Econ 222B F2000
Mid-Term Questions and Solutions:
Part I:
1. The country of Old Jersey produces milk and butter, and it has
published the following macroeconomic data, where quantities are in
gallongs and prices are in dollars per gallon.

			1998				1999

Good		Quantity	Price		Quantity	Price

Milk		500		$2		900		$3

Butter		2000		$1		3000		$2

(i) Calculate the percentage change in the price level between 1998 and
1999 as measured by a variable-weight price index.

Answer:
Variable Weight Price Index:
Base, 1998 = 100 (no need for calculation)

Index 1999 = 100 x (1999 Quantities x 1999 Prices) / (1999 Quantities x  1998 Prices)

           = 100 x ((900 x 3) + (3000 x 2)) / ((900 x 2) + ((3000 x 1))

           =181.25

The percentage change in price level is: PoI₁₉₉₉ -
PoI₁₉₉₈ = 181.25-100 = 81.25%

{it is still correct if you use Base Index = 1 but in that case you need
to multiply by 100 to get the percentage.}

(ii) Calculate the real GDP in 1999 using the price index calculated
in part (i).


Answer:

Real GDP in 1999= 100 x (Nominal GDP 1999)/(Price Index 1999)
		= 100 x (1999 Quantities x 1999 Prices)/181.25
		= 100 x (8700/181.25) =4800 


2. Monica grows coconuts and catches fish.  Last year she harvested 1500
coconuts and 600 fish.  She values on fish as worth 3 coconuts.  She gave
Rachel 300 coconuts and 100 fish for helping her harvest coconuts and
catch fish, all of which was consumed by Rachel.  Monica set aside 200
fish to help with next year's harvest.  Use the income approach to
calculate the GDP in this island economy in terms of fish.  Explain your
steps.
Answer:

GDP(Income)= Income of Monica + Income of Rachel
Monica's Income = (1500-300)Coconuts + (600-100)Fish
Rachel's Income =       300 Coconuts +      100 Fish
		--------------------------------------
            GDP =      1500 Coconuts +      600 Fish
                =       500 Fish +          600 Fish
		
                = 1100 Fish

3. Derive the expression for the Uses-Of-Savings identity, starting from
the definition of private disposable income.  Explain its meaning using an
example.  If a government in an open economy incurs a budget deficit, what
are the possibilities of financing it according to the uses-of savings
identity?

Answer:
Private disposable income = PI
PI = GNP - Taxes + Transfers + Interest
   = Y + NFP - T + TR + INT

Private Savings = Spvt = PI - Consumption
Spvt = Y + NFP - T + TR + INT - C
   = C + I + G + NX + NFP - T + TR +INT -C
   = I +[G-T+TR+INT] + [NX+NFP]
   = investment + gov't deficit + current acct.

Spvt = I + (-Sgvt) + CA

Private savings can be used for financing private investment, financing
gov't deficit or CA surplus (lending to foreiners). =>Gov't deficit can be
financed by private savings or by running down current account (CA<0)
=>borrowing from abroad.

4. Explain the similarities and differences between the following two:
   Consumer price index and GDP deflator

Answer:
Similarities:
-CPI and GDP deflator both measure price level in the economy
Differences:
-CPI is based on fixed weight index
-GDP deflator is a variable weight index
CPI, therefore, measures the change in the price of buying a
fixed(expenditures of a representative Canadian household) bundle of
goods, whereas the GDP deflator measures the average price
level of all final goods produced in the economy.

5.  Explain whether each of the following statements is true, false or
uncertain: (be brief)
a) If a Canadian construction company built a road in Kuwait, this
activity would be included in Kuwait's GDP.
b) Suppose Toyota built a new automobile plant in Mexico using Japanese
management practices and Mexican labour.  The portion of output
contributed by Mexican labour would be included in Mexican GDP but not in
Mexican GNP.
c) Private disposable income equals NNP+NFP-Taxes+Transfers+Interest.
d) Because government services are not sold in markets, the government
tries to estimate their market value and uses this to measure the
government's contribution to GDP.
e) If the price index last year was 1.0 and today it is 1.4, the inflation
rate over this period is 1.4%

Answer:
a) True: the activity takes place in Kuwait so it will be included in
their GDP.

b) False: It will be included in both measures.

c) False: PDI = GNP - taxes + transfers + interest 

d) False: government services are valued at the cost of provision.

e) False: inflation rate = 1.4-1.0 = 40% not 1.4%

6.  For the economy of Lower Volta, the MPN (marginal product of labour)
is given by: MPN = 400-0.5N, where N is the aggregate employment.  The
aggregate quantity of labour supplied is: N = 500+w. Calculate the level
of aggregate employment and real wage in equilibrium.

Answer:
dd F'n:  w = MPN = 400-0.5N   (1)
ss F'n:  N = 500 + w

Solving: substitute (2) into (1)

N = 500 + [400 - 0.5N]  => 1.5N=900
                        => N=600	=>w=400-0.5(600)
                                           =100

7. Explain what is meant by full employment output.  Explain how the
full-employment output will be affected by an economy wide beneficial
productivity shock.  Draw diagrams and explain.

