ECON 102 Tutorial: Week 6

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ECON 102 Tutorial: Week 6
Ayesha Ali
www.lancaster.ac.uk/postgrad/alia10/econ102.html
[email protected]
office hours: 8:00AM – 8:50AM tuesdays LUMS C85
Cost and Production Questions
Key Concepts needed for these questions:
 Perfectly competitive firms are price takers, so for them MR = P.
 For all firms, profit is maximized at the quantity where MR = MC.
 When we want to understand how a firm makes entry/exit
decisions, we use the shutdown conditions – these are different
for the short run and the long-run:
 Short-run shutdown condition:
A firm should shut down when MR < AVC.
If the firm is perfectly competitive, this is when P < AVC.
This can also be written as when TR < VC.
 Long-run shutdown condition:
A firm should shut down when MR < ATC.
If the firm is perfectly competitive, this is when P < ATC.
This can also be written as when TR < TC or when profit < 0.
Question 1: Ch. 5 Problem 2
A price-taking firm makes air conditioners. The market price of one of
their new air conditioners is €120. Its total cost information is given in
the table below.
How many air conditioners should the firm
Air conditioners Total cost
per day
(€ per day)
1
100
2
150
3
220
4
310
5
405
6
510
7
650
8
800
produce per day if its goal is to maximise its
profit?
Question 1: Ch. 5 Problem 2
A price-taking firm makes air conditioners. The market price of one of
their new air conditioners is €120. Its total cost information is given in
the table below.
How many air conditioners should the firm produce per
day if its goal is to maximise its profit?
Air conditioners Total cost
per day
(€ per day)
1
100
2
150
3
220
4
310
5
405
6
7
8
510
650
800
Marginal Cost
(€ per day)
50
70
90
95
Profit is maximized where MR = MC.
Because this firm is a price taker, we know
that MR = P. So what we want to find is at
what quantity is MC = P?
The MC for each of the first 6 air
conditioners produced each day is less than
€120 (MC<P), but the marginal cost of the
7th air conditioner is €140, (MC>P).
105
140
150
So the company should produce 6 air
conditioners per day.
Question 1: Ch. 5 Problem 3(a)
The Paducah Slugger Company makes baseball bats out of lumber supplied
to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat.
Paducah’s only factors of production are lathe operators and a small building
with a lathe. The number of bats per day it produces depends on the
number of employee-hours per day, as shown in the table below.
If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and
building is €60, what is the profit-maximising quantity of bats?
Number of Number of
Number of Number of
bats per day employeebats per day employeehours per day
hours per day
0
0
5
5
10
15
20
25
30
30
35
35
0
0
1
1
2
4
7
11
16
16
22
22
Total
Revenue
(€/day)
TR = P*Q
Total cost
Profit
Total labor
(€/day)
(€/day)
cost
(€/day)
VC = wage* TC = FC + VC π=TR – TC
# of employee hrs.
Question 1: Ch. 5 Problem 3(a)
The Paducah Slugger Company makes baseball bats out of lumber supplied
to it by Acme Sporting Goods, which pays Paducah €10 for each finished bat.
Paducah’s only factors of production are lathe operators and a small building
with a lathe. The number of bats per day it produces depends on the
number of employee-hours per day, as shown in the table below.
If the wage is €15 per hour and Paducah’s daily fixed cost for the lathe and
building is €60, what is the profit-maximising quantity of bats?
As indicated by the
entries in the last
column of the table
to the right, the
profit-maximizing
quantity of bats for
Paducah is 20/day,
which yields daily
profit of €35.
Number of Number of
Total
bats per day employee- Revenue
hours per day (€/day)
0
5
10
15
20
25
30
35
0
1
2
4
7
11
16
22
0
50
100
150
200
250
300
350
Total labor
cost
(€/day)
Total
cost
(€/day)
Profit
(€/day
)
0
15
30
60
105
165
240
330
60
75
90
120
165
225
300
390
-60
-25
10
30
35
25
0
-40
Question 1: Ch. 5 Problem 3(b)
What would be the profit-maximising number of bats if the firm’s
fixed cost were not €60 per day but only €30?
