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 A demand function is a function that
represents a demand curve. The demand
function shows us the exact relationship
between price and quantity demanded.
Demand functions are also just shorthand
ways of representing both a demand curve
and a demand schedule. . When we have a
demand function, we can actually plot a
demand curve AND find points on the
demand schedule.
A supply function is a function representing
the exact relationship between price and
quantity supplied. Supply functions are also
shorthand representations – they can be used
to find both supply curves and to find points
in a supply schedule.
With the supply and demand functions, we
have easy ways of representing sellers’ and
buyers’ intentions in a market. These
functions are also handy to have for finding
equilibrium outcomes in a market. Rather
than visually having to scope out exactly
where quantity supplied equals quantity
demanded on a demand and supply schedule
or on a market graph, we can find exact
equilibrium outcomes using demand and
supply functions and a little bit of algebra.
Let’s consider the market for wheat.
Measuring quantity in millions of bushels,
suppose we have a market demand curve that
is given by:
QD = 50 – 2P
 The following table shows some points:
When price = Quantity demanded =
$10 per bushel 30 million bushels
$8 per bushel 34 million bushels
$6 per bushel 38 million bushels
$4 per bushel 42 million bushels
$2 per bushel 46 million bushels
 The supply curve for the wheat market is
given by
QS = -6 + 12P
This is normal for a supply function – they
usually don’t start at the origin point of the
graph, but up a bit on the price axis.
 The following table shows some points:
When price = Quantity supplied =
$10 per bushel 114 million bushels
$8 per bushel 90 million bushels
$6 per bushel 66 million bushels
$4 per bushel 42 million bushels
$2 per bushel 18 million bushels
 QD = 50 – 2P, QS = -6 + 12P
E = (Qd = Qs)
 50 – 2P = -6 + 12P
 50 + 6 – 2P = 12P
 56 = 12P + 2P
 56 = 14P
 P = $4 per bushel wheat
 QD = 50 – 2P
 QD = 50 – 2 ($4)
 QD = 50 – 8 = 42 million bushels of wheat
Qs = -6 + 12P
Qs = -6 + 12 ($4)
Qs = -6 +48 = 42 million bushels of wheat
Number 1
 Demand equation: Qd = 100- 2P
 Supply equation: Qs = -20 + 4P
Find out the equilibrium quantity and price.
Number 2
The demand and supply equations are the
following:
 Qd = 400 – 20P Qs = - 200 + 10P
Find out the equilibrium quantity and price.
 Number 3
Demand and supply in a market are described
by the equations
Qd = 66-3P
Qs = -4+2P
Find out equilibrium quantity and price.
 The demand and supply functions of a good
are given by
Qd = 110-5P
Qs = 6P
 (i) Find the inverse demand and supply
functions
Qd = 110-5P
5P = 110-Qd
P = 110-Qd/5
Qs = 6P
P = Qs/6
(ii) Find the equilibrium price and quantity
Solve simultaneously:
Qd = 110-5P
Qs = 6P
At equilibrium Qd = Qs
110-5P = 6P
Collect the terms
-5P-6P = -110
1P = 110
P = 110/11
P = 10
Solve for Quantity
Qd = Qs = 6P = 6(10) = 60 = Q
Suppose supply and demand functions of a
good are given by:
Demand function: Qd = 920 – 8P
Supply Function: Qs = -120 + 2P
(i) Calculate Equilibrium price and quanity
(ii) Calculate excess demand when price 90$
(iii) Calculate excess supply when price 105 $
(iv) Calculate the profit made on the black
market if a price ceiling of $ 65 is imposed.
Use the data below and answer the following
questions.
Quantity of
Peanuts
Total utility from
peanuts
Quantity of
Beans
Total Utility
from Beans
0 0 0 0
1 5 1 11
2 9 2 19
3 12 3 26
4 14 4 30
(i) What is the marginal utility of peanuts and
beans at each level of Quantity?
