed) may be used.
Though PEDs for most demand schedules vary depending on price, they can be modeled assuming constant
elasticity. Using this method, the PEDs for various goods – intended to act as examples of the theory described
above - are as follows. For suggestions on why these goods and services may have the PED shown, see the
above section on determinants of price elasticity.
 Cigarettes (US)[41]
 -0.3 to -0.6 (General)
 -0.6 to -0.7 (Youth)
 Alcoholic beverages (US)[42]
 -0.3 or -0.7 to -0.9 as of
1972 (Beer)
 Rice[48]
 -0.47 (Austria)
 -0.80 (Bangladesh)
 -0.80 (China)
 -0.25 (Japan)
 -0.55 (US)





 -1.0 (Wine)
 -1.5 (Spirits)
Airline travel (US)[43]
 -0.3 (First Class)
 -0.9 (Discount)
 -1.5 (for Pleasure Travelers)
Livestock
 -0.5 to -0.6 (Broiler
Chickens)[44]
Oil (World)
 -0.4
Car fuel[45]
 -0.25 (Short run)
 -0.64 (Long run)
Medicine (US)
 -0.31 (Medical
insurance)[46]
 -.03 to -.06 (Pediatric Visits)
[47]
 Cinema visits (US)
 -0.87 (General)[46]
 Live Performing Arts (Theater, etc.)
 -0.4 to -0.9 [49]
 Transport
 -0.20 (Bus travel US)[46]
 -2.80 (Ford compact automobile)[50]
 Soft drinks
 -0.8 to -1.0 (general)[51]
 -3.8 (Coca-Cola)[52]
 -4.4 (Mountain Dew)[52]
 Steel
 -0.2 to -0.3[53]
 Eggs
 -0.1 (US: Household only),[54] -0.35 (Canada),[55]
-0.55 (South Africa)
Practice Problems for Elasticity of Demand
Example 4: Recently, the price of avocados increased by 5%. As a result, 4% fewer were sold. What is
the elasticity of demand? Is this elastic or inelastic?
Solution: Using the formula,
E=
% changein quantity 0.04

 0.8
% changein price
0.05
Answer: The elasticity is -0.8. This is inelastic, meaning the quantity sold is not too sensitive to
changes in price.
When calculating elasticity, sometimes you must calculate the percentage change yourself. However,
when computing elasticity, use a modified percent formula, that uses the midpoint as the base:
percent change =
new amount  old amount
midpoint of the amounts
Example 5: Yesterday, the price of envelopes was $3 a box, and Julie was willing to buy 10 boxes. Today, the
price has gone up to $3.55 a box, and Julie is now willing to buy 8 boxes. Is Julie's demand for envelopes elastic
or inelastic? What is Julie's elasticity of demand? Is it elastic or inelastic?
Solution
To find Julie's elasticity of demand, we need to divide the percent change in quantity by the percent change in
price.
Step 1: find the % Change in Quantity: the quantity decreased from 8 to 10. The midpoint is 9.
new amount  old amount 8  10 2


 0.222
midpoint of the amounts
9
9
percent change =
Step 2: find the % Change in Price: the price increased from $3.00 to $3.55. The midpoint is 3.275
percent change =
new amount  old amount 3.55  3.00 0.55


 0.1679
midpoint of the amounts
3.275
3.275
Step 3: find the Elasticity
E = (-0.222)/(0.1679) = 1.32 (rounded off)
Answer: The elasticity is 1.32. Julie's elasticity of demand is elastic, meaning she the quantity she will buy is
sensitive to price changes.
Example 6: Which of the following goods are likely to have elastic demand, and which are likely to have
inelastic demand?
Home heating oil
Pepsi
Chocolate
Water
Heart medication
Oriental rugs
Solution
Elastic demand: Pepsi, chocolate, and Oriental rugs
Inelastic demand: Home heating oil, water, and heart medication
Section 5: Price elasticity of supply
From Wikipedia, the free encyclopedia
In economics, price elasticity of supply (PES) is an elasticity defined as a numerical measure of the
responsiveness of the supply of a given good to a change in the price of that good.
Calculation
Price elasticity of supply is a measure of the sensitivity of the quantity of a good supplied in a market to changes
in the market price for that good.
