# MGEA02H3 Lecture Notes - Lecture 2: Demand Curve

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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:

www.notesolution.com

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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

www.notesolution.com

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3

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

www.notesolution.com

## Document Summary

Week 2: demand and supply in a competitive market. 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!) N maximizing a value (or utility) function along ppf calculating opportunity cost on ppf. N shifts in demand and supply: how they affect equilibrium. 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.