MGEB05 Assignment 1 Answer Key – Winter 2024
Question 1 (20 points)
Allocation of goods traded to different components of GDP.
Consumption Investment
Government spending
Good 1 25%
25%
25%
Good 2 30%
70%
Good 3 100%
Good 4
20%
50%
Good 5
20%
60%
Good 6 30%
10%
Exports
25%
Imports
30%
40%
30%
20%
60%
Formula used – 0.5 pt will take off for each mistake and the remaining points are for showing work
•
Nominal GDPt = ∑𝑛𝑖=1 𝑃𝑖,𝑡 𝑄𝑖,𝑡
•
Real GDPt = ∑𝑛𝑖=1 𝑃𝑖,𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟 𝑄𝑖,𝑡
•
GDP deflatort =
•
Cost of Baskett = ∑𝑛𝑖=1 𝑃𝑖,𝑡 𝑄𝑖,𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟
•
CPIt = 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑏𝑎𝑠𝑘𝑒𝑡
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝐺𝐷𝑃𝑡
𝑅𝑒𝑎𝑙 𝐺𝐷𝑃𝑡
𝐶𝑜𝑠𝑡 𝑜𝑓 𝑏𝑎𝑠𝑘𝑒𝑡𝑡
𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟
× 100
× 100
(Nominal) Consumption
(Nominal) Investment
(Nominal) Government spending
(Nominal) Exports
(Nominal) Imports
Nominal GDP
Real GDP
GDP deflator
Cost of consumption basket (in CPI)
CPI
MGEB05 Assignment 1 Answer Key (Winter 2024)
Year 1
11997
4582
8093
7628
4064
28236
28736
98.26
13530
111.44
Year 2
14635
5693
9984
9278
4905
34685
33940
102.98
14121
116.31
Year 3
12141
5529
10185
8325
4086
32094
32094
100
12141
100
1
Question 2 (30 points)
Part (a) (7 points)
• Long-run level of output, Y:
Y = 4K⅓L⅔ = 4(64000)⅓(8000)⅔ = 64000 (1 pt)
• Taxes, T:
T = 0.1125  64000 = 7200 (1 pt)
• Government spending, G:
G = T – GBB = 4800 – 0 = 7200 (1 pt)
• According to the long-run classical model, equilibrium is given by:
64000 – [8700 + 0.75(64000 – 7200) – 200r] – 7200 = 7500 – 300r
5500 + 200r = 7500 – 300r
500r = 2000
r = 4 (i.e., 4%) (1 pt)
• Investment, I: (1 pt)
I = 7500 – 300(4) = 6300
• Real rental price for capital, R/P: (1 pt)
𝑅
4
= MPK = (3) (64000−⅔ )(8000⅔ ) = ⅓
𝑃
•
Real wage for labour, W/P: (1 pt)
𝑊
8
= MPL = ( ) (64000⅓ )(8000−⅓ ) = 5⅓
•
•
If Y is incorrect but the logic is correct, you would get 4 out of 5.
If T or G is incorrect but the logic is correct, you would get 3 out of 5.
𝑃
3
Part (b) (7 points)
• New stock of capital: K = 64000 – 21125 = 42875 (1 pt)
• Long-run level of output, Y:
Y = 4K⅓L⅔ = 4(64000)⅓(8000)⅔ = 56000 (1 pt)
• Taxes, T:
T = 0.1125  56000 = 6300 (1 pt)
• Government spending, G:
G = T – GBB = 4800 – 0 = 6300 (0.5 pt)
• According to the long-run classical model, equilibrium is given by:
64000 – [8700 + 0.75(56000 – 6300) – 200r] – 6300 = 7500 – 300r
3725 + 200r = 7500 – 300r
500r = 3775
r = 7.55 (i.e., 7.55%) (1 pt)
• Investment, I: (0.5 pt)
I = 7500 – 300(7.55) = 5235
• Real rental price for capital, R/P: (1 pt)
𝑅
4
=
MPK
=
(
) (42875−⅔ )(8000⅔ ) = 0.4354
𝑃
3
•
Real wage for labour, W/P: (1 pt)
𝑊
8
= MPL = ( ) (42875⅓ )(8000−⅓ ) = 4⅔
𝑃
3
MGEB05 Assignment 1 Answer Key (Winter 2024)
2
Part (c) (9 points)
r
Market for Loanable Funds
(5 pts; 3 pts only if the supply of loanable fund is not upward sloping)
S1
S0
r1= 7.55%
B (part b)
r0= 4%
A (part a)
I0(r)
I, S
,1
,1
,0
,0
5235 = I* = S*
I* = S* = 6300
Note:
• The diagram is not drawn to scale.
• Supply of loanable funds must be upward sloping since C is negatively related to interest rate.