Answer:



Part II
1.  You are given the following behavioral relationships for the economy
of Onga.

Labour Market:

Marginal Product of Labour = MPN = 500 - 0.5N , N=aggregate employment
Labour supply =              N = 500 + 0.5w ,  w=real wage rate

Goods Market:

Consumption Function = C^d = 200 + 0.9Y - 10000r , r=real interest rate
Investment Function  = I^d = 1000 - 10000r
Government           = G = 300

a) Calculate the equilibrium real wage (w) and aggregate employment (N)
b) Assuming that full-employment output is 5000, derive the desired
savings function.
c) Explain the goods market equilibrium condition.  Solve the equilibrium
value of r (assuming full-employment output is 5000).  Also, calculate the
level of desired consumption and desired savings in equilibrium.
d) Suppose that there is a temporary increase in gov't spending financed
by borrowing in the market.  Explain how it will affect the goods market
equilibrium, and the equilibrium levels of real interest rate, desired
savings and desired consumption.  Draw a diagram to illustrate the changes
in the goods market equilibrium.

Answer:
a) w= 500 - 0.5N
   N= 500 + 0.5w
=> N*=600 and w*=200

b) Y^f=Y=5000
   S^d= Y - C^d - G 
     = Y - (200 +.9Y -10000r) - 300
     = 0.1Y - 500 + 10000r
     =0.1(5000) -500 + 10000r
     =500-500+10000r
     =10000r
as r increases S^d increases =>positively sloped function

c) Goods Market equilibrium condition:

		S^d=I^d
	or	Y=C^d+I^d+G

using the first => 10000r=1000-10000r
                   20000r=1000
                        r=1000/20000
                         =0.5 or 5%
so:
C^d= 200 + 0.9(5000) - 10000r = 200 + 4500 - 500 = 4200
S^d= 10000(0.05) = 500
I^d= 500  => C^d+I^d+G = 4200+500+300=5000 = Y^f 

d)



2. This question consists of two parts:

a) A firm has a current and future marginal productivity of capital given
by:
		MPK = 5000 - 2K
The price of capital is $1000.  The real interest rate is 10% and the
depreciation rate is 10%.  Calculate the tax rate on firm's revenue(/&tau)
if the desired capital stock(K) is equal to 150.  Calculate the
tax-adjusted user cost of capital.  (note: some bowsers don't support the
code used here for the lower case greek letter tau.  If you see the symbol
/&tau it should be the lower case greek letter tau.)

b) Explain how each of the following events will affect the equilibrium
real interest rate and equilibrium desired savings.  Depict the change in
the goods market equilibrium in a diagram (for each case).
	(i) A technological improvemnt that increase the expected future
	marginal product of capital.
	(ii) A temporary increase in income taxes with current and future
	government spending unchanged, assuming Ricardian Equivalence.
	(iii) A stock market crash.

Answer:
a) MPK = 5000 - 2K
     K = 150  => MPK = 5000-300 = 4700

user cost  UC = (r+d)Pk = (0.1+0.1)(1000)
              =0.2(1000) = 200

tax adjusted uc = uc/(1-/&tau)

equilibrium: MPK = UC/(1-/&tau)  => 4700=200/(1-/&tau)
				 => 1-/&tau = 200/4700 = 0.0426
                                    /&tau = 1-0.0426 = 0.9574

                   so tax adjusted UC = 200/(1-0.9574) = 200/0.0426 = 4694.835

b) 
 

3.  

a) Growth accounting formula:  /&DeltaY/Y = /&DeltaA/A + /&alpha/&DeltaK/K
+ /&Beta/&Delta L/L
so  /&DeltaA/A = /&DeltaY/Y - /&alpha/&DeltaK/K - /&Beta/&Delta L/L
               = 6% - 0.3(2%) - 0.7(4%)
               = 2.6%

(note: some bowsers don't support the
code used here for the lower case greek letters capital delta, alpha and
beta. If you see the symbols /&Delta /&alpha /&Beta they should be the
upper case greek letters Delta, alpha and Beta.)

b) Nominal GDP 1997 = 674.8   => Real GDP 1997 = 100x(674.8/121.6) = 554.93
   Nominal GDP 1998 = 688.4   => Real GDP 1998 = 100x(688.4/123.3) = 558.31

   -> Inflation rate = 100x(123.3-121.6)/121.6 = 1.398%
   -> Growth rate of real GDP = 100x(558.31-554.93)/554.93 = 0.61%

c)(1)Uncertain/false: Spvt + Sgovt = I
	it could be financed by private or gov't savings
  
  (2)False: Unemployment rate = # of unemployed/labour force
	when workers are discouraged and drop out of labour force, both
	the numerator and denominator drop.  The unemployment rate
	generally falls.  However, employment rate = employed/working age
	population so as discouraged workers are already in the working
	age population, this figure is unlikely to change.
   
   (3)False: If constant returns to scale then the demand curve of labour
	is horizontal.  This implies that MPL is the same for all L.