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Economics for Management Studies

MGEB06H3

Jack Parkinson

Fall

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ECMB06 Assignment 1 Answer Key – Fall 2011
Question 1 (25 points)
Part (a) (5 points) (Must show work for credit)
Output, Y:
Y = AK L1/4 3/= 2(10000) (50625) 3/= 67500
Taxes, T:
T = 0.1Y = 0.1(67500) = 6750
Government spending, G:
G = T + 0.15Y = 6750 + 0.15(67500) = 16875
Equilibrium of the long-run classical model is given by: S = Y – C – G = I (1 pt)
67500 – [30000 + 0.5(67500 – 6750) – 1500r] – 16875 = 16500 – 1000r
– 9750 + 1500r = 16500 – 1000r
r = 10.5 (10.5%)
Consumption, C: (1 pt)
C = 30000 + 0.5(67500 – 6750) – 1500(10.5)
C = 44625
Investment, I: (1 pt)
I = 16500 – 1000(10.5) I = S = Y – C - G
I = 6000 I = 67500 – 44625 – 16875 = 6000
Real wage for labour, W/P: (1 pt)
W/P = MPL = (3/4)[2K L 1/4 –1] = (3/4)[2(10000) (50525) –1/]
W/P = 1
Real rental price for capital, R/P: (1 pt)
R/P = MPK = (1/4)[2K –3/L ] = (1/4)[2(10000) –3/(50625) ]/4
R/P = 1.6875
Part (b) (5 points)
The level of total factor productivity increases by 50%, the new production function:
Y = 3(10000) (50625) 3/= 101250
Taxes, T:
T = 0.1Y = 0.1(101250) = 10125
Government spending, G:
G = T + 0.15Y = 10125 + 0.15(101250) = 25312.5
Equilibrium of the long-run classical model is given by: S = Y – C – G = I (1 pt)
101250 – [30000 + 0.5(101250 – 10125) – 1500r] – 25312.5 = 16500 – 1000r
375 + 1500r = 16500 – 1000r
r = 6.45 (6.45%)
Consumption, C: (1 pt)
C = 30000 + 0.5(101250 – 10125) – 1500(6.45)
C = 65887.5
Investment, I: (1 pt)
I = 16500 – 1000(6.45) I = S = Y – C - G
I = 10050 I = 101250 – 65887.5 – 25312.5 = 10050
Real wage for labour, W/P: (1 pt)
W/P = MPL = (3/4)[3K L 1/4 –1] = (3/4)[3(10000) (50525) –1/]
ECMB06 Assignment 1 Answer Key (Fall 2011) 1 W/P = 1.5
Real rental price for capital, R/P: (1 pt)
–3/4 3/4 –3/4 3/4
R/P = MPK = (1/4)[3K L ] = (1/4)[3(10000) (50625) ]
R/P = 2.53125
Part (c) (10 points)
By comparing the answers in parts (a) and (b), when the level of total factor of productivity
rises:
Y, C, I, G, T, W/P, and R/P rise.
r falls.
FYI: Output, Y = F(A, K, L):
In the long run, output is determined by the state of technology (TFP), capital stock and
labour force.
When A rises, the economy can make use of its production factors more effectively, so the
level of output rises.
FYI: Taxes, T, & Government spending, G:
Taxes = 10% of Y When Y , T by 3375.
Government spending = 25% of Y (as the size of the budget deficit is 15% of Y) When Y
, G by 8437.5.
Equilibrium real interest rate, r (2 pts – must mention in Y, C & G affect S for full credit)
Real interest rate is determined by the demand for and supply of funds in the loanable funds
market.
Supply of funds = National saving, S = Y – C – G:
Y , S by 33750.
C = C(Y – T, r) (Y – T) by 30375 C by (MPC (Y – T)) = 0.5 30375 =
15187.5 S by 15187.5
G by 8437.5 S by 8437.5
Overall, S by 10125.
Given S , the supply of funds to S .
At the initial real interest rater (r= 10.5%), there is an excess supply of loanable funds.
Point B is the new equilibrium:
r to r (r = 6.45%).
Consumption, C: (1 pt)
When the economy reaches its new equilibrium, the in (Y – T) and the in r (as the cost of
borrowing falls) lead to higher level of consumption.
At point B, C = 0.5 (Y – T) – 1500 r = 0.5(30375) – 1500 (6.45 – 10.5) = 21262.5
Investment, I: (1 pt)
When the equilibrium real interest rate falls to 6.45%, the cost of borrowing and I by
(1000 r ) = [1000 6.45 – 10.5] = 4050.
ECMB06 Assignment 1 Answer Key (Fall 2011) 2 Alternatively,
For a closed economy, equilibrium in the market for loanable funds requires S = I.
When the level of total factor productivity increases by 50%, the (equilibrium) level of
