1. In the past ten years, Kamuza's total output has increased from 2000 to 3000, the capital stock has risen from 4000 to 5200, and the labour force has increased from 400 to 580. Suppose the production function in both years had an exponent of 0.4 on capital, an exponent of 0.6 on labour and the total factor productivity is A (i.e., Y=AF(K,N)):
a) How much did capital contribute to economic growth over the decade?
a) How much did labour contribute to economic growth over the decade?
a) How much did productivity contribute to economic growth over the decade?
2. (a) Suppose the marginal product of labour for unskilled labour is given by MPN = 200 - 0.5N
The supply of unskilled labour is given by 100 + 4w. (Let P=1, so that w is the real wage). The government imposes a minimum wage of 60. How much unemployment will this create among unskilled labour?
(b) Suppose for the economy of Lower Volta, the MPN is given by MPN = 400 - 0.2N
where N is the aggregate employment. The aggregate quantity of labour supplied is 500 + 10(1-t)w, where t is the income tax rate. Assume t is 50%. What is the before-tax real wage?
3. Suppossse the Okun's Law coefficient is 2, the full-employment level of output is $6000 billion and the natural rate of unemployment is 5.5%.
(a) What is the current level of output if the current unemployment rate is 8%?
(b) Suppose the unemployment rate falls to 5%; what is the curent level output?
(c) Suppose structural changes in the economy raise the natural rate of unemployment to 7%, and lower the full-employment level of output to $5500 billion. If the current unemployment rate is 8%, what is the current level of output?
4. (a) Calculate the user cost of capital of a machine that costs $5000 and depreciates at a rate of 25%, when the interest rate is 5%.
(b) Suppose that tax rate on revenue is 25%, what will be the after-tax user cost of the same machine?
(c) What will be the effect of (b) on the desired level of the capital stock?
5. An economy has governmental purchases of 2000. Desired national saving and desired investment are given by
Sd = 200 + 5000r + 0.10Y - 0.2G Id = 1000 -4000r
When the full-employment level of output equals 5000, calculate the real interest rate that clears the goods market.
(b) A large open economy has desired national saving of Sd = 20 + 200Rw and desired national investment of Id = 30 - 200Rw
where Rw is the real world interest rate. The foreign economy has has desired national saving of Sdf = 40 + 100Rw and desired national investment of Idf = 75 - 400Rw
(i) Calculate the equilibrium values of Rw, CA, CAf, S,I, Sf and If.
(ii) Suppose Sd rises by 45 so that now Sd = 65 + 200 Rw. Calculate the equilibrium values of Rw, CA, CAf, S,I, Sf and If.
(iii) Suppose withe Sd back to Sd = 20 + 200 Rw, as in (a), that Id rises by 45 to Id = 75 - 200 Rw. Calculate the equilibrium values of Rw, CA, CAf, S,I, Sf and If.
6. Canadian merchandise trade balance (D72003) receives considerable attention in the news media. But the current account balance (CA), which describes growth of our foreign debt is found by adding the merchandise trade balance, the services balance (D72005), investment income (D72006) and tranfers (D72007). From the CANSIM (numbers in parantheses) database,
(a) Find annual values for these four components of the Canadian CA for 1991, 1992, 1993 and 1994.
(b) What is the rate of growth of CA from 1992 to 1993?
(c) What are the rates of growth of the merchandise trade balance (as a percentage of the CA) from 1992 to 1994?
1. Denoting the change in X by dX, the growth equation is
dY/Y = dA/A + 0.4 dK/K + 0.6 dN/N
P.S : Output increased by 50%
Contribution by
(a) capital = 0.4 dK/K = .12
(b) labour = 0.6 dN/N = .27
(c) productivity = dA/A = .5 - (.12 + .27) = .11
P.S : Some students might expressed these values in raw percentages, so that the three contributions add up to 100%. In this case, (a) 24% (b) 54% (c) 22%
2. (a) The demand for labour is given by:
MPN = real wage
i.e., Nd = 2x(200-w)
Equilibrium requires Nd=Ns:
i.e., 2x(200 - w) =100 + 4w which implies w = 50.
If minimum wage = 60, Nd = 2x(200 - 60) = 280 and Ns = 100 + 240 = 340.
Therefore this policy will make 60 unskilled labour unemployed.
(b) Similar to (a). Find Nd using MPN = w.
Substituting t=0.5 into Nd = Ns, you get w = 150.
3. Let Yfe = full-employment output and Un = natural rate of unemployment then Okun's Law is given by:
(Yfe - Y)/Yfe = 2x(U - Un)
Yfe = 6,000, Un = 5.5%
(a) U = 8%, then Y = 5,700.
(b) if U = 5%, then Y = 6,060.
(c) Now Yfe = 5,500 and Un = 7%, if U = 8%, then Y = 5,489.
4. (a) user cost , uc = (r + d)xPk = 5000x(0.25 + .05) = $1,500.
(b) tax-adjusted user cost = (r + d)xPk/(1-t) = $2,000
(c) the tax will reduce the desired level of the capital stock. (this can be illustrated with a diagram)
5. (a) Sd = 200 + 5000r + 0.10Y - 0.2G
Id = 1000 -4000r
When Yfe = 5000, Sd = Id implies r = .0778 ( or 7.78%).
(b) For two large open economies, CA + CAf = 0.
i.e., Sd + Sdf = Id + Idf
(i) So 60 + 300Rw = 105 - 600 Rw which implies Rw = .05 (or 5%).
Susbt. into the formulas : S = 30, I = 20, CA = 10
Sf = 45, If = 55, and CAf = -10.
(ii) we now get 900 Rw = 0 which implies Rw = 0.
Susbt. into the formulas : S = 65, I = 30, CA = 35
Sf = 40, If = 75, and CAf = -35.
(iii) with increase in Id, we get 900 Rw =90 , or Rw = .01 (or 10%).
Susbt. into the formulas : S = 40, I = 55, CA = -15
Sf = 50, If = 35, and CAf = 15.
6. The CANSIM data in million of Canadian dollars
1991 1992 1993 1994
------ ------ ------ ------
Merchandise balance 3616 6200 9323 15047
Services balance -11573 -12267 -12487 -9430
Investment income -19187 -19999 -26068 -28894
Transfers balance 108 171 438 979
------- -------- -------- ------
Current Account -27036 -25895 -28794 -22298
P.S : CA deficit for all the years (1991 to 1994)
(b) The CA deficit grew by about 11.2% from 1992 to 1993.
(c) Merchandise balance as a percentage of CA balance
1992 : -23.94% of CA deficit.
1993 : -32.38% of CA deficit
1994 : -67.48% of CA deficit
Growth of merchandise trade balance (as a percentage of the CA)
from 1992 to 1993 = (32.38 - 23.94)/23.94 = 35.25%
from 1993 to 1994 = (67.48 - 32.38)/32.38 = 108.8%