Per the law of supply, it is posited that at a given price and corresponding quantity supplied in a market, a price
increase will also increase the quantity supplied. PES is a numerical measure (coefficient) of by how much that
supply is affected. Mathematically:
In other words, PES is the percentage change in quantity supplied that one would expect to occur after a 1%
change in price. For example, if, in response to a 10% rise in the price of a good, the quantity supplied increases
by 20%, the price elasticity of supply would be 20%/10% = 2.
Interpretation
If the law of supply holds, an upward-sloping supply curve would result from this. As a ratio of two percentages,
the price elasticity is not tied to any specific units. However, the exact value can yield more inferences about the
good in question.
When the coefficient is less than one, the supply of that good can be described as inelastic; when the coefficient
is greater than one, the supply can be described as elastic. An elasticity of zero indicates that quantity supplied
does not respond to a price change: it is "fixed" in supply. Such goods often have no labor component or are not
produced, limiting the short run prospects of expansion. If the coefficient is exactly one, the good is said to be
unitary elastic.
The quantity of goods supplied can, in the short term, be different from the amount produced, as manufacturers
will have stocks which they can build up or run down.
Determinants
Availability of raw materials: for example, availability may cap the amount of gold that can be produced in a
country regardless of price. Likewise, the price of Van Gogh paintings is unlikely to affect their supply.
Length and complexity of production: Much depends on the complexity of the production process. Textile
production is relatively simple. The labor is largely unskilled and production facilities are little more than
buildings - no special structures are needed. Thus the PES for textiles is elastic. On the other hand, the PES for
specific types of motor vehicles is relatively inelastic. Auto manufacture is a multi-stage process that requires
specialized equipment, skilled labor, a large suppliers network and large R&D costs.
Time to respond: The more time a producer has to respond to price changes the more elastic the supply. Supply
is normally more elastic in the long run than in the short run for produced goods, since it is generally assumed
that in the long run all factors of production can be utilised to increase supply, whereas in the short run only
labor can be increased, and even then, changes may be prohibitively costly. For example, a cotton farmer cannot
immediately (i.e. in the short run) respond to an increase in the price of soybeans because of the time it would
take to procure the necessary land.
Excess capacity: A producer who has unused capacity can (and will) quickly respond to price changes in his
market assuming that variable factors are readily available.
Inventories: A producer who has a supply of goods or available storage capacity can quickly increase supply to
market.
Various research methods are used to calculate price elasticities in real life, including analysis of historic sales
data, both public and private, and use of present-day surveys of customers' preferences to build up test markets
capable of modelling such changes. Alternatively, conjoint analysis (a ranking of users' preferences which can
then be statistically analysed) may be used.
Graphical representation
It is important to note that elasticity and slope are, in the most part, unrelated. Thus, when supply is represented
linearly, regardless of the slope of the supply line, the coefficient of elasticity of any linear supply curve that
passes through the origin is 1 (unit elastic). The coefficient of elasticity of any linear supply curve that cuts the yaxis is greater than 1 (elastic), and the coefficient of elasticity of any linear supply curve that cuts the x-axis is
less than 1 (inelastic). Likewise, for any given supply curve, it is likely that PES will vary along the curve.
Selected Supply Elasticities
 Heating Oil
 1.57 (Short Run) [11]
 Gasoline
 1.61 (Short Run) [11]
 Tobacco
 7.0 (Long Run) [11]
 Housing
 1.6-3.7 (Long Run) [11]
 Cotton
 0.3 (Short Run) [12]
 1.0 (Long Run) [12]
 Steel
 1.2 (Long Run, from Minimills) [13]
Section 6: Power functions
Definition: a Power function is a function with the form
f(x) = kxp
Where k and p are nonzero constants. In realistic settings, the domain of the function (the x) is
usually restricted to positive numbers.
Here are some examples of power functions:
f(x) = 3.2 x 0.4
H(t) = 489 t -1/2
D(q) = 4 q 2
Graphs of power functions
The basic shape depends on the power, p.
Example 7: Graph f(x) = 3x1.5
Set up an Excel sheet and make a scatterplot:
=3*A2^1.5
A
x
1
2
3
4
5
6
B
f(x)
1
2
3
4
5
3
8.485281
15.58846
24
33.54102
f(x)
40
35
30
25
20
15
10
5
0
0
1
2
3
4
5
6
As you can see, the curve is bent slightly upward. Since the exponent is greater than 1, the
function is increasing, but also the rate of increase is increasing. This type of shape is called
concave up. For all power functions, if the power is greater than 1, then the curve is always
concave up.