(ii) If the price of peanut is $1 for each and
the price of beans is $2 for each. John wants
to makes his maximizes his utility, and he has
$10 to spend on it. How much quantity of
peanuts and beans; he will buy to get
maximum satisfaction?
Q.2 Suppose that price of Good X is $2 and for
Good Y is $1. Consumer has 10$ to spend on
it.
Combination Good X Good Y
A 1 12
B 2 8
C 3 5
D 4 3
E 5 2
(1) Calculate Slope of the indifference curve
and slope of the budget constraint for Good X
and Good Y by using above data.
(ii|) Draw the graph of indifference curve and
budget constraint curve by using above data.
Q.3 There are two goods, X and Y, and marginal
utility from each is as shown below. If income is
$9 and prices of X and Y are $ 2 and $1,
respectively.
I. What quantities of good X and Y will you
purchase to maximize utility?
II. Calculate the total utility of Good X and Y at
each level of output.
III. Assume that, other things are remaining
unchanged; the price of X falls to $1, what
quantities of good X and Y, will you purchase to
maximize utility.
IV. Using above two prices and quantities of good
X, draw the demand curve. Comment on your
graph.
Units of X MUx Units of Y MUy
1 10 1 8
2 8 2 7
3 6 3 6
4 4 4 5
5 3 5 4
6 2 6 3
 Q.4 Suppose a consumer only buys two goods: hot dogs
and hamburgers. The price of hot dogs is $1, the price of
hamburgers is $2, and the consumer's income is $20.
 (a) Plot the consumer's budget constraint and measure the
quantity of hot dogs on the vertical axis and the quantity of
hamburgers on the horizontal axis. Explicitly plot the points
on the budget constraint associated with the even
numbered quantities of hamburgers (0, 2, 4,6….)
 (b) Suppose the individual chooses to consume six
hamburgers. What is the maximum amount of hot dogs that
he can afford? Draw an indifference curve on the figure
above that establishes this bundle of goods as the
optimum.
 (c) What is the slope of the budget constraint? What is the
slope of the consumer's indifference curve at the optimum?

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Algebraic representation of demand and supply

  • 1.
  • 2.  A demand function is a function that represents a demand curve. The demand function shows us the exact relationship between price and quantity demanded. Demand functions are also just shorthand ways of representing both a demand curve and a demand schedule. . When we have a demand function, we can actually plot a demand curve AND find points on the demand schedule.
  • 3. A supply function is a function representing the exact relationship between price and quantity supplied. Supply functions are also shorthand representations – they can be used to find both supply curves and to find points in a supply schedule.
  • 4. With the supply and demand functions, we have easy ways of representing sellers’ and buyers’ intentions in a market. These functions are also handy to have for finding equilibrium outcomes in a market. Rather than visually having to scope out exactly where quantity supplied equals quantity demanded on a demand and supply schedule or on a market graph, we can find exact equilibrium outcomes using demand and supply functions and a little bit of algebra.
  • 5. Let’s consider the market for wheat. Measuring quantity in millions of bushels, suppose we have a market demand curve that is given by: QD = 50 – 2P
  • 6.  The following table shows some points: When price = Quantity demanded = $10 per bushel 30 million bushels $8 per bushel 34 million bushels $6 per bushel 38 million bushels $4 per bushel 42 million bushels $2 per bushel 46 million bushels
  • 7.  The supply curve for the wheat market is given by QS = -6 + 12P This is normal for a supply function – they usually don’t start at the origin point of the graph, but up a bit on the price axis.
  • 8.  The following table shows some points: When price = Quantity supplied = $10 per bushel 114 million bushels $8 per bushel 90 million bushels $6 per bushel 66 million bushels $4 per bushel 42 million bushels $2 per bushel 18 million bushels
  • 9.  QD = 50 – 2P, QS = -6 + 12P E = (Qd = Qs)  50 – 2P = -6 + 12P  50 + 6 – 2P = 12P  56 = 12P + 2P  56 = 14P  P = $4 per bushel wheat
  • 10.  QD = 50 – 2P  QD = 50 – 2 ($4)  QD = 50 – 8 = 42 million bushels of wheat Qs = -6 + 12P Qs = -6 + 12 ($4) Qs = -6 +48 = 42 million bushels of wheat
  • 11. Number 1  Demand equation: Qd = 100- 2P  Supply equation: Qs = -20 + 4P Find out the equilibrium quantity and price. Number 2 The demand and supply equations are the following:  Qd = 400 – 20P Qs = - 200 + 10P Find out the equilibrium quantity and price.
