ECON 100 Tutorial: Week 6

1
ECON 100 Tutorial Week 6

• www.lancaster.ac.uk/postgrad/murphys4/
• s.murphy5_at_lancaster.ac.uk
• office LUMS C85

2
Past exam questions
3
If an indifference curve is smooth and convex to
the origin, then

1. The two goods are said to be convex combinations
   of each other
2. There is a diminishing marginal rate of
   substitution
3. The indifference curve is said to be normal
4. None of the above

Q5
4
From Tutorial 4 worksheet Question 1

• Assuming an indifference curve which is convex to
  the origin, what can this tell us about a
  consumers marginal rate of substitution between
  coffee and muffins?

5
A profit maximizing firm would like to produce at
least the number of units which minimises short
run

• Average total cost
• Average fixed cost
• Average variable cost
• Marginal cost
• Note A profit-maximizing firm produces at the
  efficient scale the quantity of output that
  minimizes ATC. We can find this quantity where MC
  ATC.

Q18
6
Long Run Exit Condition

• In the long run, firms will continue if there is
  a profit, so the exit condition is
• Profit lt 0
• TR TC lt 0
• TR lt TC
• AR lt ATC
• P lt ATC

7
Short Run Exit Condition

• In the short run, fixed costs are sunk costs and
  firms will run if there is greater profit from
  continuing than from exiting. The firm pays the
  fixed cost whether it continues or exits the
  market, so the exit condition is
• TR (VCFC) lt -FC
• TR-VC-FC lt -FC
• TR VC lt 0
• TR lt VC
• AR lt AVC
• P lt AVC

8

• So a firms short run exit condition is P lt AVC
• Since a firms supply curve is equal to its
  Marginal Cost Curve, and since MC AVC at the
  minimum of AVC, if Q is less than the quantity
  that minimizes AVC, P will be less than AVC for
  that Q.

P, C
MCS
AVC
q
0
9
Suppose demand curve written D120-2P, and the
supply curve is S202P. What is the equilibrium
price and quantity?

• P70 and Q25
• P25 and Q70
• P50 and Q35
• P35 and Q50
• Note Set the two equations equal to each other
  and solve for P. Plug that value back in to
  either equation to solve for Q.

Q22
10

• Suppose a product has a demand curve written D
  120 2P, and the supply curve is S 20 2P.
  What is the equilibrium price and quantity.
• Equilibrium occurs where D S, i.e.
• 120 2P 20 2P
• 100 4P
• P 25
• Then, substitute P 25 into either the D or S
  equation
• D 120 2 25 70
• or
• S 20 225 70
• P 70 and Q 25
• P 25 and Q 70
• P 50 and Q 35
• Q 35 and P 50

11
Suppose demand is given by D120-2P and supply is
originally S202P but the government imposes a
tax of 10 on this good. What happens to the
equilibrium price?

1. Rises by 10
2. Rises by 8
3. Rises by 5
4. Rises, but its not possible to say by how much

Q23
12

• We have D120-2P and S202P
• Then a tax of 10 is imposed on this good.
• What happens to the equilibrium price?
• There are two ways we can solve this.
• By assuming that the tax is placed on consumers,
  thus affecting the Demand curve (shifting it to
  the left)
• By assuming that the tax is placed on
  suppliers/sellers, thus affecting the Supply
  curve (shifting it to the left).
• Ill work through both methods in the following
  slides.

13

• We have D120-2P and S202P
• Then a tax of 10 is imposed on this good.
• By assuming that the tax is placed on consumers,
  thus affecting the Demand curve (shifting it to
  the left)
• The new demand curve can be written as
• D 120 2(PT), where T 10.
• D 120 2P -20
• D 100 2P
• We then need to find where this new
• demand curve crosses the supply curve.
• D S
• 100 2P 20 2P
• 80 4P
• P 20
• This gives us the new market equilibrium price.
  It is the price that the consumers will give to
  the suppliers for each good purchased.
• On top of this, the consumers must pay the tax of
  10, so the total cost to the consumers will be P
  T 30.
• So the actual price consumers pay will rise by 5
  because of this tax.

14

• We have D120-2P and S202P
• Then a tax of 10 is imposed on this good.
• By assuming that the tax is placed on suppliers,
  thus affecting the Supply curve (shifting it to
  the left)
• The new Supply curve can be written as
• S 20 2(P-T), where T 10.
• S 200 2P -20
• S 2P
• We then need to find where this new supply
• curve intersects with our original demand curve.
• D S
• 120 2P 2P
• 120 4P
• P 30
• This gives us the new market equilibrium price.
  It is the price that the consumers will give to
  the suppliers for each good purchased. From this,
  the sellers have to pay the government a tax of
  10, so the total cost to the consumers will be P
  30 and the total amount that sellers receive
  will be 20. So the actual price consumers pay
  will rise by 5 because of this tax.

