Transcript ECON 100 Tutorial: Week 5

ECON 100 Tutorial: Week 5
www.lancaster.ac.uk/postgrad/murphys4/
[email protected]
office: LUMS C85
Outline
• Question 6 – 15 min.
• Question 7 – 15 min.
• Past Exam Multiple Choice questions - 15 min.
• Suggested solutions for other questions will
be included/added to slides so you can check
your own answers.
Tutorial 5 Worksheet Questions and
Corresponding Textbook Page #’s
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Question 1: pgs. 268
Question 2: pgs. 269-270
Question 3: pg. 270; Figure 13.2
Question 4: pgs. 275-276; Figure 13.4
Question 5: pgs. 269-271; Figure 13.2
Question 6: pgs. 271-275
Essay Question: pgs. 278-280
Question 1
Distinguish between the short run and the long run
in production
In the short run, fixed costs are fixed.
In the long run, fixed costs can change or become
variable.
Question 2
Why does marginal product decline as total
product increases?
Diminishing marginal product is the result of
diminishing marginal returns to the inputs of
production.
Question 3
Explain the relationship between the production
function and the total cost curve. Use diagrams to
help illustrate your answer and explain why the
curves are shaped as they are.
(See figure 13.2 for a detailed discussion)
Question 3
Question 3
Question 3
Explain the relationship between the production
function and the total cost curve. Use diagrams to
help illustrate your answer and explain why the
curves are shaped as they are.
So the production function curve gets flatter while
the cost curve gets steeper, but both because of
diminishing marginal returns as Q increases.
Question 4
Why does the marginal cost curve cut the average
cost curve at its lowest point?
• When MC < ATC, ∆ATC < 0
– When the cost of one more unit is below the average
cost, it drags the average down
• When MC > ATC, ∆ATC > 0
– When the cost of one more unit is above the average
cost, it pulls the average up
• As a result, MC = ATC at the minimum of ATC
Question 5(a)
Complete the following table. It describes the production and cost of hamburgers
at a roadside stand. All figures are measured per hour.
= Labor (L) = Quantity (Q) = Change in Output = Fixed Cost
(FC)
= (Q2 – Q1)/(L2-L1)
= Variable Cost = TC
(VC)
= FC+VC
Question 5(a) ctd.
=Q
=(Q2-Q1)/(L2-L1)
=FC
=VC
=FC + VC
25+0=
(6-0)/(1-0)=
25+5=
(11-6)/(2-1)=
25+10=
15-11=
25+15=
18-15=
25+20=
20-18=
25+25=
Question 5(b)
Plot the production function.
• Slope of the production
function is the marginal
product of labour (the
change in output that
results from a change in
one unit of input)
• MPL is diminishing and
the slope of the
production function gets
flatter as a greater
number of inputs are
used
Question 5(c)
What happens to the marginal product of labour as
more workers are added to the production facility?
Why?
It diminishes because additional workers have to share the
production equipment and the work area becomes more
crowded.
Use this information about the marginal product of
labour to explain the slope of the production function
you plotted above.
The slope of the production function is the change in output
from a change of one unit of input, which is the marginal
product of labour. Since it is diminishing, the slope of the
production function gets flatter as a greater number of
inputs are used.
Question 5(d) & 5(e)
d) Plot the total-cost curve.
e) Explain the shape of the
total cost curve.
• The Total Cost
curve begins at
€25, due to Fixed
Costs
• As output
increases, the
curve gets
steeper due to
diminishing
marginal product
of labour
Some useful equations for Q6
Total Cost
TC = FC + VC
Average Fixed Cost
AFC = FC / Q
Average Variable Cost
FC (fixed cost)
VC (variable cost)
TC (total cost)
AFC (average fixed cost)
AVC (average variable cost)
ATC (average total cost)
MC (marginal cost)
AVC = VC / Q
Average Total Cost
ATC = TC / Q or ATC = AFC + AVC
Marginal Cost
MC = (TC2 – TC1)/(Q2-Q1)
Question 6
The information below is for Bastien’s blue jeans manufacturing plant. All data is per hour.
Note the following abbreviations: FC (fixed cost), VC (variable cost), TC (total cost), AFC
(average fixed cost), AVC (average variable cost), ATC (average total cost), MC (marginal cost).
Question 6
Question 6(a)
Plot AFC, AVC, ATC, and MC.
Question 6(b)
Explain the shape of each of the curves in part (a)
• AFC ↓ as Q↑
• MC ↓ for the first four units,
due to increasing marginal
product of the variable input.
