Two students studying microeconomics are trying to understand why the tangent condition studied in this chapter means utility is at a maximum. Let’s listen: Student A. If a person chooses a point on...

THE UNIVERSITY OF THE WEST INDIES
ST. AUGUSTINE
FACULTY OF SOCIAL SCIENCES
DEPARTMENT OF ECONOMICS
ECON2000: INTERMEDIATE MICROECONOMICS I – 2012/13
TUTORIAL SHEET 1
THE THEORY OF CONSUMER BEHAVIOUR
PROBLEMS
1. The following data represent 5 points on the supply curve for orange juice:
PRICE ($ PER GALLON) QUANTITY (MILLIONS OF GALLONS)
1 100
2 300
3 500
4 700
5 900
and these data represent 5 points on the demand curve for orange juice:
PRICE ($ PER GALLON) QUANTITY (MILLIONS OF GALLONS)
1 700
2 600
3 500
4 400
5 300
a. Graph the points of these supply and demand curves for orange juice. Be sure to put price on
the vertical axis and quantity on the horizontal axis.
Answer:
. Do these points seem to lie along two straight lines? If so, figure out the precise alge
aic
equation of these lines. (Hint: If the points do lie on straight lines, you need only consider two
points on each of them to calculate the lines.)
Answer: Yes, these points lie on two straight lines.
Equation of demand curve: (P – 1)/(Q-700) = (1 – 2)/(700-600)
Or, P – 1 = -0.01(Q – 700)
Or, P – 1 = 7 – 0.01Q
So, Q = 800 – 100P
Equation of supply curve: (P – 1)/(Q – 100) = (1 – 2)/(100-300)
0
1
2
3
4
5
6
0 200 400 600 800 1000
Price
Quantity
Demand-Supply
Supply
Demand
Or, P – 1 = 0.005(Q – 100)
Or, P – 1 = 0.005Q – 0.5
Or, 0.005Q = P – 0.5
Or, Q = 200P – 100
c. Use your solutions from part b to calculate the ‗‗excess demand‘‘ for orange juice if the
market price is zero.
Answer:
At P = 0
Demand = Qd = 800
Supply = Qs = – 100
Therefore, Excess demand = (800 + 100) = 900
d. Use your solutions from part b to calculate the ‗‗excess supply‘‘ of orange juice if the orange
juice price is $6 per gallon.
Answer:
At P = 6
Demand = Qd = 800 – 600 = 200
Supply = Qs = 1200 – 100 = 1100
Therefore, Excess supply = (1100 – 200) = 900
2 Marshall defined an equili
ium price as one at which the quantity demanded equals the
quantity supplied.
a. Using the data provided in problem 1.1, show that P = 3 is the equili
ium price in
the orange juice market.
Answer:
At P = 3
Demand = Qd = 800 – 300 = 500
Supply = Qs = 600 – 100 = 500
Therefore, Demand = Supply = 500
. Using these data, explain why P = 2 and P = 4 are not equili
ium prices.
Answer:
At P = 2
Demand = Qd = 800 – 200 = 600
Supply = Qs = 400 – 100 = 300
Therefore, Demand ≠ Supply
There is an excess demand of (600 – 300) = 300
At P = 4
Demand = Qd = 800 – 400 = 400
Supply = Qs = 800 – 100 = 700
Therefore, Demand ≠ Supply
There is an excess supply of (700 – 400) = 300
c. Graph your results and show that the supply demand equili
ium resembles that
shown in Figure 1.3.
Answer:

