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Lecture 2

MGEA02H3 Lecture Notes - Lecture 2: Demand Curve


Department
Economics for Management Studies
Course Code
MGEA02H3
Professor
Gordon Cleveland
Lecture
2

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Week 2: Demand and Supply in a Competitive Market
NEWS FLASHES!
- Our first midterm test will be written on Saturday, October 17th at 5 pm (2 hour period with 90
minutes test) (less than 4 weeks away)
- Tentative date for next midterm at Friday November 20th (3 to 5 pm)
- More parts of Course Handbook are up on the UTSC Intranet
- Tutorials start this week…schedule is on website, under ECMA04/Professor and TAs
- Office Hours for help from T.A.s in MW-369 are also up on website in same place (If you need
help…go get it…TAs are paid to help you!)
What did we learn last week?
x definition of economics
x opportunity cost
x production possibilities model
x calculating opportunity cost on PPF
x PPF with increasing costs
x maximizing a value (or utility) function along PPF
Agenda for this week:
x Overview of the competitive market model
x What is a market?
x What is competition?
x Demand
x Supply
x Equilibrium
x Shifts in Demand and Supply: how they affect equilibrium
Don’t forget your tutorials this week. And our 6 new T.A.’s have office hours!
Leslie, Juan, Lisa, Zuoyi, Sam and Shoeb
(check www.utsc.utoronto.ca/~cleveland for the time of office hours in MW-369 and the time and
location of tutorials. Click on the button for ECMA04 and then on the button on the right-hand side for
“Professor and TAs”).
Use questions from a test in previous years to review material on opportunity cost and PPF.)
1-3. A country produces goods X and Y and has the following equation for its production possibilities
frontier: Y2 + 4X2 = 400 or Y = [400 - 4X2]0.5
Questions 1 through 3 concerns this country.
1. You are told that the economy is producing efficiently and has chosen to produce and consume 6 units
of X and 16 units of Y. At this point on the production possibilities frontier, you can use calculus to
obtain the opportunity cost of X as:
ANSWER:
dY/dX = 0.5[400 - 4X2]-0.5(-8X) = -4X[400 - 4X2]-0.5
To get opportunity cost of X, use -dY/dX, which is 4X[400 - 4X2]-0.5
Evaluate this expression at X = 6 to get the opportunity cost of X as = (4 x 6) (1/[256]0.5) = 24/16 = 3/2
2. Now you are told that the economy is producing efficiently and has chosen to produce and consume 8
units of X. At this point on the production possibilities frontier, you can use calculus to obtain the
opportunity cost of Y as:
ANSWER:
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To get opportunity cost of Y, use -dX/dY, or inverse of -dY/dX. The opportunity cost of X is 4X[400 -
4X2]-0.5. When this expression is evaluated at X = 8, we have (4 x 8) (1/[144]0.5) = 32/12 = 8/3.
We want the opportunity cost of Y which is the inverse or 3/8.
3. Suppose that those in charge of this economy want to maximize the utility of the residents of the
country, where utility can be computed according to the equation U = XY2 The point on the PPF that
will maximize the value of the output involves the production of how many units of X (rounding to two
decimal places)?
ANSWER:
We need to find the point which satisfies both the utility function and the production possibilities
function. Substitute the PPF, expressed in terms of Y, into the utility (or value) function.
So U = X[400 - 4X2] = 400X - 4X3
Then set dU/dX = 0 for maximum.
dU/dX = 400 – 12X2 = 0 or X = 5.774
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4-5. The Canadian economy can produce two goods, represented by X and Y. The production
possibilities frontier is shown on the diagram below, along with several points, each of which
represents a combination of X and Y. Questions 4 and 5 deal with this diagram.
4. A business leader suggests that Canadian taxes are too high, that this is discouraging Canadian
workers and investors, and that the effect of all this is that we are operating inefficiently. The
leader argues that if taxes were cut, efficiency would improve, and we would all be made better
off. Relating this to the diagram, we might say that the business leader is suggesting that wiser
tax policy would allow us to move from:
ANSWER:
The business leader suggests we are inefficient, so we start at a point like A; he wants us to cut
taxes to become efficient, that is, to move to a point like B or C.
5. A newspaper columnist suggests that Canadians are consuming too much X and that it is
eroding their moral fibre (whatever that means). Relating this to the diagram, we might say that
the columnist is suggesting that Canadians should shift their consumption so as to move from:
ANSWER:
The newspaper columnist suggests we want more Y and less X, but does not suggest we are
inefficient, so he is suggesting a move from C to B
Now…on to Demand and Supply
Y
X
C
B
A
D
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