national saving by 4050.
When the (equilibrium) level of national saving , so does the (equilibrium) level of I.
Real wage, W/P: (1 pt)
When the level of total factor productivity , labour becomes more productive MPL
demand for labour to LD = MPL . 1
0
At the initial real wage, (W/P) , there is excess demand for labour.
Point B’ is the new equilibrium in the labour market:
(W/P) to (W/P) 1
Real rental price of capital, R/P: (1 pt)
When the level of total factor productivity , capital becomes more productive MPK
1 1
demand for (rental) capital to KD = MPK . 0
At the initial real rental price of capital, (R/P) , there is excess demand for (rental) capital.
Point B” is the new equilibrium in the labour market:
1
(R/P) to (R/P)
Market for loanable funds (2 pts)
r S 0
1
S
A Graph: 2 pts will be subtracted if the
0
r = 10.5% supply of funds curve is not upward
sloping.
r = 6.45% B
0
I (r)
I, S
I* =S* ,0 I* =S* ,1
= 6000 = 10050
Labour Market (1 pt) Rental Market for Capital (1 pt)
W/P LS R/P KS
1.5 B’
2.53125 B”
1.0 A’
1.6875 A”
LD = MPL 1 KD = MPK 1
0 0 0 0
LD = MPL KD = MPK
L* = 50625 L K* = 10000 K
ECMB06 Assignment 1 Answer Key (Fall 2011) 3 Part (d) (5 points)
Suppose the government wants to lower the level of interest rate to 5%:
Using the investment function to find the level of investment when r = 5%: (1 pt)
I = 16500 – 1000(5)
I = 11500
The level of government spending that will keep r at 5%:(2 pts)
In equilibrium, S = I and the equilibrium level of investment = 11500
11500 = 101250 – [30000 + 0.5(101250 – 10125) – 1500(5)] – G
G = 21687.5
Government budget balance, GBB: (2 pts – must discuss what happens to GBB)
GBB = T – G = 10125 – 21687.5 = – 11562.5
Since G and there is no change in taxes, GBB improves (i.e., the government runs a
smaller budget deficit, GBB = – 11562.5 – (– 15187.5) = 3625.
Question 2 (25 points)
Part (a) (10 points)
Suppose the level of the capital stock falls by 10% and the size of the labour force falls by 25%:
Output, Y: (1 pt)
Y = F(A, K, L) K & L , Y .
National saving, S = Y – C – G
3 pts Y , S by Y.
C = C(Y – T) when Y , C by (MPC Y) S by (MPC Y).
Overall, S by (1 – MPC) 1 Y.
S , supply of funds to S .
At r , there is excess demand for funds r to r . (1 pt)
Note: you must mention there is a in C and there are 2 forces causing a in S for full credit.
Point B is the new equilibrium:
r to r .
I* by (1 – MPC) Y to I* . (1 pt)
C* by (MPC Y). (1 pt)
r
S 1 S 0
r1 B Graph: 3 pts
0
r A
I(r)
S, I
I* =S* ,1 I* =S* ,0
ECMB06 Assignment 1 Answer Key (Fall 2011) 4 Part (b) (15 points)
Suppose the level of the capital stock falls by 10% and the size of the labour force falls by 25%:
K K
Given k L , K by 10% and L by 25%, then k L . (1 pt)
,0 1
k f1om k* to k .
3 pts At k , sy < (n + )k k < 0.
k begins to decrease.
k continues to decreases until k = k* .
Point A is,0he new steady state:
k = k* (no change)
Growth rate of output per worker, y/y:
FYI: Immediately after the rise in capital-labour ratio:
When k , y because y = Af(k).
Since y , y/y > 0.
During transition to steady state: (4 pts)
sy < (n + )k k < 0 k .
Since y = Af(k), y when k .
When y , y/y turns negative.
As k approaches its steady-state value, k is decreasing at a slower rate, so does y y/y
slows down.
In steady state: (3 pts) ,0
In steady state, k = k* and does not change.
Since k does not change, so does y.
y/y = 0.
y, sy, (n + )k
(n + )k
,0 y
y* k < 0
sy
A
Graph: 4pts
No credit if you shift any curve
k = K/L
k* ,0 k1
ECMB06 Assignment 1 Answer Key (Fall 2011) 5 Question 3 (25 points)
Part (a) (4 points) (1 pt for showing work)
Production function: Y = AK L 1 –
Per worker production function, y = Y/L
1 –
Y/L = y = (AK L )/L

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