ECON 100 Tutorial: Week 23

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ECON 100 Tutorial Week 23

• www.lancaster.ac.uk/postgrad/alia10/
• s.murphy5_at_lancaster.ac.uk
• office hours 300PM to 400PM Monday LUMS C85

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Exam 4 Next Week

• 40 Multiple Choice Questions
• 28 from Gerry Steele
• Mostly theory and definitions, some problems
• Best ways to study Review Lecture notes,
  tutorial questions, and past exam questions
• 12 from David Peel
• Math or mathematical applications of IS-LM and
  Consumption functions
• Best ways to study Review David Peels Lecture
  notes (on Moodle), practice Math questions

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Background Info for Question 1

• What is a reserve requirement?
• When you deposit money at the bank, the bank only
  keeps a portion of that money in its vaults, the
  rest it can loan out to other customers. The
  portion it keeps is called the reserve.
• The proportion of money a bank keeps as a reserve
  is often dictated by law.
• Lowering reserve requirements can increase money
  supply but can increase the probability that
  the bank will default.

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Background Info for Question 1

•  

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Question 1

• If the commercial banking sector holds 18
  reserve assets (cash narrow money) if the
  general public holds cash to bank deposits in the
  ratio 18 and if the volume of narrow money
  (cash) is 100 units, what is the volume of broad
  money (that is, cash and bank deposits held by
  the general public) in circulation?
• In this problem, we are given the following
  information
• Cash on hand at Banks/Bank Deposits CB/BD
  0.18
• Cash on hand by Public/Bank Deposits CP/BD
  1/8 0.125
• Narrow Money (C CB CP) 100
• We are asked to find M. We know M CP BD.

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Question 1

• We are given We know
• CB/BD 0.18 Narrow Money C CB CP
• CP/BD 0.125 Broad Money M CP BD
• 100 CB CP
• We have to find M, where M CP BD
• Step 1. Solve for CB and CP by rewriting 1 and 2
  
• CB 0.18BD
• CP 0.125BD
• Step 2. To solve for BD, plug CP and CB into the
  Narrow Money equation
• 100 CB CP
• 100 (0.18) BD (0.125) BD
• 100 (0.305) BD
• BD 100/0.305 327.87
• Step 4. We now have both CP and BD, so we can
  solve for M.
• M 0.125BD BD
• M 0.125327.87 327.87
• M 368.85

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General Form Solution

•  

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Question 1

• If the commercial banking sector holds 18
  reserve assets (cash narrow money) if the
  general public holds cash to bank deposits in the
  ratio 18 and if the volume of narrow money
  (cash) is 100 units, what is the volume of broad
  money (that is, cash and bank deposits held by
  the general public) in circulation?
• (a) is CB/BD 0.18 (b) is CP/BD 0.125
•  
• C 100 CB CP (0.18) BD (0.125) BD
  0.305 BD
• BD 100/0.305 327.87
• CP 327.869/8 40.98
• M CP BD 368.85
• NB the money multiplier (1 b)/(a b)100
• (1
  0.125)/(0.18 0.125)100 368.85

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Question 2

• Explain why the whole amount of narrow money is
  not included in the total amount of broad money.
• i.e. Why is C not included in the formula for
  Broad Money?
• Narrow money is money that is on hand, held by
  banks and the public C CB CP
• Broad money is cash held by the public plus money
  in bank deposits M CP BD
• Money deposited in the Bank is partially kept on
  hand at the bank (CB), and partially used for
  other activities such as making loans or
  purchasing assets (Non-Reserve Assets).
•  
• If broad money were defined as cash plus bank
  deposits, C BD, then there would be a
  double-counting of CB
•  
• C BD CB CP BD
• CB CP CB Non-Reserve Assets
• 2CB CP Non-Reserve Assets

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Question 3(a)

• Given the respective spot and forward prices
  below,
• calculate the annual yield to producers of
  wheat and barley
• Note In this problem, annual yield refers to the
  percentage change between spot prices and
  one-year forward prices.
• change (final initial)/initial
• (1-year forward price spot price)/spot
  price
• (165 150) / 150 15/150 0.1 10
• So the annual yield for wheat is 10

wheat barley
spot prices 150 100 per tonne
one-year forward prices 165 95 per tonne
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Question 3(a)

• Given the respective spot and forward prices
  below,
• calculate the annual yield to producers of
  wheat and barley
• Lets do the same calculation for barley
• change (1-year forward price spot
  price)/spot price
• (95 100) / 100 -5/100 -0.05 -5
• So the annual yield for barley is -5

wheat barley
spot prices 150 100 per tonne
one-year forward prices 165 95 per tonne
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Question 3(b)

• Given the respective spot and forward prices
  below,
• calculate the annual inter-temporal price ratios
  for wheat and barley respectively
• Inter-temporal price ratio one-year forward
  price/spot price
• For wheat this is
• 165/150 1.10
• For barley this is
• 95/100 0.95

wheat barley
spot prices 150 100 per tonne
one-year forward prices 165 95 per tonne
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Question 3(c)

• Given the respective spot and forward prices
  below,
• How would you advise farmers in planting wheat
  and/or barley
• Advise switching production from barley to wheat.
  