• MC ↑ after the first four units, due to decreasing
marginal product (MC is U-shaped)
• AVC is U-shaped for the same reasons as MC
• ATC ↑ at higher levels of production due to decreasing
marginal product
• At lower levels of production, ATC ↓ because AFC ↓ and
because of increasing marginal product
Question 6(c)
Explain the relationship between ATC and MC.
• When MC < ATC, ∆ATC < 0
– When the cost of one more unit is below the
average cost, it drags the average down
• When MC > ATC, ∆ATC > 0
– When the cost of one more unit is above the
average cost, it pulls the average up
• As a result, MC = ATC at the minimum of ATC
Question 6(d) & 6(e)
Explain the relationship
between ATC, AFC, and AVC.
ATC = AFC + AVC
(also, ATC = TC / Q)
Question 6(e)
What is Bastien’s efficient scale? How do you find the efficient scale?
Efficient scale is the quantity (output) that minimizes ATC. It is where
MC = ATC.
Why is the efficient scale important?
For a firm that is a price-taker, ATR
(Average Total Revenue) is fixed as Q
varies, or we can say, ATR = P.
If Average Profit = ATR – ATC and ATR is
fixed at P, then in order for a firm to
maximize profit, the must minimize ATC.
So the efficient scale is the amount of
output that a price-taking firm will
produce.
Question 7(a)
Suppose utility depends on income (M) and the
consumption of food (F) such that U=M+F and
suppose that the price of a unit of money is £1 and
the price of a unit of food is also £1.
Imagine that income is £10. How much food is
bought? What is the utility level of the household?
HINT: Substitute the budget constraint M=10-F
into the utility function then find the slope of this
function (using the simple rule) and then solve for
the value of F that makes the slope of U zero.
Question 7(a)
There are two ways we can approach this problem.
We have a utility function: U=M+F
Where M is money and F is food and the price of a
unit of money and the price of a unit of food are both
£1. Income is £10.
We need to find how much food is bought and what is
the utility level of the household.
HINT: Substitute the budget constraint M=10-F into
the utility function then find the slope of this function
(using the simple rule) and then solve for the value of
F that makes the slope of U zero.
This is a standard constrained optimization problem. To
solve it, we will take our budget constraint, M=10-F, and
plug it in to the utility function, U=M+F, then take the
derivative of that and set it equal to zero and solve
for F.
Step 1: plug in M=10-F into U=M+F
U=10-F+F
𝑑𝑈
𝑑𝐹
1
= −1 +
2 𝐹
Step 2: Set this equal to zero and solve for F.
0 = −1 +
1=
1
2 𝐹
1
F =
2
1
F=
4
1
2 𝐹
We solved for F, how much food is bought, now
1
we need to find the level of utility when F = .
4
Note, Utility is a function of both M and F
(U=M+F), so we need to find M before we are
able to solve for U.
1
4
To solve for M, we plug F= into the budget
constraint:
M=10-F
M = 10 M = 9.75
1
4
1
4
Now, we have F= and M = 9.75
So, we can plug these in to the Utility function:
U = M+F
1
4
U = 9.75 +
U = 9.75 +
U = 10.25
1
2
Question 7(b)
Suppose the government is concerned with the poor
nutrition of households with such low levels of
income. It decides to give a voucher for 1 unit of food
to such households. What happens to the amount of
food that such a household will consume? And utility?
In this scenario, the consumption of F rises to F + 1
(the amount of money spent on F) + (1 unit of F from
the voucher)
That changes our utility function from U = M+F to
U=M+ 𝐹+1
The budget constraint remains unchanged, because
there is no change to our initial endowment or income
of £10. So, the budget constraint is M=10-F.
This is the same type of problem as in part (a), so we’ll use the same
methods. We will take our budget constraint, M=10-F, plug it in to the new
utility function, U = M + 𝐹 + 1. then take the derivative of that and set it
equal to zero and solve for F.
Step 1: plug in M=10-F into U = M + 𝐹 + 1
U=10-F+ 𝐹 + 1
𝑑𝑈
𝑑𝐹
1
= −1 +
2 𝐹+1
Step 2: Set this equal to zero and solve for F.
0 = −1 +
1=
𝐹+1=
1
2
1
2 𝐹+1
F+1=
3
1
2 𝐹+1
1
4
F=4
This indicates to us, that given this consumer’s utility function and budget
constraint, they would prefer to sell the £1 Food voucher and continue
consuming at F=1/4. In this problem, we are supposed to assume that the
vouchers cannot be sold, which limits us to a corner solution where the
consumer spends all of their income on M (M= 10) and none of their income
on Food (F = 0) and that they then only consume 1 unit of food, which they
get from the £1 food voucher.
