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Economics for Management Studies

MGEA02H3

Michael Krashinsky

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18 October 2012
For the exams, ignore the origins of TC/AC/MC etc., they will
just assume we know them and work with it.
Typical graph of AC, AVC, MC:
AFC is a constant divided by quantity, is always going down
but starts off extremely high (asymptotic). AVC begins to rise
at a certain point because of diminishing marginal
productivity. If AC is the sum of AFC + AVC, it starts off high
because AFC is very high, then it lowers, but comes back up
because of the rising VC. AVC + AC start becoming closer and
closer together as AFC asymptotes towards 0. MC goes
through the minimum point on the AVC and AC curve – this
always must be true.
Example:
TC = 400 + 5q + q , q>2 AC = 400/q + 5 + q Find minimum of AC, AVC
FC = 300, q>2 AFC = 300/q Min AC = 45 at q = 20
2
VC = 100 + 5q + q , q> 2 AVC = 100/q + 5 + q Min AVC = 25 at q = 10
Minimum of the curve is always where the first derivative is equal to 0.
AC = 400/Q + 52+ q
dAC/dQ = -400/q + 1 = 0
1 = 400/q2
q = 400
q = 20
Plug 20 into the AC curve, so AC (20) = 45
MC = 5 + 2q
Min AC = 45 at q = 20 At q = 20 the minimum value of the AC and MC are the same.
MC = 5 + 2q = 45
Min AVC = 25 at q = 10 At q = 10 the minimum value of the AVC and MC are the same.
MC = 5 + 2q = 25
Notice the relationship of AC, AVC, and MC, this is no accident.
AC = TC/q
dAC/dq = 0 at min AC
dAC/dq = [q(dTC/dq)−TC]/q2
AVC = TVC/q
dAVC/dq = 0 at min AVC
The only difference between variable cost and total cost is the fixed cost, so the derivative of total cost
and total variable cost has got to be the same. Imagine looking at the function of average height of everybody in the
room. Everybody is lined in order from short to tall. Then, we add one
more person to the room (marginal person), that person’s height
would be the marginal height. If the marginal person is taller, the
average is pulled up, if the marginal person is shorter, it pulls the
average is down. It must always pass through the minimum AC point.
What would be sensible rule for firm to use in deciding how much labour to hire? Goal of firm is to
maximize profits, this must include all costs:
Profit = π = TR − TC
Example:
Owner runs a video store:
Every week: $2500 in rental income, pay out $1000 for rental of space, $800 for new videos, getting an
accounting profit of $700.
ECONOMIC PROFIT must include ALL COSTS, including costs of any labour by owner, any interest on
owner invested capital (more of an issue for large corporations).
ACCOUNTING PROFIT > ECONOMIC PROFIT
Accounting profit can be positive when economic profit zero or even negative.
Keep hiring labour as long as one more worker adds more to revenue than it does to cost. As long as P < L
P MP . Since MP is falling, this means produce where P = P MP .
Q L L Q L
In long run choose optimal amount of capital. Each SAC is associated with one level of capital (generally
cost is lower in the long run than in the short run). Graph of every possible SAC you could have for every
possible amount of capital: There is an optimal point
associated with each level of capital. There are an infinite
amount of curves. In the long run, you get to choose which of
these curves you get to be on. For each level of output, you
choose to be on the best possible curve – the lowest one. LAC
= long run average cost curve. The LAC is defined by all the
possible SAC, it is the envelop of all the SAC. The general shape
of the LAC is U-shaped. The output associated with minimum
efficient scale is called qMES.
IRTS: Increasing return to scale, the bigger you get means more
efficiency (IE: bigger grocery store has more variety).
CRTS: Constant return to scale, where the scale does not seem
to matter. This is the range where most of the firms are.
DRTS: Decreasing return to scale, when firms become too big,
things are harder to manage (IE: when enterprise gets so big
people no longer know each other). Keep hiring labour as long as one more worker adds more to revenue than it does to cost. As long as P <
L
PQMP . Lroduce where P (CosL of one more worker) = P MP (ValQe ofLwhat extra worker produces).
How much output should you produce?
