Economics 100A
Prof. Yang

Solutions to Homework Problems                     Chapter:  1  2  3  4  5  6  7  8

Chapter 3

Numerical

1.  a) 1000 + 12W/P = 2000 - 8W/P
         W/P = 50.    N = 1600

            Yes, it exhibits diminishing marginal product.

    c)  N = 1600;  Y = 4000 in equilibrium

2.    D Y/Y = D A/A + .7D N/N + .3D K/K
         .05 =D A/A + .7(.02) + .3(.04)
      D A/A = .024

      If D K/K rises by .01, then D Y/Y rises by .003 (1/3 of 1%). A rise in D N/N of .01
      increases D Y/Y by .007.

Analytical

1.    Equilibrium employment is the number employed when the labor market is in equilibrium.  The fraction
       of the labor force not working at this point is the natural rate of unemployment.  Potential GDP and
       equilibrium ouptut both refer to the level of output that can be produced at equilibrium employment.

3.    a)  Per capita GDP growth of 1% per year means that GDP itself must grow by 2% per year, since
            population is assumed to grow by 1%.

       b)  Using the Solow growth equation and substituting the appropriate values for real GDP growth (2%),
            labor input growth (1%), and productivity growth (.5%), we find that the capital stock must grow
            by 2.7% to hit the target of 2% growth in real GDP.  If productivity growth were completely absent,
            the capital stock would need to grow by 4.3%.

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