  • 12.  Number 3 Demand and supply in a market are described by the equations Qd = 66-3P Qs = -4+2P Find out equilibrium quantity and price.
  • 13.  The demand and supply functions of a good are given by Qd = 110-5P Qs = 6P  (i) Find the inverse demand and supply functions Qd = 110-5P 5P = 110-Qd P = 110-Qd/5 Qs = 6P P = Qs/6
  • 14. (ii) Find the equilibrium price and quantity Solve simultaneously: Qd = 110-5P Qs = 6P At equilibrium Qd = Qs 110-5P = 6P Collect the terms -5P-6P = -110 1P = 110 P = 110/11 P = 10 Solve for Quantity Qd = Qs = 6P = 6(10) = 60 = Q
  • 15. Suppose supply and demand functions of a good are given by: Demand function: Qd = 920 – 8P Supply Function: Qs = -120 + 2P (i) Calculate Equilibrium price and quanity (ii) Calculate excess demand when price 90$ (iii) Calculate excess supply when price 105 $ (iv) Calculate the profit made on the black market if a price ceiling of $ 65 is imposed.
  • 16. Use the data below and answer the following questions. Quantity of Peanuts Total utility from peanuts Quantity of Beans Total Utility from Beans 0 0 0 0 1 5 1 11 2 9 2 19 3 12 3 26 4 14 4 30
  • 17. (i) What is the marginal utility of peanuts and beans at each level of Quantity? (ii) If the price of peanut is $1 for each and the price of beans is $2 for each. John wants to makes his maximizes his utility, and he has $10 to spend on it. How much quantity of peanuts and beans; he will buy to get maximum satisfaction?
  • 18. Q.2 Suppose that price of Good X is $2 and for Good Y is $1. Consumer has 10$ to spend on it. Combination Good X Good Y A 1 12 B 2 8 C 3 5 D 4 3 E 5 2
  • 19. (1) Calculate Slope of the indifference curve and slope of the budget constraint for Good X and Good Y by using above data. (ii|) Draw the graph of indifference curve and budget constraint curve by using above data.
  • 20. Q.3 There are two goods, X and Y, and marginal utility from each is as shown below. If income is $9 and prices of X and Y are $ 2 and $1, respectively. I. What quantities of good X and Y will you purchase to maximize utility? II. Calculate the total utility of Good X and Y at each level of output. III. Assume that, other things are remaining unchanged; the price of X falls to $1, what quantities of good X and Y, will you purchase to maximize utility. IV. Using above two prices and quantities of good X, draw the demand curve. Comment on your graph.
  • 21. Units of X MUx Units of Y MUy 1 10 1 8 2 8 2 7 3 6 3 6 4 4 4 5 5 3 5 4 6 2 6 3
  • 22.  Q.4 Suppose a consumer only buys two goods: hot dogs and hamburgers. The price of hot dogs is $1, the price of hamburgers is $2, and the consumer's income is $20.  (a) Plot the consumer's budget constraint and measure the quantity of hot dogs on the vertical axis and the quantity of hamburgers on the horizontal axis. Explicitly plot the points on the budget constraint associated with the even numbered quantities of hamburgers (0, 2, 4,6….)  (b) Suppose the individual chooses to consume six hamburgers. What is the maximum amount of hot dogs that he can afford? Draw an indifference curve on the figure above that establishes this bundle of goods as the optimum.  (c) What is the slope of the budget constraint? What is the slope of the consumer's indifference curve at the optimum?