15
Suppose D10/P, work out the price elasticity at
P10 and P 20 and P30.

1. Not possible to say without knowing what the
   corresponding level of demand is.
2. -1, -2, -3
3. -3, -2, -1
4. -1, -1, -1

Q25
16
Suppose D10/P, work out the price elasticity at
P10 and P 20 and P30.

•  

Q25
17

•  

(remember, in equilibrium D S Q, so when P
10, Q 1))
Q25
18
Suppose supply is perfectly elastic at a price of
10 and the government imposes a tax of 2 on a
good whose demand curve is given by D100-5P.
Compute the amount of tax revenue raised, the
deadweight loss of the tax, and the change in
consumer surplus.

1. 10, 80, 90
2. 80, 10, 90
3. 10, 90, 100
4. 10, 75, 85

Q26
19
Suppose supply is perfectly elastic at a price of
10 (i.e. the S curve is horizontal) and the
government imposes a tax of 2 (so the S curve
shifts upward by 5) on a good whose demand curve
is given by D 100 5P. Compute the amount of
tax revenue raised, the deadweight loss of the
tax, and the change in consumer surplus.
P 20 1/5 D To find horizontal intercept 0
20 1/5 D 1/5 D 20 D 100 If P 10, 10
20 1/5 D D 50 If P 12, 12 60 ½ D D
40
P
20 12 10
D
S
S
0
D
40 50 100
20
Continued Compute the amount of tax revenue
raised, the deadweight loss of the tax, and the
change in consumer surplus.

• Tax Revenue
• 2 40 80
• DWL
• ½ 10 2 10
• CS ½ 50 10 250
• CS ½ 40 8 160
• CS CS 90
• 10, 80, 90
• 80, 10, 90
• 10, 90, 100
• 10, 75, 85

P
20 12 10
D
S
Tax
S
0
D
40 50 100
21
Suppose the TC curve for a firm where TC124QQ2
and MR8. What level of output will the firm
produce in order to maximise profit (ie where
MCMR)?

1. 0
2. 2
3. 4
4. 8

Q30
22

• Suppose the TC curve for a firm where TC 12
  4Q Q2 and
• MR 8. What level of output will the firm
  produce in order to maximise profit (i.e. where
  MC MR)?
• Remember the rule
• slope of Y b.Xc is c.b.Xc-1
• 0
• 2
• 4
• 8

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Exam this Friday

• 50 minutes
• 30 questions 20 Caroline, 10 Ian
• Check your timetable for exam time and location.
• Dont forget to bring the following items
• Library Card Number
• Pencil and Eraser
• Basic calculator (no programmable calculators or
  cell phones will be allowed.)
• Good Luck!
• (For next week, check Moodle for a worksheet)

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This Thursday Martin Ravallion  Edmond D.
Villani Chair in Economics, Georgetown
University Research Associate NBER
Non-Resident Fellow CGD Formerly Director of
the World Banks Research Department will
deliver the Esmée Fairbairn Lecture EntitledThe
Idea of Anti-Poverty Policy Lecture Theatre 1,
Leadership Centre, Management School,6.00pm
Thursday 14th November 2013
                                                  
                                           
                               
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Question 1

• If the industry under perfect competition faces a
  downward-sloping demand curve, why does an
  individual firm face a horizontal demand curve?
• In a perfectly competitive market, each firm is
  quite small and unable to affect price on its
  own. We say that firms are price takers.
• This means that in a perfectly competitive
  market, P MR MC.

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Question 2

• If supernormal profits are competed away under
  perfect competition, why will firms have an
  incentive to become more efficient?
• Improving efficiency can lower costs and lead to
  positive short run profits, based on the time it
  takes for competing firms to adopt the more
  efficient methods.
• In the long run, profits will go back to zero,
  however.

27
Question 3

• Why is the marginal cost curve of a competitive
  firm its supply curve?

28
Question 4(a)

• The following table contains information about
  the revenues and costs for Ernsts Golf Ball
  Manufacturing. All data are per hour. Complete
  the first group of columns which correspond to
  Ernsts production if P 3.

Quantity TR (P3) TC Profit (P3) MR (P3) MC
0   1      
1   2      
2   4      
3   7      
4   11      
5   16      
Total Revenue Price X Quantity TR
(P)(Q) Profit Total Revenue Total Cost
Profit TR TC Marginal Revenue
Change in Revenue/Change in Quantity MR
(TR2-TR1)/(Q2-Q1) Marginal Cost Change in
Cost/Change in Quantity MC
(TC2-TC1)/(Q2-Q1)
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Question 4(a)

• The following table contains information about
  the revenues and costs for Ernsts Golf Ball
  Manufacturing. All data are per hour. Complete
  the first group of columns which correspond to
  Ernsts production if P 3. (TR total
  revenue, TC total cost, MR marginal revenue,
  MC marginal cost)

Quantity TR (P3) TC Profit (P3) MR (P3) MC
0 0 1 -1 3 1
1 3 2 1 3 2
2 6 4 2 3 3
3 9 7 2 3 4
4 12 11 1 3 5
5 15 16 -1    
30
Question 4(b)

• If the price is 3 per golf ball, what is Ernsts
  optimal level of production? What criteria did
  you use to determine the optimal level of
  production?