π = TR − TC
dπ/dq = dTR/dq − dTC/dq = MR − MC =0
But if TR = PQQ, then dTR/dq = P (Qssuming PQ constant)
dTC/dq = MC
PQ = MC
As long as marginal cost is below the cost of the output, produce it. If it is greater than the cost of the
output, do not produce it. This resembles a supply curve. 22 October 2012
Perfect Competition is a particular model of how the economy works. We look at markets in which
there are a lot of firms competing with each other. This is more than just an “abstract model,” in fact;
perfect competition is the model underlying supply and demand.
Assume:
Many firms (atomistic) PRICE TAKERS
Homogeneous product
Perfect information (everyone knows what price is), no transaction costs LAW OF ONE PRICE
Free entry and exit in long run
q = output of firm
Q = output of industry
Example:
TC = 400 + 5q + q , q>2 Min AC = 45 at q = 20
FC = 300 Min AVC = 25 at q = 10
Suppose P = 51
π = TR – TC = Pq – TC = 51q – (400 + 5q + q ) = -q + 46q – 400
dπ/dq = -2q + 46 = 0
2q = 46
q = 23
Maximize MC = 5 + 2q = 51
q = 23 2q = 46
π = -529 + 1058 – 400 = 129 q = 23
Suppose P = 47
2 2
π = TR – TC = Pq – TC = 47q – (400 + 5q + q ) = -q + 42q – 400
dπ/dq = -2q + 42
2q = 42
q = 21
Maximize MC = 5 + 2q = 47
q = 21 2q = 42
π = q = 21
Suppose P = 45 Suppose P = 35
q = 20 q = 15
π = 0 π = -157
Suppose P = 27 Suppose P = 23
q = 11 q = 9 (WRONG ANSWER) 0
π = -279 π = -319 (WRONG ANSWER) -300 So the short run P = MC, as long as π > -TFC. (In this case -300. If you are doing better than -300, then
produce, but as soon as your losses are greater than -300, shut the firm down).
We can do this even more simply:
Pq - TC > −TFC
Pq - TVC - TFC > -TFC
Pq - TVC > 0
Pq > TVC
P > AVC
LOGIC: “sunk costs” are gone, “don’t throw good money after bad.”
As soon as price drops below AVC curve, produce 0. If the price is
above the AVC, the supply curve is just the MC. If the price is below
the AVC, the firm is going to shut down, and the supply of the firm is
on the vertical axis (0). If the price of the firm is equal to the
minimum AVC, then you lose your fixed cost whether you produce or
not – you really do not care.
MC above AVC
If P = 25 TR = 250
MC = 5 + 2q = 25 TC = 550
q = 10 π = -300
Example:
TC = 36 + 2q + q , q>2
FC = 20
TVC = 16 + 2q + q2
AVC = 16/q + 2 + q
2
dAVC/dq = -16/q + 1 = 0 => q = 4
AVC = 16/q + 2 + q = 10
MC = 2 + 2q
q<2 is part where it is not marginal cost and is not defined. 2 0, if economic profits are positive, the firm is covering all of its
costs, making a reasonable return on capital and getting reasonable compensation for the efforts (time)
of the entrepreneur plus getting something extra (the economic profits). Positive profits make this a very attractive industry for entrepreneurs looking to make money. Buried
behind this is the implicit assumption that there are entrepreneurs hunting for exactly these kinds of
opportunities. So π > 0 leads these entrepreneurs to enter the industry as new firms.
More firms π shift supply curve to the right, ENTRY SUPPLY SHIFTS PRICE FALLS PROFITS FALL.
This continues until the entry stops, but entry continues as
long as π > 0. So entry continues until profits are driven down
to zero. They go down towards zero because as long as there
is positive, you get more entry.
Negative profits make this a very unattractive industry for entrepreneurs, because they are not earning
a decent return on their efforts. As soon as they can (that is, in the long run when they can get rid of
their capital), they leave the industry to look for better opportunities elsewhere. So π < 0 leads these
entrepreneurs to exit the industry.
Fewer firms, π shifts supply curve to the left, EXIT SUPPLY SHIFTS PRICE RISES PROFITS RISE.
This continues until the exit stops, but exit continues as long
as π < 0. So exit continues until profits are driven up to zero.
So, in both cases, profits are driven to zero.
π = TR - TC = Pq - (AC)q
π = q(P - AC)
So profits are zero where P = AC
We are in the long run, so this means that P must be driven
to the minimum point on the LAC.