Now, if we have F= 0 and M = 10
We can plug these in to the Utility function:
U=M+ 𝐹+1
U = 10 + 0 + 1
U = 10 + 1
U = 11
Question 7(c)
Suppose the government gives £1 instead of a £1
food voucher.
In this scenario, The amount of F does not change,
but rather M is increased by £1. So, M=£11.
Our budget constraint now becomes 11 = M + F
The utility function is still U = M+F.
We use the same methods as in parts (a) and (b),
1
and should find that F = , M = 10.75 and U = 11.25
4
Question 7(d)
Draw a picture of what the above shows. What
important principle does this show?
a) When we have an income of £10, U = 9.75.
b) When we receive a £1 non-transferrable food
voucher in addition to our £10 income, U = 11.
c) When we receive £1 in cash in addition to our
£10 income, U = 11.75.
So, this suggests that based on this particular
utility function, we get a higher utility from cash
than from a food voucher (in-kind transfer).
Question 8
Scherer (Journal of Economic Literature 2001) tells the
story of a famous German music publisher – Hartel –
who calculated the cost of printing music (using
engraved plates – it was 1796) and used his analysis to
determine his production decisions. Hartel figures that
fixed costs of a page, F, was 900 pfennigs. And the
marginal cost of printing subsequent copies of the
same page was 5 p.
In those days music publishers bought compositions,
did their own printing, and sold to the public. People
bought the latest music to play themselves - there
were no ipods (or even “gramophones”). The
publishers had to decide on what price to charge the
public.
Some useful equations for Q6 Q8
Total Cost
TC = FC + VC
Average Fixed Cost
AFC = FC / Q
Average Variable Cost
FC (fixed cost)
VC (variable cost)
TC (total cost)
AFC (average fixed cost)
AVC (average variable cost)
ATC (average total cost)
MC (marginal cost)
AVC = VC / Q
Average Total Cost
ATC = TC / Q or ATC = AFC + AVC
Marginal Cost
MC = (TC2 – TC1)/(Q2-Q1)
Question 8
Hartel figures that fixed costs of a page, F, was 900 pfennigs. And
the marginal cost of printing subsequent copies of the same page
was 5 p.
From this statement, we know that:
FC = 900 and MC = 5
In this case, because MC is constant, AVC = MC = 5.
Part (a) says to graph TC, ATC, AVC, and MC; we can find equations
for each of these, which can then be graphed by plotting points.
Because AVC = VC/Q, then VC = AVC(Q), so VC = 5Q
We know that TC = FC + VC, so we can find our total cost:
TC = 900 + 5Q
Average total cost (ATC) is TC/Q:
ATC = 900/Q + 5
AVC is MC
Question 8(b)
Would it make sense for a composer to award a
printing contract to just one firm, or to use more
than one? Why?
Answer: Since MC and AVC is constant, ATC falls
with Q indefinitely, just like AFC. So it makes sense
to use just one publisher no matter how many (or
few) copies you think you might sell rather than
having two publishers paying the fixed costs.
Question 8(c)
Hartel thought he could sell 300 copies of a good piece of music
for about 15p per page. What is the most he would have been
prepared to pay a good composer – per page?
Answer: This changes our cost function. Our new cost function
equals our old cost function plus the cost paid to the composer.
Let the cost paid per page be w, so:
TC = 5Q + 900 + wQ
In a competitive market:
Profit = 0
So,
TR - TC = 0
TR = 15Q so,
15Q – (5Q + 900 + wQ) = 0
If Q = 300,
15(300) – (5(300) + 900 + w(300)) = 0
So,
4500 – (1500 + 900 + 300w) = 0
Or,
4500 – 2400 – 300w = 0
Hence,
2100 = 300w
And,
w=7
Past Exam Essay Question (2011)
Show how short and long run cost curves (total, average
and marginal) can be derived from a firm’s production
function (where output depends on just two inputs). What
properties would we expect those cost functions to have?
If this firm operated in a competitive industry how would
its output respond to an increase in demand?
Next Week
• Exam 1 is next Friday.
– 20 Questions from Caroline
– 10 Questions from Ian
– You will have 50 minutes, starting at either 4 or 5 pm.
• We will do more practice Multiple Choice
Questions during tutorial
• Tutorial 6 Worksheet on Moodle
Practice Multiple Choice Questions
Please note: Tutors are not given “solutions” to
past exams. The answers in my slides are
suggestions only.
Note: to view suggested answers, you will need to
either click on the animations tab or view in
slideshow mode.
Practice Multiple Choice Questions
All of the following shift the supply curve of a
good to the right except
a) an advance in the technology used to
manufacture the good.
b) an increase in the price of the good
c) a decrease in the wage of workers employed
to manufacture the good.
d) subsidizing workers employed to manufacture
the good
Practice Multiple Choice Questions, ctd.