Same quantity as in part a, but now profit is €65, or €30 more
than before.
Q
Number of
Total
(bats/day) employee- Revenue
hours per (€/day)
day
0
0
0
1
5
50
2
10
100
4
15
150
7
20
200
11
25
250
16
30
300
22
35
350
Total labor Total
cost
cost
(€/day) (€/day)
0
15
30
60
105
165
240
330
30
45
60
90
135
195
270
360
Profit
(€/day)
-30
5
40
60
65
55
30
-10
Question 1: Ch. 5 Problem 7
For the pizza seller whose marginal, average variable and average
total cost curves are shown in the diagram below, what is the profitmaximising level of output and how much profit will this producer
earn if the price of pizza is €2.50 per slice?
Question 1: Ch. 5 Problem 7
For the pizza seller whose marginal, average variable and average
total cost curves are shown in the diagram below, what is the profitmaximising level of output and how much profit will this producer
earn if the price of pizza is €2.50 per slice?
To answer this question, we use the same rule as we
did in Ch. 5 Problem 2: For a perfectly competitive
firm, profit is maximized where MC = P.
This firm will sell 570 slices per day, the quantity for
which P = MC.
Its profit will be:
π = (P-ATC)*Q
π = (€2.50/slice - €1.40/slice)*(570 slices/day)
π = €627/day.
Question 1: Ch. 5 Problem 8
For the pizza seller whose marginal, average variable and average total cost
curves are shown in the diagram below, what is the profit-maximising level
of output and how much profit will this producer earn if the price of pizza is
€0.80 per slice?
Question 1: Ch. 5 Problem 8
For the pizza seller whose marginal, average variable and average total cost
curves are shown in the diagram below, what is the profit-maximising level
of output and how much profit will this producer earn if the price of pizza is
€0.80 per slice?
This firm will sell 360 slices per day, the quantity
for which P = MC.
Its profit will be:
π = (P-ATC)*Q
π = (€0.80/slice - €1.03/slice)*(360 slices/day)
π = -€82.80/day.
Question 1: Ch. 5 Problem 9
For the pizza seller whose marginal, average variable and average total cost
curves are shown in the diagram below, what is the profit-maximising level
of output and how much profit will this producer earn if the price of pizza is
€0.50 per slice?
Question 1: Ch. 5 Problem 9
For the pizza seller whose marginal, average variable and average total cost
curves are shown in the diagram below, what is the profit-maximising level
of output and how much profit will this producer earn if the price of pizza is
€0.50 per slice?
Because price is less than the minimum value of
AVC, this producer will shut down in the short run.
He will experience a loss equal to his fixed cost.
Fixed cost is the difference between total cost and
total variable cost.
For Q = 260 slices/day, we know both ATC and AVC, so for that output level
we can calculate:
TC = ATC*Q = (260 slices/day)*(€1.18/slice) = €306.80/day
VC = AVC*Q = (260 slices/day)*(€0.68/slice) = €176.80/day.
So fixed cost, FC = TC - VC = €306.80/day - €176.80/day = €130/day.
This producer’s profit is thus - €130/day.
Perfect Competition Questions
Question 1: Ch. 7 Problem 3(a)
John Jones owns and manages a café whose annual revenue is
€5,000. The annual expenses are as in the table below.
Expense
Labour
Food and drink
Electricity
Vehicle lease
Rent
Interest on loan for equipment
Calculate John’s annual accounting profit.
€
2,000
500
100
150
500
1,000
John's accounting profit is his
revenue minus his explicit costs, or
€750 per year.
Question 1: Ch. 7 Problem 3(b)
John Jones owns and manages a café whose annual revenue is
€5,000. The annual expenses are as in the table below.
Expense
Labour
Food and drink
Electricity
Vehicle lease
Rent
Interest on loan for equipment
€
2,000
500
100
150
500
1,000
John could earn €1,000 per year as a
recycler of aluminium cans. However,
he prefers to run the café. In fact, he
would be willing to pay up to €275 per
year to run the café rather than to
recycle cans. Is the café making an
economic profit? Should John stay in
the business? Explain.