Example 8: A cost function is C(q) = 400 + 4.5q0.25
Make a graph of this function.
Solution: Again, set up an Excel sheet and make a scatterplot
B
f(x)
404.5
405.351
405.922
406.364
406.729
A
x
1
2
3
4
5
6
1
2
3
4
5
=400+4.5*A2^0.25
f(x)
407
406.5
406
405.5
405
404.5
404
0
1
2
3
4
5
6
This is a fairly typical cost function. As quantity increases, according to economy of scale, the
costs per unit start to decrease. So the cost function, although it is still increasing, is increasing at
a slower rate. This type of shape is called concave down. Any power function, where the power is
between 0 and 1, is always concave down.
Example 9: A demand function is D(q) = 326 q -0.45. Make a graph of the demand function
Solution: You know the drill:
1
2
3
4
5
A
x
B
f(x)
1
2
3
4
326
238.646
198.844
174.699
=326*A2^(-0.45)
5
6
158.009
The parentheses around the exponent are not essential, but sometimes Excel is fickle with
negative numbers. So just to be safe, put the negative numbers inside parentheses.
f(x)
350
300
250
200
150
100
50
0
0
1
2
3
4
5
6
Anytime the power is negative, the function will decrease. However, as q gets larger, the function
decreases at a slower and slower rate. This shape is also called concave up.
Summary
Power
Negative
Example
H(t) = 489 t -1/2
direction
Decreasing
Shape
Concave
up
Between 0
and 1
f(x) = 3.2 x 0.4
Increasing
Concave
down
Greater
than 1
D(q) = 4 q 2
Increasing
Concave
up
Picture
Derivatives of Power Functions
The power rule (the derivative of cxn is ncxn-1) applies for all values of n, so it applies to all power
functions.
Example 10: A cost function is C(q) = 32 + 3.4q0.78. What is the marginal cost?
Solution: The 32 drops out, then multiply the power (0.78) times the coefficient (3.4). then
decrease the power by 1 (0.78 – 1.00 = -0.22):
Answer: MC(q) = 2.652q-0.22
Section 7: Solving Power Function Equations
Like most equations, the procedure is to do something to both sides of an equation that will undo
a particular operation. For instance:
Solve x + 5 = 8
add -5 to both sides to undo the addition
Solve 3x = 20
take log of both sides to undo the exponentiation
The way to solve a power function is usually to take the reciprocal power of each side.
Example 11: Solve x2 = 25
Solution: The procedure would be to find the square root of each side of this equation. But we
want a method that would work for any power function. So, the reciprocal of 2 is ½. So we’ll take
each side to the ½ power. (remember that ½ power is equivalent to square root)
( x2 )1/2 = (25)1/2
On the left side of the equation, 2 times ½ equals 1, so the left side becomes x1, which is just x.
That’s the nice thing about reciprocals! You always get 1.
x = 5 (normally, plus or minus 5, but we’re only interested in positive numbers for solutions)
Answer: x = 5
Now for a tougher one:
Example 12: Solve 67 x -0.45 = 38.9
Solution:
first, divide both sides by 67:
x -0.45 = 38.9/67
x -0.45 = 0.580597
then, take both sides to the 1/(-0.45) power (the reciprocal of -0.45)
(x -0.45 )1/(-0.45) = (0.580597)1/(-0.45)
On the left side, we’ll have x1. The right side will take some serious calculatorbutton-pushing:
0.580597^(1/-0.45) = 3.34752
Answer: x = 3.34752
Example 13: Suppose a demand function for steel is D(q) = 23q-2.1, and the supply function for
steel is S(q) = 12q0.45.
a) Use Excel to graph both
b) Find the equilibrium point.