W/P
Labour Market (2 pt)
LS
R/P
(R/P)1
0
(W/P)
Rental Market for Capital (2 pts)
KS1
KS0
B″ (part b)
A(part a)
A″ (part a)
(R/P)0
1
(W/P)
B (part b)
L*
LD0 = MPL0
LD1 = MPL1
L
KS*,1
K*,0
KD = MPK
K
Part (d) (7 points)
Suppose the government wants to keep the level of real interest rate to 5%:
• From the investment function: (3 pts)
I = 7500 – 300(5)
I = 6000
• The level of government spending that will keep r at 5%: (2 pts)
6000 = 56000 – [8700 + 0.75(56000 – 6300) – 200(5)] – G
6000 = 11025 – G
G = 5025
• Budget balance, GBB:
GBB= T – G = 6300 – 5025 = 1275 (1 pt)
 Budget balance improves or it changes from a balanced budget to a budget surplus. (1 pt)
MGEB05 Assignment 1 Answer Key (Winter 2024)
3
Question 3 (25 points)
Part (a) (20 points)
Suppose the government increases the contribution limit of the TSFA:
Market for Loanable Funds:
• When the government increases the contribution limit of the TSFA, it provides incentive to
households to increase their savings. (1 pt)
 To save more, households spend less  autonomous consumption . (1 pt)
 National savings  because  S = Y – C(Y – T)  – G. (1 pt)
 The supply of funds increases to S1. (1 pt)
• Point B is the new equilibrium:
r  to r1
S*  to S*,1
I*  to I*,1
Labour Market:
• Since the size of the labour force does not change, there is no change in the supply of labour. (1 pt)
• There are no changes in total factor productivity and the stock of capital, there is no change in the
demand for labour. (1 pt)
𝑊
• Point A remains as the equilibrium: No change in ( 𝑃 )
Variable
Output
Real interest rate
National savings
Real wage
price level
Change
(1 pt each)
―


―

Reason
(1 pt each)
Y = F(A, K, L) & no change in A, K & L.
Supply of funds   a decrease in real interest rate
Canadians increase their savings as the incentive to save
increases with the increase in the TSFA contribution limit.
No change in the demand and supply of labour.
P=
̅̅̅̅̅
𝑀𝑆
L( r+πe , Y) 
because when r , the opportunity cost of
holding money  and there will be an increase in money
demand and price level decreases
MGEB05 Assignment 1 Answer Key (Winter 2024)
4
r
Loanable funds market (2 pts)
S0
S1
r0
A
r1
B
I(r)
I, S
,0
,0
,1
,1
I* = S* I* = S*
Note: We accept any answer with an upward sloping supply of funds curve.
Labour Market (2 pts)
W/P
LS0
(W/P)0
A
LD0
L*,0
L
Part (b) (5 points)
Since the change in capital stock is given by investment (i.e., K = I):
• When the level of investment increases as mentioned in part (a), the capital stock will increase over
time. (3 pts)
• The long-run level of output increases because  Y = F(A, K , L). (2 pts)
MGEB05 Assignment 1 Answer Key (Winter 2024)
5
Question 4 (25 points)
Part (a) (10 points)
Suppose the government lowers the minimum legal working age and, at the same time, the adoption of
greener production methods has made some of the country’s machinery and equipment obsolete:
• When the minimum legal working age decreases, more young workers are eligible to work  the
labour force . (2 pts)
 When labour force , each unit of rental capital becomes more productive  the demand for
rental capital (or MPK)  to KD1 (or MPK1). (1 pt)
• The move to greener production methods has made some of the country’s machinery and equipment
obsolete, some capital stock can no longer be used in the production process. (2 pts)
 When capital stock , the supply of rental capital  to KS1. (1 pt)
• Point B is the new equilibrium:
𝑅
𝑅 1
𝑃
𝑃
( )  to ( ) . (1 pt)
(R/P)
(R/P)1
KS1
KS0
B
(R/P)0
Graph: 3 pts
A
KD1 = MPK1
KD0 = MPK0
K*,1
K
K*,0
Part (b) (5 points)
Suppose the public holds a larger portion of their wealth in the form of cash:
• The demand for money increases, i.e., L(r + e, Y) . (1 pt)
•
•
̅̅̅̅̅
𝑀𝑆
This increase in money demand will lower the aggregate price level because  P = L(↑ r+πe, Y)  (1 pt)
To achieve price stability, the central bank conducts expansionary monetary policy (1 pt) such that
the effect of an increase in money demand on the price level will be fully offset by the effect of an
MS 
increase in money supply, i.e., ̅
P=
(2 pts)
e
L(↑ r+π , Y) 
MGEB05 Assignment 1 Answer Key (Winter 2024)
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Part (c) (5 points)
Introduction of mobile payment apps:
• This is an improvement in payment technology that lowers the demand for money (1 pt) since the
need to use money to facilitate transactions drops.
• Holding all else constant, the public does not need to use money for purchases, money changes hands
faster than before  velocity of money, V, . (2 pts)
• According to the quantity equation, an increase in the velocity will lead to an increase in the aggregate
price level because  P=
̅ V
M
̅
Y
. (2 pts)
Part (d) (5 points)
• Growth rate of output (from the growth accounting equation):
∆Y
∆A
∆K
∆L
= A +  ( K ) +(1- ) ( L )
Y
∆Y
•
•
•
= 0.012 + ⅓(0.03) + ⅔(0.045) (2 pts) = 0.052 (i.e., 5.2%) (1 pt)
Quantity theory of money:
%  in MS + %  in V = %  in P (= ) + %  in Y
If the velocity of money is rising at 2% and the central bank wants to obtain an inflation of 2.5%,
then the monetary growth rate should be:
%  in MS =  + %  in Y – %  in V
%  in MS = 2.5% + 5.2% – 2% (1 pt) = 5.7% (1 pt)
The central bank should set the monetary growth rate to 5.7%.
Y
MGEB05 Assignment 1 Answer Key (Winter 2024)
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