Yes: his opportunity cost of his labour to run the café is €1,000 €275, or €725 per year. Adding this implicit cost to the explicit costs
implies that the café is making an economic profit of €25 per year.
And since €25>0, John should stay in business.
Question 1: Ch. 7 Problem 3(c)
John Jones owns and manages a café whose annual revenue is
€5,000. The annual expenses are as in the table below.
Expense
Labour
Food and drink
Electricity
Vehicle lease
Rent
Interest on loan for equipment
€
2,000
500
100
150
500
1,000
Suppose the café’s revenues and expenses
remain the same, but recyclers’ earnings
rise to €1,100 per year. Is the café still
making an economic profit? Explain.
John's opportunity cost rises by €100, to €825 per year. The café is
thus now making an economic loss of €75 per year.
Question 1: Ch. 7 Problem 3(d)
John Jones owns and manages a café whose annual revenue is
€5,000. The annual expenses are as in the table below.
Expense
Labour
Food and drink
Electricity
Vehicle lease
Rent
Interest on loan for equipment
€
2,000
500
100
150
500
1,000
Suppose John had not had to get a
€10,000 loan at an annual interest rate of
10 per cent to buy equipment, but instead
had invested €10,000 of his own money in
equipment. How would your answers to
parts (a) and (b) change?
The accounting profit would now be €1,750/yr. The answer to part b. would
not change. If John had €10,000 of his own to invest in the café, he would
forgo €1,000/yr in interest by not putting the money in a savings account.
That amount is an opportunity cost that must be included when calculating
economic profit.
Question 1: Ch. 7 Problem 3(e)
John Jones owns and manages a café whose annual revenue is
€5,000. The annual expenses are as in the table below.
Expense
Labour
Food and drink
Electricity
Vehicle lease
Rent
Interest on loan for equipment
€
2,000
500
100
150
500
1,000
If John can earn €1,000 a year as a recycler,
and he likes recycling just as well as running
the café, how much additional revenue
would the café have to collect each year to
earn a normal profit?
To earn a normal profit, the café would have to cover all its implicit and
explicit costs. The opportunity cost of John's time is €1,000/yr, whereas the
café's accounting profit is only €750/yr. Thus, the café would have to earn
additional revenues of €250/yr to make a normal profit.
Perfect Competition Q2(a)
Dave owns a firm that produces and sells gizmos in a perfectly competitive
market.
His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2.
(given this variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.).
Assume that each firm in this market has the same costs as Dave, and the
costs I’ve described include both implicit and explicit costs.
If the current market price of gizmos is $60, how many gizmos does Dave
produce to maximize his profit? How much economic profit does Dave earn?
Perfect Competition Q2(a)
Dave owns a firm that produces and sells gizmos in a perfectly competitive market.
His fixed costs are $200 per day, and his variable costs are VC(Q) = 2Q2. (given this
variable cost curve, Dave’s marginal cost curve is: MC(Q) = 4Q.). Assume that each
firm in this market has the same costs as Dave, and the costs I’ve described include
both implicit and explicit costs.
If the current market price of gizmos is $60, how many gizmos does Dave produce
to maximize his profit? How much economic profit does Dave earn?
We know that Dave’s marginal cost curve is MC(Q) = 4Q.
Because Dave’s firm is in a perfectly competitive market, we know that it
maximizes profit when MC(Q) = P.
We can re-write this as:
4Q = 60
And solve for Q:
Q = 15
To find Dave’s economic profit, we use the equation: π = TR – TC, where TR = P*Q
and TC = FC + VC. When Dave produces Q = 15 units, his total variable costs are:
VC(Q) = 2Q2 = 2(15)2 = 450 and his fixed costs are FC = 200. We can plug these in
to the equation for economic profit: π = TR – TC
π = P*Q – FC - VC
π = 15*60 – 200 - 450
π = 900 – 650
π = 250
Perfect Competition Q2(b)
Is the market price of $60 sustainable in the long run?