If the quantity of available housing in the UK is
less than the quantity of houses demanded,
then UK house prices:
(a) Will not change.
(b) Will fall, thus clearing the market.
(c) Will rise, thus clearing the market.
(d) Will either fall or remain unchanged.
Practice Multiple Choice Questions, ctd.
With an inferior good, a price change:
(a) Leads to opposing income and substitution
effects
(b) Creates a large income effect
(c) Produces a large substitution effect
(d) Leads to conspicuous consumption
Practice Multiple Choice Questions, ctd.
Which one of the following statements regarding
indifference curves is correct?
• (a) Indifference curves are normally drawn as concave
to the origin.
• (b) The further to the left an indifference curve lies,
the more total utility it yields to the consumer.
• (c) Indifference curves normally slope downwards
from right to left.
• (d) None of the above
Practice Multiple Choice Questions, ctd.
When goods X and Y are being consumed, a
consumer is in equilibrium when:
• (a) The marginal rate of substitution equals the
slope of the isocost curve
• (b) MUx/MUy = Py/Px
• (c) The indifference curve touches the budget
line
• (d) All of the above
Practice Multiple Choice Questions, ctd.
• 10. According to the law of diminishing marginal
utility, the additional satisfaction that you get
from consuming beer decreases:
• (a) As the price of beer falls
• (b) As you get older
• (c) As your income rises and you can substitute
beer with whiskey
• (d) With every additional unit of beer that you
consume
Practice Multiple Choice Questions, ctd.
Which one of the following would shift the
demand curve of a normal good to the right?
a) An increase in the price of that good.
b) A decrease in the price of that good
c) A fall in income
d) A decrease in the price of a complement to
the good
Practice Multiple Choice Questions, ctd.
If an increase in consumer incomes leads to a
decrease in the demand for a good, then it must
be the case that the good is:
a) a normal good
b) an inferior good
c) a complementary good
d) a substitute good
Practice Multiple Choice Questions, ctd.
• 6. If the price of a good is above the
equilibrium price,
• a) there is a surplus and the price will rise.
• b) there is a shortage and the price will fall.
• c) there is a shortage and the price will rise.
• d) there is a surplus and the price will fall
Practice Multiple Choice Questions, ctd.
• 7. An increase (rightward shift) in the demand for
a good (whose supply curve is upward sloping)
will tend to cause
• a) an increase in the equilibrium price and
quantity.
• b) an increase in the equilibrium price and a
decrease in the equilibrium quantity.
• c) a decrease in the equilibrium price and an
increase in the equilibrium quantity.
• d) a decrease in the equilibrium price and
quantity.
Practice Multiple Choice Questions, ctd.
The price of a good increases by 10% and the
quantity demanded falls by 20%. This indicates
that demand is
a) elastic
b) inelastic
c) unit elasticity Δ
d) perfectly elastic
Practice Multiple Choice Questions, ctd.
16. The shut down condition for a perfectly
competitive firm in the long run is:
a) Average total costs are greater than
marginal costs
b) Average variable costs are greater than
marginal costs
c) Average total costs are less than
marginal costs
d) Average variable costs are less than
marginal costs
Practice Multiple Choice Questions, ctd.
• 1. When goods X and Y are being consumed, a
consumer is in equilibrium when:
• (a) The marginal rate of substitution equals the
slope of the isocost curve
• (b) MUx/MUy = Py/Px
• (c) The indifference curve touches the budget
line
• (d) All of the above
Practice Multiple Choice Questions, ctd.
When two goods are complements of each other:
(a) The cross price elasticity of demand is negative
(b) The cross price elasticity of demand equals zero
(c) The cross price elasticity of demand is positive
(d) The cross price elasticity of demand may be
either positive or negative
Practice Multiple Choice Questions, ctd.
All the following will cause the demand curve to
shift to the left except:
(a) A reduction in income if the good is normal
(b) An increase in the price of a complementary
good
(c) An increase in the price of a substitute good
(d) An increase in income if the good is inferior
Practice Multiple Choice Questions, ctd.
If the price elasticity of demand for bubblegum is
2.0 and bubblegum prices increase by 15 percent.
The quantity demanded changes by:
(a)
(b)
(c)
(d)
15 percent
20 percent
3 percent
None of the above
30 percent
Practice Multiple Choice Questions, ctd.
• 9. Considering any linear downward sloping
demand curve, lower prices along the demand
curve are associated with:
• (a) Lower absolute price elasticities
• (b) Lower quantities demanded
• (c) Different points of unit elasticity
• (d) Higher absolute price elasticities