• As farmers switch to wheat, the one-year forward
  price of wheat will go down (since supply will
  increase)
• With resource transfers, there is a tendency for
  yields to equalize
• the Law of One Price

wheat barley
spot prices 150 100 per tonne
one-year forward prices 165 95 per tonne
Annual yields 10 -5
Inter-temporal price ratios 165/150 i.e., 1.10 95/100 i.e., 0.95
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Question 4(a)

• Which effects of an increase in investment
  expenditure are examined by a Keynesian
  macroeconomic model?
•  
• Investment is the I in AE AD CIG
• Investment can be a function of interest rates
• There can be a multiplier effect on total income
  from increasing investment

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Question 4(b)

• Which effects of an increase in investment
  expenditure are examined by a business
  entrepreneur?
• Investment is often how new businesses are
  created and how innovation occurs.
• Profits can only be made when investment allows
  business to function.
• Keynes model may under-emphasize the key role of
  investment in entrepreneurship

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Question 4

• Which effects of an increase in investment
  expenditure are examined by
• a) a Keynesian macroeconomic model
•  
• The impact upon aggregate demand.
• Investment is merely a category of expenditure
  one among many.
•  
• b) a business entrepreneur
•  
• The impact upon the capacity to sell future
  additional goods/services yielding a profit .

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Question 5

• New bonds (with a redemption value of 1000) pay
  a coupon of 5 per cent over 40 years.
• (NB you will need to use the formula
• V c 1 (1 r)-n/ r
• to obtain the capitalised value (V) of an annuity
  (c), where r is the discount rate and n is the
  number of years to maturity but dont forget the
  redemption value!)
•  
• a) Use a discount rate of 0.03 to obtain the
  current value of the bond.
• V 50 1 (1 0.03)-40/0.03
  1000(1.03)-40 1462.30
•  
• b) Use a discount rate of 0.05 to obtain the
  current value of the bond.
• V 50 1 (1 0.05)-40/0.05
  1000(1.05)-40 857.95 142.05 1000
• c) If the coupon value were doubled, would the
  bond price double?
• NO! Because the coupon (50) is absent in the
  capitalisation of the redemption value.
  1000(1r)-n
• d) With interest rates anticipated to rise, how
  does this affect the bond price?
• It would fall.

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Question 5

• To find the capitalized value (V) of an annuity,
  we use the following formula for the discounted
  present value of a stream of annuity payments for
  a fixed number of years
• V c 1 (1 r)-n/ r
• V capitalized value (discounted present value)
  of an annuity (or bond)
• c yearly annuity payment (the Coupon Rate X the
  Redemption Value)
• r discount rate
• n number of years to maturity
• We also need to find the discounted present value
  of the redemption payment of the bond
• V b (1 r)-n
• b bond redemption value (what you get paid when
  the bond matures)
• So, adding these two parts together, our formula
  is
• V c 1 (1 r)-n / r b (1 r)-n

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Question 5(a)

• Find the Capitalized value (V) of an annuity
  using the following formula
• V c 1 (1 r)-n / r b (1 r)-n
• New bonds (with a redemption value of 1000) pay
  a coupon of 5 per cent over 40 years. Use a
  discount rate of 0.03 to obtain the current value
  of the bond.
• c annuity payment 1000 x 5 50
• r discount rate 3 or 0.03
• n number of years to maturity 40 years
• b bond redemption value 1000
• Using these values, we can fill in the formula
  and solve for V
• V 50 1 (1 0.03)-40 / 0.03 1000 (1
  0.03)-40
• V 1462.30

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Question 5(b)

• Find the Capitalized value (V) of an annuity
  using the following formula
• V c 1 (1 r)-n / r b (1 r)-n
• New bonds (with a redemption value of 1000) pay
  a coupon of 5 per cent over 40 years. Use a
  discount rate of 0.05 to obtain the current value
  of the bond.
• c annuity payment 1000 x 5 50
• r discount rate 5 or 0.05
• n number of years to maturity 40 years
• b bond redemption value 1000
• Using these values, we can fill in the formula
• V 50 1 (1 0.05)-40 / 0.05 1000 (1
  0.05)-40 1000
• The interesting thing to note here, is that as
  the discount rate increased, the value of the
  bond actually decreased.

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Question 5(c)

• If the coupon value were doubled, would the bond
  price double?
• Lets try it using the values in Question 2(b),
  lets double the coupon rate.
• c annuity payment 1000 x 10 100
• r discount rate 5 or 0.05
• n number of years to maturity 40 years
• b bond redemption value 1000
• V 100 1 (1 0.05)-40 / 0.05 1000 (1
  0.05)-40
• V 1857.95
• Compared to the answer we had in 2(b), V 1000.
  
• No, it does not double.

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Question 5(d)

• With interest rates anticipated to rise, how does
  this affect the bond price?
• If interest rates rise, reflecting a rise in the
  discount rate, the bond price (the present value
  of the bond) will fall.
• Comparing answers in 2(a) and 2(b), we can see
  that this occurs.

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Next week

• What do you want to cover next week?
• The options are
• Gerrys tutorial worksheet questions
• (on Moodle)
• 2013 Past Exam multiple choice questions
• Week 25 tutorial
• Past Exam essay question review

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Next Week

• All tutorials are back to regular schedule.

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Practice Past Exam QuestionsPlease Note
Solutions are not given to tutors for these
questions. The solutions Ive prepared are only
suggestions only I cant guarantee they are
correct.