To find the optimal level of production, we find
where MR MC. Optimal production is either two
or three golf balls per hour. This level of
production maximizes profit (at 2) and it is the
level of output where MC MR (at 3).
Quantity TR (P3) TC Profit (P3) MR (P3) MC
0 0 1 -1 3 1
1 3 2 1 3 2
2 6 4 2 3 3
3 9 7 2 3 4
4 12 11 1 3 5
5 15 16 -1    
31
Question 4(c)

• Is 3 per golf ball a long-run equilibrium price
  in the market for golf balls? Explain. What
  adjustment will take place in the market for golf
  balls and what will happen to the price in the
  long run?
• Answer No, because Ernst is earning positive
  economic profits of 2. These profits will
  attract new firms to enter the market for golf
  balls, the market supply will increase, and the
  price will fall until economic profits are zero.

Quantity TR (P3) TC Profit (P3) MR (P3) MC
0 0 1 -1 3 1
1 3 2 1 3 2
2 6 4 2 3 3
3 9 7 2 3 4
4 12 11 1 3 5
5 15 16 -1    
32
Question 4(d)

• Suppose the price of golf balls falls to 2. Fill
  out the remaining three columns of the table
  above.

Quantity TR (P3) TC Profit (P3) MR (P3) MC TR (P2) Profit (P2) MR (P2)
0 0 1 -1 3 1 0 -1 2
1 3 2 1 3 2 2 0 2
2 6 4 2 3 3 4 0 2
3 9 7 2 3 4 6 -1 2
4 12 11 1 3 5 8 -3 2
5 15 16 -1     10 -6  
33
Question 4(d)

• What is the profit-maximizing level of output
  when the price is 2 per golf ball? How much
  profit does Ernsts Golf Ball Manufacturing earn
  when the price of golf balls is 2?
• Answer Optimal production is either one or two
  golf balls per hour. Zero economic profit is
  earned by Ernst.

Quantity TR (P3) TC Profit (P3) MR (P3) MC TR (P2) Profit (P2) MR (P2)
0 0 1 -1 3 1 0 -1 2
1 3 2 1 3 2 2 0 2
2 6 4 2 3 3 4 0 2
3 9 7 2 3 4 6 -1 2
4 12 11 1 3 5 8 -3 2
5 15 16 -1     10 -6  
34
Question 4(e)

• Is 2 per golf ball a long-run equilibrium price
  in the market for golf balls? Explain. Why would
  Ernst continue to produce at this level of
  profit?
• Answer Yes. Economic profits are zero, therefore
  firms will neither enter nor exit the industry.
• Zero economic profits means that Ernst doesnt
  earn anything beyond his opportunity costs of
  production but his revenues do cover the cost of
  his inputs and the value of his time and money.

35
Question 4(f)

• Describe the slope of the short-run supply curve
  for the market for golf balls. Describe the slope
  of the long-run supply curve in the market for
  golf balls.
• The slope of the short-run supply curve is
  positive because when P 2, quantity supplied
  is one or two units per firm and when P 3,
  quantity supplied is two or three units per firm.
  
• In the long run, supply is horizontal (perfectly
  elastic) at P 2 because any price above 2
  causes firms to enter and drives the price back
  to 2.

36
Question 5(a)

• Draw the isoquant corresponding to the following
  table, which shows the alternative combinations
  of labour and capital required to produce 100
  units of output per day of good X.

Capital 16 20 26.67 40 60 80 100
Labour 200 160 120 80 53.33 40 32
37
Question 5(b)
Assuming that capital costs are 20 per day and
the wage rate is 10 per day, what is the
least-cost methods of producing 100 units? What
will the daily total cost be?
Given
Solve for
Capital Labour
16 200
20 160
26.67 120
40 80
60 53.33
80 40
100 32
cost of capital cost of labour total cost
320 2000 2320
400 1600 2000
533.4 1200 1733.4
800 800 1600
1200 533.3 1733.3
1600 400 2000
2000 320 2320
The least-cost method of production uses 40 units
of Capital and 80 units of Labor. This method
costs 1600 per day.
Price of Capital 20/day Price of Labor 10/day
38
Question 5(b)
Use Excel to graph, or graph by hand, the
isoquant curve and the Isocost lines
39
Question 5(c)
Now assume that the wage rate rises to 20 per
day. Draw a new series of isocosts. What will be
the least-cost method of producing 100 units now?
How much labour and capital will be used?
Given
Solve for
Capital Labour
16 200
20 160
26.67 120
40 80
60 53.33
80 40
100 32
cost of capital cost of labour total cost
320 4000 4320
400 3200 3600
533.4 2400 2933.4
800 1600 2400
1200 1066.6 2266.6
1600 800 2400
2000 640 2640
The least-cost method of production uses 60 units
of Capital and 53.33 units of Labor. This method
costs approximately 2,267 per day.
Price of Capital 20/day Price of Labor 20/day
40
Question 6