Price must be driven to this point, if it is below this point;
everybody is losing money, even in the long run. If it is
above this point, somebody is making money so people will
enter the industry and push the price down. The only place
profits will be 0 in the long run is right at the minimum
point on the AC (We assume there is only ONE LAC point to
solve problems). P > min LAC π > 0 entry P down, π up
P < min LAC π < 0 exit P up, π up
In each case, end up at P = min LAC and π = 0
To do “long run problems”, we must know the minimum point of the
LAC (given) or will tell you the minimum point, both the value of q and
the minimum LAC at that q, or will use a “trick” and tell you that the
short run average cost curve touches the LAC at the minimum (that is,
the SAC, which you will be given, and the LAC share the same minimum
point, so that the minimum of the SAC is the minimum of the LAC). We
assume that costs do not change as firms enter or exit called “constant
costs.”
Return to problem above where we start with 500 firms:
TC = 98 + 4q + 2q2
FC = 48
Min AC at q = 7, AC = 32
Suppose that you are told that this also the minimum LAC.
Case 1:
Demand is P = 40 - .004Q
We know that P = 32, because profits must be zero
We know that each firm produces q = 7
From the demand curve, we know that 32 = 40 - 0.004Q
Thus, Q = 8/0.004 = 2000
We know that Q = Nq 2000 = 7N
N = 2000/7 = 286 (approx), so there must be 286 firms in the long run.
Case 2:
Demand is P = 52 - .004Q
We know that P = 32, because profits must be zero
We know that each firm produces q = 7
From the demand curve, we know that 32 = 52 - 0.004Q
Thus, Q = 20/.004 = 5000
We know that Q = Nq 5000 = 7N
So N = 5000/7 = 714 (approx), so there must be 714 firms in the long run. 29 October 2012
An invisible hand mechanism shifts resources around the
economy. If consumers want more: Demand increases, price rises
in short run, positive profits. In long run, entrepreneurs respond to
lure of profits, shift resources into this sector by opening new
firms. Production responds automatically to additional demand, at
the end, prices return to minimum LAC.
DEMAND INCREASES PRICE INCREASES SUPPLY INCREASES
PRICE FALLS
If consumers want less: Demand decreases, price falls in short run,
negative profits. In long run, entrepreneurs respond to losses, shift
resources out of this sector by closing firms. Production responds
automatically to fall in demand, at the end, prices return to
minimum LAC.
Demand: P = 100 − 0.001Q
In long run, given that min LAC occurs at q = 20, LAC = $40
P = $40
q = 20
π = 0
(There is no elaborate computations for these, we know price is
going to have to be driven to the minimum point on the LAC $40,
and we know each firm is going to have to produce at that point
because it is the only breakeven point, and we know profit is 0
because P=AC).
Q = 60,000
N = 3000
Now suppose that in LR there is technological change that reduces
min LAC so that it occurs at q = 40, LAC = $30
P = $30
LR
q = 40
π = 0
30 = 100 – 0.001Q
0.001Q = 70
Q = 70,000
N = Q/q = 70,000/40 = 1750 This is the way you can link it up. Do not make the mistake of putting LAC ON supply and demand
diagram (as you can see, the quantity is very different; the only link is the price).
Try a variant on the Long Run problem we just looked at (forgetting about technological change).
Demand: P = 100 − .001Q
In long run, given that min LAC occurs at q = 20, LAC = $40
P = $40
q = 20
π = 0
Q = 60,000
N = 60,000/20 = 3000
Now, suppose short run MC for firm is MC = −20 + 3q
Short run supply: P = −20 + 3(q/3000) = −20 + .001Q
Suppose demand increases to: P = 160 − .001Q
In short run,
Q = 90,000
P = $70
So there must be positive profits
In long run,
Min LAC occurs at q = 20, LAC = $40
P = $40
q = 20
π = 0
Q = 120,000
N = 120,000/20 = 6000 31 October 2012
What happens if demand falls so much that price goes down to shut down price?
