ECON 100 Tutorial: Week 23

www.lancaster.ac.uk/postgrad/alia10/a.ali11@lancaster.ac.uk

office hours: 2:00PM to 3:00PM tuesdays LUMS C85

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 Peel’s Lecture notes

(on Moodle), practice Math questions

Maths Worksheet

There is an error in the worksheet I printed out for class:– MPC should be: – And APC should be:

Please correct this before solving for MPC and APC.

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.

Background Info for Question 1

Some terms to know for Question 1:Cash on hand at banks = CBCash on hand held by the public = CPBank deposits = BD

Bank Reserve Ratio = =

There are 2 concepts for money used in this question:Narrow Money = Cash on hand at banks + Cash on hand by public C = CB + CPBroad money = Bank deposits + Cash on hand by public M = BD + CP

Question 1If the commercial banking sector holds 18% reserve assets (cash ≡ narrow money); if the general public holds cash to bank deposits in the ratio 1:8; 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:1. Cash on hand at Banks/Bank Deposits = CB/BD = 0.18

2. Cash on hand by Public/Bank Deposits = CP/BD = 1/8 = 0.125

3. Narrow Money (C = CB + CP) = 100

We are asked to find M. We know M = CP + BD.

Question 1We are given: We know:

1. CB/BD = 0.18 Narrow Money = C = CB + CP

2. CP/BD = 0.125 Broad Money = M = CP + BD

3. 100 = CB + CPWe have to find M, where M = CP + BD

Step 1. Solve for CB and CP by rewriting 1 and 2 :CB = 0.18*BDCP = 0.125*BD

Step 2. To solve for BD, plug CP and CB into the Narrow Money equation:100 = CB + CP100 = (0.18) BD + (0.125) BD 100 = (0.305) BDBD = 100/0.305 = 327.87

Step 4. We now have both CP and BD, so we can solve for M.M = 0.125*BD + BDM = 0.125*327.87 + 327.87M = 368.85

General Form SolutionWe just solved for M, given C and BD. Another way to solve for M give C, is to use the money multiplier:

M = mC, where m is the money multiplier.

From Question 1, we know that: the currency-deposit ratio (CDR) = CP/BDand the reserve ratio (RR) = CB/BD

So, we could re-write the money multiplier as:

In question 1, we could calculate the money multiplier because we have CP, CB, and BD. So then, we can multiply the money multiplier with C to find M.

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 + CPBroad 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

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 barleyspot prices £150 £100 per tonne

one-year forward prices £165 £95 per tonne

Question 3(a)

Given the respective spot and forward prices below,

calculate the annual ‘yield’ to producers of wheat and barley:

Let’s 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 barleyspot prices £150 £100 per tonne

one-year forward prices £165 £95 per tonne

Question 3(b)

Given the respective spot and forward prices below,

calculate the annual inter-temporal price ratios for wheat and barley respectivelyInter-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 barleyspot prices £150 £100 per tonne

one-year forward prices £165 £95 per tonne

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 barleyspot 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

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 = C+I+G• Investment can be a function of interest rates• There can be a multiplier effect on total income

from increasing investment

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

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]/ rV: capitalized value (discounted present value) of an annuity (or bond)c: yearly annuity payment (the Coupon Rate X the Redemption Value)r: discount raten: 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

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 0.03n: number of years to maturity: 40 yearsb: 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

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 0.05n: number of years to maturity: 40 yearsb: 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.

Question 5(c)

If the coupon value were doubled, would the bond price double?

Let’s try it; using the values in Question 2(b), let’s double the coupon rate.c: annuity payment: €1000 x 10% = €100 r: discount rate: 5% or 0.05n: number of years to maturity: 40 yearsb: 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.

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.

Next WeekAll tutorials are back to regular schedule:

T01/01 Monday 3PM – Carter A02 T01/48 Monday 5PM – Carter A04 T01/05 Monday 6PM – Fylde C48 T01/11 Tuesday 1 PM – Carter A02

There should be a tutorial worksheet on Moodle. I’ll also try to review some past exam multiple choice questions, time permitting.