• In a downturn firms want to layoff some workers.
  This has an effect on productivity (output per
  employee). On the one hand, it frees up some
  machinery that the remaining workers can use more
  flexibly you dont have to hang around so much
  waiting for a machine to become free. On the
  other hand, workers have to do a wider ranges of
  tasks because there are fewer workers so the
  firm loses some of the advantages of
  specialisation.
• Suppose the output of the firm, Q, depends on the
  number of workers, L, and the number of machines,
  K, in such a way that QLaKb Suppose a0.4 and
  b0.6.

41
Question 6(a)

• Suppose the output of the firm, Q, depends on the
  number of workers, L, and the number of machines,
  K, in such a way that QLaKb Suppose a0.4 and
  b0.6.
• Write down an expression for the average product
  of labour, APL. HINT APLQ/L.
• Well start with APLQ/L
• And plug in QLaKb for Q
• APL LaKb /L
• This can be simplified to APL La-1Kb
• Now we can plug in a0.4 and b0.6 APL
  L-0.6K0.6
• APL (K/L)0.6

42
Question 6(b)

• Now Suppose L10 and K10. What is the firms
  output? And its APL?
• To find the firms output, we plug in L10 and
  K10 into our Output function from part (a)
• Q LaKb
• From part (a), we know that a0.4 and b0.6, so
• Q L0.4K0.6
• Plugging in L10 and K10 Q 100.4100.6
• Q 101
• Q 10
• So the firms output is 10 units.
• We solved for APL in part (a)
• APL (K/L)0.6
• So, we can plug in L10 and K10
• APL (10/10)0.6
• APL 1.
• So the firms average product of labor is 1.

43
Question 6(c)

• If the number of workers is reduced by 1 (i.e
  10) what happens to output? And the APL?
• So, now L 9 and K 10. We will go through the
  same steps in part (b).
• From part (a), we know that Q LaKb and that
  a0.4 and b0.6, so
• Q L0.4K0.6
• Plugging in L9 and K10 Q 90.4100.6
• Q 9.6
• So the firms output has fallen from 10 to 9.6,
  or it has fallen by 4.
• We solved for APL in part (a)
• APL (K/L)0.6
• So, we can plug in L9 and K10
• APL (10/9)0.6
• APL 1.065
• So the firms average product of labor has gone
  from 1 to 1.065, or it has risen by 6.5.

44
Question 7

• Cost functions depend on the nature of the firms
  technology (i.e. its production function) and
  input prices.
• Suppose beer is produced according to the
  production function
• Q1.5 L0.4 K0.6
• Assume that K is fixed at 100 units in the short
  run. The price of a unit of K is 8. So fixed
  cost is 800.

45
Question 7(a)

•  

46
Question 7(b)

•  

47
Question 7(c)

• Suppose beer is produced according to the
  production function
• Q1.5 L0.4 K0.6
• Assume that K is fixed at 100 units in the short
  run. The price of a unit of K is 8. So fixed
  cost is 800.
• The only variable factor is L in the short run.
  Derive AVC
• We know that AVCVC/Q
• We solved for VC in part (b) and can plug that in
  here
• AVC 0.0089 Q2.5/Q
• AVC 0.0089 Q1.5

48
Question 7(d)

• Suppose beer is produced according to the
  production function Q1.5 L0.4 K0.6
• Assume that K is fixed at 100 units in the short
  run. The price of a unit of K is 8. So fixed
  cost is 800.
•  Derive MC. HINT You will need to find the slope
  of the VC function.
• Marginal cost is the slope of variable cost
  curve, or the derivative of VC
• From (b) we know VC 0.0089 Q2.5
• MC slope of VC dVC/dQ
• dVC/dQ 2.50.0089 Q(2.5-1)
• 0.022 Q1.5

49
Question 7(e)

• Suppose beer is produced according to the
  production function
• Q1.5 L0.4 K0.6
• Assume that K is fixed at 100 units in the short
  run. The price of a unit of K is 8. So fixed
  cost is 800.
• Use Excel to graph MC, AFC, AVC and AC against Q
  (from a range of Q from 0 to, say 300)