Davenport Mathematical Foundations for Economic Models Problem Set complete on attached file
1.The table below contains typical economic data. It shows the quantity of a good that is demanded by purchasers and the quantity supplied by producers at various prices.
Price
Quantity Demanded
Quantity Supplied
$100
10
25
$80
20
20
$60
30
15
$40
40
10
$20
50
5
$0
60
0
At which price is quantity supplied equal to 10?
At which price is quantity demanded equal to 10?
At which price are quantities demanded and quantities supplied the same? (Note: This is the equilibrium price.)
At which price is the quantity demanded less than the quantity supplied? (This represents a surplus.) What is the size of the surplus? (That is, how much more is supplied than demanded?)
At a price of $20 we see that the quantity demanded is greater than the quantity supplied. This represents a shortage. What is the size of the shortage? (That is, how much more is demanded than supplied?)
2. Refer to the graph below, which represents typical economic information about the amount of a product demanded (downward-sloping line) and supplied (upward-sloping line) at various prices.
At what price is quantity demanded equal to 2000?
At what price is quantity demanded equal to zero?
At what price is quantity supplied equal to 1400?
What is the equilibrium quantity? (Where quantity demanded and quantity supplied are equal.)
What is the equilibrium price? (Where quantity demanded and quantity supplied are equal.)
Using Equations to Explain Economic Models (WLO 1.4)
3. Text ch 3 Prob 1. The following function describes the demand condition for a company that makes caps featuring names of college and professional teams in a variety of sports.
Q = 2,000 – 100P
where Q is cap sales and P is price.
How many caps could be sold at $12 each?
What should the price be in order for the company to sell 1,000 caps?
At what price would cap sales equal zero?
4. Text ch 3 Prob 3. The following relations describe the supply and demand for posters.
Demand: QD = 65,000 – 10,000P
Supply: Qs = -35,000 + 15,000P
Use the equations to fill in Qs and Qd at the prices listed in the table.
Price
Qs
Qd
Surplus or Shortage
$6.00
$5.00
$4.00
$3.00
$2.00
$1.00
Find the difference between Qs and Qd at each price. Indicate if it is a surplus, , a shortage, or neither. (Surplus if Qs is greater and shortage if Qd is greater.)
What is the equilibrium price? (Where Qd = Qs) Problem Set 1: Mathematical Foundations for Economic Models
Using Tables and Graphs to Explain Economic Models (WLO 1.4)
1. The table below contains typical economic data. It shows the quantity of a good that is
demanded by purchasers and the quantity supplied by producers at various prices.
Price
Quantity Demanded
Quantity Supplied
$100
10
25
$80
20
20
$60
30
15
$40
40
10
$20
50
5
$0
60
0
a. At which price is quantity supplied equal to 10?
b. At which price is quantity demanded equal to 10?
c. At which price are quantities demanded and quantities supplied the same? (Note: This
is the equilibrium price.)
d. At which price is the quantity demanded less than the quantity supplied? (This
represents a surplus.) What is the size of the surplus? (That is, how much more is
supplied than demanded?)
e. At a price of $20 we see that the quantity demanded is greater than the quantity
supplied. This represents a shortage. What is the size of the shortage? (That is, how
much more is demanded than supplied?)
2. Refer to the graph below, which represents typical economic information about the amount
of a product demanded (downward-sloping line) and supplied (upward-sloping line) at
various prices.
a.
b.
c.
d.
At what price is quantity demanded equal to 2000?
At what price is quantity demanded equal to zero?
At what price is quantity supplied equal to 1400?
What is the equilibrium quantity? (Where quantity demanded and quantity supplied are
equal.)
e. What is the equilibrium price? (Where quantity demanded and quantity supplied are
equal.)
Problem Set 1: Mathematical Foundations for Economic Models
Using Equations to Explain Economic Models (WLO 1.4)
3. Text ch 3 Prob 1. The following function describes the demand condition for a company
that makes caps featuring names of college and professional teams in a variety of sports.
Q = 2,000 – 100P
where Q is cap sales and P is price.
a. How many caps could be sold at $12 each?
b. What should the price be in order for the company to sell 1,000 caps?
c. At what price would cap sales equal zero?
4. Text ch 3 Prob 3. The following relations describe the supply and demand for posters.
Demand: QD = 65,000 – 10,000P
Supply: Qs = -35,000 + 15,000P
a. Use the equations to fill in Qs and Qd at the prices listed in the table.
Price
Qs
Qd
Surplus or Shortage
$6.00
$5.00
$4.00
$3.00
$2.00
$1.00
b. Find the difference between Qs and Qd at each price. Indicate if it is a surplus, , a
shortage, or neither. (Surplus if Qs is greater and shortage if Qd is greater.)
c. What is the equilibrium price? (Where Qd = Qs)
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