d. Suppose the demand for orange juice were to increase so that people want to buy 300
million more gallons at every price. How would that change the data in problem
1.1? How would it shift the demand curve you drew in part c?
P
Qs Qd
Qd1 (New
demand)
1 100 700 1000
2 300 600 900
3 500 500 800
4 700 400 700
5 900 300 600
This will shift the demand curve to the right. This is shown below:
e. What is the new equili
ium price in the orange juice market, given this increase in
demand? Show this new equili
ium in your supply demand graph.
Answer:
Equation of new demand curve: (P – 1)/(Q-1000) = (1 – 2)/(1000-900)
Or, P – 1 = -0.01(Q – 1000)
Or, P – 1 = 10 – 0.01Q
So, Q = 1100 – 100P
Equation of supply curve: (P – 1)/(Q – 100) = (1 – 2)/(100-300)
Or, P – 1 = 0.005(Q – 100)
Or, P – 1 = 0.005Q – 0.5
0
1
2
3
4
5
6
0 200 400 600 800 1000 1200
Price
Quantity
Demand-Supply
Supply
Demand
New demand
Or, 0.005Q = P – 0.5
Or, Q = 200P – 100
Equating, New demand = Supply, we get,
1100 – 100P = 200P – 100
Or, 300P = 1200
Therefore, P* = 4
This is shown in the following figure:

f. Suppose now that a freeze in Florida reduces orange juice supply by 300 million
gallons at every price listed in problem 1.1. How would this shift in supply affect
the data in problem 1.1? How would it affect the alge
aic supply curve
calculated in that problem?
P Qs Qd New Supply
1 100 700 -200
2 300 600 0
3 500 500 200
4 700 400 400
5 900 300 600
This will shift the supply curve to the left


Equation of new supply curve: (P – 1)/(Q + 200) = (1 – 2)/(-200)
Or, P – 1 = 0.005(Q + 200)
Or, P – 1 = 0.005Q +1
Or, 0.005Q = P – 2
0
1
2
3
4
5
6
-400 -200 0 200 400 600 800 1000
Price
Quantity
Demand-Supply
Supply
Demand
New Supply
Or, Q = 200P – 400
g. Given this new supply relationship together with the demand relationship shown in
problem 1, what is the equili
ium price in this market?
Answer:
Equation of demand curve: (P – 1)/(Q-700) = (1 – 2)/(700-600)
Or, P – 1 = -0.01(Q – 700)
Or, P – 1 = 7 – 0.01Q
So, Q = 800 – 100P
Equation of new supply curve: Q = 200P – 400
Equating, Demand = Supply, we get,
800 – 100P = 200P – 400
Or, 300P = 1200
Therefore, P* = 4
h. Explain why P = 3 is no longer an equili
ium in the orange juice market. How
would the participants in this market know P = 3 is no longer an equili
ium?
At P = 3
Demand = Qd = 800 – 300 = 500
Supply = Qs = 600 – 400 = 200
Therefore, Demand ≠ Supply
There is an excess demand of (500 – 200) = 300
i. Graph your results for this supply shift.
0
1
2
3
4
5
6
-400 -200 0 200 400 600 800 1000
Price
Quantity
Demand-Supply
Supply
Demand
New Supply
3. Suppose a person has $8.00 to spend only on apples and bananas. Apples cost $.40
each, and bananas cost $.10 each.
a. If this person buys only apples, how many can be bought?
If this person buys only apples, he can buy (8/0.4) = 20 apples.
. If this person buys only bananas, how many can be bought?
If this person buys only bananas, he can buy (8/0.1) = 80 bananas.
c. If the person were to buy 10 apples, how many bananas could be bought with the
funds leftover?
Cost of 10 apples = $(0.4*10) = $4
Therefore, income left = $(8 – 4) = $4
Therefore, he can buy (4/0.1) = 40 bananas with the left over funds.
d. If the person consumes one less apple (that is, nine), how many more bananas could
e bought? Is this rate of trade-off the same no matter how many apples are
elinquished?
Cost of 1 apple = $0.4
With $0.4, he can buy (0.4/0.1) = 4 bananas.
This rate of trade-off will remain the same no matter how many apples are relinquished.
e. Write down the alge
aic equation for this person‘s budget constraint, and graph it
showing the points mentioned in parts a through d (using graph paper might...