Demand: P = 100 − .001Q
Start in long run and short run equilibrium, given that min LAC occurs at q = 20, LAC = $40
P = $40
q = 20 Q = 60,000
π = 0 N = 60,000/20 = 3000
Suppose short run MC for firm is MC = −20 + 3q
Shut down price is 28
So short run supply is P = −20 + 0.001Q, P ≥ 28
Q = 0 P < 28
Suppose that demand falls to P = 64 − .001Q
Short run:
-20 + 0.001Q = 64 - 0.001Q
Q = 42,000
P = 22
The price is not allowed to be below 28; therefore, we have the wrong answer. If the price goes one
penny below 28, we have no production at all – excess demand, if the price goes one penny above 28,
then all the firms stay open and we have excess supply. The only possible equilibrium is at the price of
28, where some of the firms open and some shut down.
So, P = 28, QD = 36,000
100 – 0.001Q = -20 + 0.001Q
0.002Q = 120
28 (Shutdown price) = 64 – 0.001Q
Q D 36/0.001 = 36000
36000/16 = 2250 (2250 firms that operate, supply
16 units each)
750 firms shut down.
Long run:
40 = 64 – 0.001Q
0.001Q = 24
Q = 24000
N = Q/q = 24000/20 = 1200 Economists like perfect competition. In short run
outcome maximizes sum of producer and consumer
surplus. CS + PS = what is between supply and demand
curve, that maximizes the area. Any additional output
would have the cost of production of an extra unit above
the benefit to consumers (marginal utility – the value of
demand curve), if we produce more or less, people are
worse off. It is getting towards the point everyone is
unpleasant.
In long run, outcome certainly maximizes consumer
surplus (and there is no producer surplus). Producing less
than Q*, we would be foregoing output. If we stop
producing at Q 1 the marginal utility of additional units is
greater than the cost of producing them. In the long run,
you would not want to accept less than Q*. At Q , the2
value of additional units you are producing is
considerably less than the cost of producing those units.
The economy should not be spending $40 to produce
goods that are worth $20. Perfect competition gets you
to Q* - generating the right amount of output.
But the process is not gentle; the impersonality of the market makes it essentially amoral. We
essentially hammer producers until they give up and go elsewhere. Producers (and those who work for
them) do not like this.
Often there are big firms, with no free entry. Polar opposite of perfect competition is monopoly where
there is a single firm, and no entry. Firm uses market power to push price up, so positive profits. For this
to continue there must be something that prevents entry in the long run. The barriers to entry are:
legality, cost advantages of size (natural) and advertising (created).
Falling LAC, which could be a natural barrier.
Issue of Minimum efficient scale: qMES
2
TC = 36 + 2q + q q = 7
FC = 20 P = 23
Demand: P = 30 − q = 30 − Q π = 62
Maximize profits = TR − TC MC = MR
dπ/dq = dTR/dq − dTC/dq = 0
2
TR= Pq = (30 − q)q = 30q – q
TC = 36 + 2q + q2
MC = 2 + 2q
30 – 2q = 2 + 2q
28 = 4q
q = 7
Monopolist does not produce at minimum AC (neither did the perfect competitor in the short run).
Demand: 30 – q
MR: 30 – 2q
These two equations are very similar having the same intercept but twice the slope. This is not an
accident.
2
TR = PQ = AB-Q
MR = dTR/dQ = A – 2bQ
Demand and marginal revenue.
Marginal revenue can go into the negative range. 5 November 2012
Monopolist would produce (maximize profits) where MR = MC. Revenue must cover variable costs. Set
MR = MC, as long as P ≥ AVC.
2
TC = 36 + 2q + q FC = 20 P = 30 − q = 30 − Q
To solve for profit maximization:
MC = 2 + 2q MR = 30 − 2Q
MR = MC → 2 + 2Q = 30 – 2Q → Q = 7
P = 23
And you get profit the normal way:
π = TR – TC = 7x23 – 99 = 62
[Notice: Because profits are positive, we don’t have to worry about the P ≥ AVC issue]
MC comes from the derivative of the total cost function.
MR is the same intercept but twice the slope of demand curve.
It does not matter if we have a q and Q because in monopoly the market and the firm is the same
quantity because there is only 1 firm.
We set MR = MC and find Q = 7. We plug Q = 7 back into the demand curve to find what the monopolist
is going to charge, which is 23. The monopolist makes the decision to what point along the demand
curve to sell the goods. Once you have chosen Q, the P is on the demand curve because monopolists
control price.
Notice that MR = 30 – 2Q while demand is P = 30 – Q. Clearly MR is below
(

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