Q1.

a) Diminishing marginal productivity of a factor means that the additional output produced by one extra unit of the factor is decreasing
   in the number of units of that factor.  That is, the more of that factor that you hire (holding all else fixed) the less productive each unit
   of that factor will be.  EX/ if you have two programmers, but only one computer, the second programmer will not add as much to your 
   productivity as the first one did.
 
b) An increase in the marginal product of labour (MPN) or productivity will increase labour demand (curve will shift up and right).
     An increase in the capital stock (K) will increase labour demand (curve will shift up and right).

c) A decrease in the working age population or a decrease in the labour participation rate or both will decrease labour supply (curve will  
    shift up and left).  each of these counts as one
   An increase in wealth will decrease the labour supply (don't need to work as much anymore)(curve will shift up and left).
   An increase in expected future real wage will decrease the labour supply (work less now, more later) (curve will shift up and left).


d) The equilibrium condition in the goods market is supply of goods =
   demand of goods, or Y = C + I + G (+NX + NFP)  the latter term equals
   the CA.  This can be rewritten as Y - C - G - CA = I.  Since the former
   term is equal to demand for saving, we have S=I as the equilibrium
   condition for the goods market.


e) Ricardian equivalence implies that tax cuts don't affect current demand
   because agents, knowing that a increase in taxes today 
   can be paid for with an decrease in taxes tomorrow (if the gov't
   maintains a balanced budget); thus, in order to smooth 
   consumption, agents will borrow off the extra future income (generated
   by a tax cut (next period), in order to pay the extra taxes in the   
   current period without having to decrease consumption at that point.
   Therefore, the effect of a temporary increase in the income tax rate
   will have no effect on consumption, but will cause a temporary decrease
   in savings, if Ricardian Equivalence holds.



Q2.  


a) TFP = A       and      A = Y/ (K0.25N0.75)

     A(1999) = 9.54
     A(2000) = 9.12

b) Growth of total factor productivity from 1999 to 2000 =  100 * [A(2000) - A(1999)] / A(1999)  
							 = 100 * [9.12 - 9.54] / 9.54 
							 = -4%  or -0.04

c) Percentage increase in real GDP between 1999 and 2000 = 100 * [GDP(2000) - GDP(1999)] / GDP(1999) = 5%  or  0.05

d) GDP in 2020 = 235,683

e)   A[(X*K)0.25(X*N)0.75] = A[X0.25(K)0.25X0.75(N)0.75] = AX[(K)0.25(N)0.75] = XY
     let X=2, and the proof is done



Q3.  




a) Real wages are determined by MPN, a firm hires labour until the marginal product of the last worker equals the real wage which the firm will have to pay to hire that worker.  The MPN
    function shows the amount of labour demanded at any real wage, thus, it is the same as the labour demand curve.

b) Firm will want to hire until MPN = w, so until MPN = $15.    15 = 0.3 (350 - N)  => N = 300
c) Wages are determined where MPN = w , so w = 0.3 (350 - N)   substitute in the labour supply.
					   w = 0.3 (350 - (600 + 22w))
					   w = -9.87
					   N = 600 + 22*(-9.87) =  382 (if rounded up 383)


Correction:  labour supply = N = 200 +22w     w = 0.3 (350 - N) substitute in the labour supply
						     w = 0.3 (350 - (200 + 22w))
						     w = 5.92
						     w = 0.3 (300 - N)  => N = 330    alternatively   N = 200 + 22*(5.92) =  330

d) With taxe rate, t = 0.4,  w = 0.3 (350 - N)   substitute in the labour supply, which is now    N = 600 + 22 (1-0.4) w
			     w = 0.3 (350 - (600 + 22(0.6)w))
			     w = -15.12
			     N = 600 + 22 (1-0.4) (-15.12) = 400 alternatively  -15.12 = 0.3 (350 - N)  => N = 400


Correction:   pre-tax labour supply N = 200 + 22w,     w = 0.3 (350 - N)   substitute in the labour supply, which is now    N = 200 + 22 (1-0.4) w
							      w = 0.3 (350 - (200 + 22(0.6)w))
							      w = 9.09
							     9.09 = 0.3 (350 - N)  => N = 319  (320 rounded up)  alternatively  N = 200 + 22 (1-0.4) (9.09) = 319 (320 rounded up)


e) The impact on the economy of a fixed real wage of $15 would be excess labour supply.  As the equilibrium real wage is much less than $15, if workers were offered $15/hr, there would 
    be more willing to work.  At the same time, if a firm is forced to pay $15/hr per worker, and still must maximize profits, they will only hire until MPN = 15



Q4. 


a) Firms will buy machines until MPK = UC.  UC or user cost of capital is given by the formula : UC = r*P + d*P , where P is the price of a machine, r is the real interest rate and d is
    depreciation.  So UC = (.12 +.13)*700 = 175.  Therefore the firm will wish to purchase 3 machines.

b) The tax adjusted user cost of capital is UC = (r*P + d*P)/(1-t) = 175/0.85 = 205.  Therefore, the firm should purchase 2 machines.  The firm will not wish to purchase 3 machines because 
     at 3 machines, the additional revenue brought in by the machine, 175, is less than the cost of purchasing the machine, 205.


Q5.  2 marks each 
a) Sometimes called potential output, full-employment output is the level of output that firms in an economy supply when wages and prices have fully adjusted, or when aggregate
    employment reaches its full employment level.  Y = AF(K, N*) where N* is full employment.

b) The rate of unemployment that prevails when output and employment are at the full employment level.  This reflects unemployment due to frictional and structural causes only.

c) Cyclical unemployment is the difference between the actual unemployment
   rate and the natural unemployment rate.  Cyclical unemployment is
   considered unemployment caused by business cycles, it increases with recessions (when output and employment drop) and decreases with booms.


Q6. optional, no marks

a) Sd = Y - Cd - G 
       = 7000 - 4300 + 3200r - 700 - 20
       = 1980 + 3200r

b) The equilibrium condition is Y = Cd + Id + G      this can also be written as   Sd = Id

c) To determine the equilibrium values of r, S and C, we simply equate the
   S and I equations.

S = 1980 + 3200r = 1900 - 6000r = I

=>   r = -0.02  

=> C = 5064   and   S = 1916

Correction:  with I = 2100 - 6000r

S = 1980 + 3200r = 2100 - 6000r = I

=>  r = 0.01

=> C = 4968   and   S = 2012

 
d)  If   G increases, investment will fall.  Intuitatively, as government
    spending increases disposable income decreases which causes savings to 
    decrease, because savings decreases then at any given r the amount
    desired to be saved will be lower, so in order to raise the necessary capital for
    investment, for any level of investment, firms will have to pay a  
    higher r. At higher r the user cost of capital is higher and firms
    will desire a lower amount of capital stock; hence investment will be lower.


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