Solution:
To set up an Excel sheet, you will need three columns:
A
1
2
3
4
5
B
D(q)
Q
C
S(q)
1
2
3
4
In cell B2, enter the demand function, which is =23*A2^(-2.1)
In cell C2, enter the supply function, which is =12*A2^(0.45)
Then copy the formulas down, and you’ll see:
A
1
2
3
4
5
Q
B
D(q)
C
S(q)
1
23
12
2 5.36494 16.39248
3 2.289672 19.67369
4 1.251416 22.39279
Select all three columns and select Insert>Scatterplot:
We can visually estimate the equilibrium point to be about (1.5, 14). To get a more precise
answer, solve D(q) = S(q):
Set the equations equal to each other:
Divide both sides by 12:
Divide both sides by q-2.1
Take the 1/2.55 power of both sides:
Compute and round off:
23q-2.1 = 12q0.45.
1.916667q-2.1 = q0.45
1.916667 = q2.55
1.9166671/2.55 = q
q = 1.2906
If we go back to our spreadsheet, and enter 1.2906 for q, then we see that supply and demand are
equal at that point (except for rounding):
A
1
2
B
C
Q
D(q)
S(q)
1.2906 13.46063 13.45977
Answer: the equilibrium point is approximately (1.3, 13.5)
Chapter 1 Practice Problems
Practice with Supply and Demand Curves
1. Suppose the supply and demand functions for oranges are D(q) = 2 – 0.002q and S(q) = 0.50 +
0.003q, where prices are in dollars per pound and q is in pounds.
a) Sketch a graph of both functions on the same grid.
b) Calculate D(200) and S(200) and explain what these mean. Then locate the points on
the graph
c) if the price was $1 per pound, what would be the quantity demanded, according to the
demand function?
d) if the price was $1 per pound, what would be the quantity supplied, according to the
supply function?
e) if the price was $1 per pound, would this indicate a shortage or a surplus?
f) Find the equilibrium point
2. Suppose the supply and demand functions for apples are D(q) = 3 – 0.005q and S(q) = 0.70 +
0.009q, where prices are in dollars per pound and q is in pounds.
a) Sketch a graph of both functions on the same grid.
b) Calculate D(300) and S(300) and explain what these mean. Then locate the points on
the graph
c) if the price was $1 per pound, what would be the quantity demanded, according to the
demand function?
d) if the price was $1 per pound, what would be the quantity supplied, according to the
supply function?
e) if the price was $1 per pound, would this indicate a shortage or a surplus?
f) Find the equilibrium point
Practice with Elasticity
3. Suppose that last year the price of a movie ticket was $9, and this year the price is
$9.50. As a result, the number of tickets sold decreased from 45,000 to 41,000.
a) What is the percent change in the quantity sold? (remember to use the midpoint
as the base)
b) What is the percent change in the price? (remember to use the midpoint as the
base)
c) Calculate the elasticity of demand
d) Based on your answer from part (d), is the demand for movie tickets elastic or
inelastic?
4. Suppose the price of tomatoes increased from $2.50 per pound to $3.50 per pound. As
a result, tomato growers decided to plant more tomato plants this year, and the supply of
tomatoes increased from 56,000 tons to 61,000 tons.
a) What is the percent change in the quantity produced?
b) What is the percent change in the price?
c) Calculate the elasticity of supply
d) Based on your answer from part (d), is the supply of tomatoes elastic or
inelastic?
5. The elasticity of demand for a product is E = -0.5. What is the effect on demand of:
a) A 3% price increase?
b) A 3% price decrease?
6. The elasticity of demand for a product is E = 2. What is the effect on demand of:
a) A 3% price increase?
b) A 3 % price decrease?
7. The elasticity of demand for peaches is 1.49 (Estimated by the USDA). Explain what
this number tells you about the effect of price increases on the demand for peaches. Is the
demand elastic or inelastic? Explain factors that contribute to the elasticity of peaches.
8. The elasticity of demand for potatoes is 0.27 (Estimated by the USDA). Explain what
this number tells you about the effect of price increases of potatoes. Is the demand elastic
or inelastic? Explain factors that contribute to the inelasticity of potatoes.
9. Would you expect the demand for heated toilet seats to be elastic or inelastic? Why?
10. There are many brands of smart phones. Assuming the quality of each brand is
similar, would you expect the elasticity of demand to be elastic or inelastic? Why?
11. If there is only one telephone company that services a city, would the demand be
elastic or inelastic? Why?
12. The demand curve for a product is D(q) = 75 - 4q. Find the elasticity of demand when
quantity changes from q = 8 to q = 12.
13. The demand curve for a product is D(q) = 90 - 10q. Find the elasticity of demand
when quantity changes from q = 4 to q = 6.
