Exercise Set 1
THE HARROD-DOMAR MODEL

Parameters       t
 		 K(t)
 		 Y(t)
 		 S(t)
 		 I(t)
 		 g
 
s = 0.2     0 1.000 0.250 0.050 0.050  
v = 4     1 1.050 0.263 0.053 0.053 0.05
K(0) = 1     2 1.103 0.276 0.055 0.055 0.05
      3 1.158 0.289 0.058 0.058 0.05
Equations     4 1.216 0.304 0.061 0.061 0.05
(1)     Y(t) = K(t)/v     5 1.276 0.319 0.064 0.064 0.05
(2)     S(t) = sY(t)     6 1.340 0.335 0.067 0.067 0.05
(3)     S(t) = I(t)     7 1.407 0.352 0.070 0.070 0.05
(4)     K(t+1) = K(t) + I(t)     8 1.477 0.369 0.074 0.074 0.05
(5)     g = [Y(t+1) - Y(t)] / Y(t)     9 1.551 0.388 0.078 0.078 0.05
      10 1.629 0.407 0.081 0.081 0.05
      11 1.710 0.428 0.086 0.086 0.05
      12 1.796 0.449 0.090 0.090 0.05
      13 1.886 0.471 0.094 0.094 0.05
      14 1.980 0.495 0.099 0.099 0.05
      15 2.079 0.520 0.104 0.104 0.05
      16 2.183 0.546 0.109 0.109 0.05
      17 2.292 0.573 0.115 0.115 0.05
      18 2.407 0.602 0.120 0.120 0.05
      19 2.527 0.632 0.126 0.126 0.05
      20 2.653 0.663 0.133 0.133 0.05

Questions

  1. What do the parameters s, v and K(0) mean?
  2. Explain what each equation represents. Describe what Y, K, S, I and g represent.
  3. In Year 20, the consumption (C) in the economy is ________. Explain.
  4. What is the growth rate of capital stock in the model? Explain.
  5. The marginal product of capital in this example is: MPK = ________. Explain.
  6. Using the equations, derive the relationship: g = s/v.
    Note that the growth rate of 5% is in fact equal to s/v, i.e. 0.2/4.
  7. Suppose the population grows at the rate of n = 4% per year. Then, per-capita GDP will grow at ____ % per year.
  8. In order to prevent "instability" in the model, the rate of population growth must be _____ % per year. Explain.
  9. Suppose s increases. Assuming a new value for s, construct a table showing the evolution of the economy over time. Sketch Y(t), S(t) and C(t) on a graph. Use Excel.
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