Explain why or why not.
No, this market price is not sustainable in the long run.
Since firms in the industry are earning positive economic
profit, new entrants will enter the industry; this will shift
the supply curve to the right and drive the price down.
Perfect Competition Q2(c)
Dave owns a firm that produces and sells gizmos in a
perfectly competitive market. His fixed costs are $200 per
day, and his variable costs are VC(Q) = 2Q2. (given this
variable cost curve, Dave’s marginal cost curve is: MC(Q) =
4Q.). Assume that each firm in this market has the same
costs as Dave, and the costs I’ve described include both
implicit and explicit costs.
Write down the expression for Dave’s total costs
The equation for Total Cost is: TC(Q) = FC + VC(Q)
So Dave’s Total Cost is:
TC(Q) = 200 + 2Q2
Perfect Competition Q2(d)
Dave owns a firm that produces and sells gizmos in a perfectly
competitive market. His fixed costs are $200 per day, and his variable
costs are VC(Q) = 2Q2. (given this variable cost curve, Dave’s marginal
cost curve is: MC(Q) = 4Q.). Assume that each firm in this market has
the same costs as Dave, and the costs I’ve described include both
implicit and explicit costs.
In part (c), we found TC(Q) = 200 + 2Q2
Write down the expression for Dave’s average total cost
Perfect Competition Q2(d)
Dave owns a firm that produces and sells gizmos in a
perfectly competitive market. His fixed costs are $200 per
day, and his variable costs are VC(Q) = 2Q2. (given this
variable cost curve, Dave’s marginal cost curve is: MC(Q) =
4Q.). Assume that each firm in this market has the same
costs as Dave, and the costs I’ve described include both
implicit and explicit costs.
Write down the expression for Dave’s average total cost
The equation for Average Total Cost is:
ATC(Q) = TC(Q)/Q
Plug in Dave’s total cost from part (c): ATC(Q) = (200 + 2Q2)/Q
So Dave’s Average Total Cost is:
ATC(Q) = 200/Q + 2Q
Perfect Competition Q2(e)
Solve for the long-run equilibrium price.
We know that we have a perfectly competitive market. FC = $200/day, variable
costs are VC(Q) = 2Q2 and Dave’s marginal cost curve is: MC(Q) = 4Q.
In parts (c) and (d), we found TC = 200 + 2Q2 and ATC = 200/Q + 2Q.
Perfect Competition Q2(e)
Solve for the long-run equilibrium price.
The long-run equilibrium price is the price where firms earn zero economic
profit. This happens at the minimum of the ATC cost curve. To find the
minimum of the ATC curve, recall that when MC = ATC, ATC is at its minimum.
So, we can set MC(Q) = ATC(Q).
We know that MC(Q) = 4Q, that was given in the problem.
In part (d) we found ATC(Q) = 200/Q + 2Q.
So let’s set
MC(Q) = ATC(Q)
Plugging in, we get:
4Q = 200/Q + 2Q
2Q = 200/Q
2Q2 = 200
Q2 = 100
Q = 10
So, ATC(Q) reaches its minimum when Q = 10. To find the value of ATC, we
can plug in Q = 10 into ATC(Q) = 200/Q + 2Q.
ATC(Q) = 200/10 + 2(10) = 40
Thus, the long-run equilibrium price is 40.
Exam on Friday
 50 minutes; 25 Questions: 16 from Rietzke, 9 from Peel.
 What to Revise: Practice MC Questions, Tutorial worksheets,
Peel’s Maths Questions, Lecture Notes, and textbook
chapters.
 Check your timetable for Exam time and location.
 Bring a pencil and erasor.

No calculators, cell phones, or electronic translators will be allowed.
(Paper versions of English-to-Other Language dictionaries will be
allowed and checked by invigilators).
 Also, for next week, there will be a tutorial worksheet on
Moodle, but no maths questions.
 Good luck and see you next week!

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