Practice with Power Functions
14. Compute the following without a calculator:
a) 642/3
b) 813/4
c) 161/2
d) 32-2/5
e) 9-1/2
15. Compute the following without a calculator:
a) 641/3
b) 163/4
c) 251/2
d) 32-3/5
e) 36-1/2
16. Compute the following with a calculator, and round to 3 digits after the decimal point:
a) 42.80.74
b) 9.31.25
c) 11.35-0.946
17. Compute the following with a calculator, and round to 3 digits after the decimal point:
a) 2.90.54
b) 7.31.45
c) 11.75-0.846
18. Convert each expression to radical form:
a)
x 2/3
b)
3q 1/2
19. Convert each expression to radical form:
a)
x 3/4
b)
3q 1/3
20. A cost function is C(q) = 20 + 4.3q0.452, where q is in thousands and costs are in
millions.
a) Compute the cost of producing 30,000 units.
b) What is the fixed cost?
c) Use Excel to make a table and graph of this cost function. Start with q = 0 and end
with q = 50, using increments of 5.
d) What is the marginal cost function?
e) What is the marginal cost when q = 10? Include units with you answer.
f) Is the marginal cost increasing or decreasing? How do you know?
21. A cost function is C(q) = 18 + 0.973q0.494, where q is in thousands and costs are in
millions.
a) Compute the cost of producing 20,000 units.
b) What is the fixed cost?
c) Use Excel to make a table and graph of this cost function. Start with q = 0 and end
with q = 50, using increments of 5.
d) What is the marginal cost function?
e) What is the marginal cost when q = 10? Include units with you answer.
f) Is the marginal cost increasing or decreasing? How do you know?
22. Solve the following equations, and round the answer to 3 digits after the decimal point:
a) 34 = x2.7
b) 12.38 = 4.2q-2.5
23. Solve the following equations and round the answer to 3 digits after the decimal point:
a) 37 = x2.2
b) 24.8 = 6.2q-1.5
24. Suppose the demand function for gummy bears is D(q) = 3.4q-0.6, and the supply function for
gummy bears is S(q) = 2.1q1.2
a) Use Excel to graph both on the same scatterplot
b) Solve for the equilibrium point
25. Suppose the demand function for sunglasses is D(q) = 19.56q-0.24, and the supply function for
sunglasses is S(q) = 3.45q0.81
a) Use Excel to graph both on the same scatterplot
b) Solve for the equilibrium point, rounded to 2 digits after the decimal point
Answers to Selected Exercises
1a)
1.5
(200, 1.6)
1
(200, 1.1)
0.5
200
400
600
800
1000
1b) D(200) = 1.6. This means at $1.60, 200 pounds of oranges would be sold. S(200) = 1.1, which
means at $1.10, 200 pounds of oranges would be supplied
c) 500 lb
d) 166.67 lb
e) shortage; buyers want 500 lb, suppliers only produce 166.67 lb
f) (300, 1.4). 300 lb of oranges, selling for $1.40 per pound.
3a) 9.3% b) 5.4% c) -1.7 d) elastic
5a) 1.5% decrease b) 1.5% increase
7) elastic. People will stop buying peaches if the price gets too high because there are
substitutes available and it's not a necessity.
9) elastic, because it is not a necessity
11) low, since the consumers have no other choice
13) quantity increases from 4 to 6 (40% increase, using the midpoint, 5, as the base) and
price decreases from 50 to 30 (50% decrease, using the midpoint, 40, as the base).
Therefore elasticity is 40/50 = 0.8
15a) 4 b) 8 c) 5 d) 1/8
17a) 1.777 b) 17.857 c) 0.124
19a)
4
x3
3
b)
3
q
21a) 22.27 million dollars b) 18 million dollars
c)
A
1
2
3
4
5
6
7
8
9
10
11
12
B
q
C(q)
(thousands) (millions)
0
18.00
5
20.15
10
21.03
15
21.71
20
22.27
25
22.77
30
23.22
35
23.63
40
24.02
45
24.38
50
24.72
d) MC(q) = 0.480662q-0.506
e) 0.1499 million dollars per thousand units
because the cost function is concave down
23a) 5.162 b) 0.397
25b) (5.22, 13.16)
f) decreasing,