Assume a standard Solow model where production function has normal features. Suppose that the economy is...

Assume a standard Solow model where production function has normal features. Suppose that the economy is initially in a steady state. Then at period t = t₀ there is a one-time doubling of the labor force (e.g., due to immigration) and labor force is assumed to stay at its new level permanently (note: population growth is zero after the initial jump in the labor force).
1. Show graphically and explain how this will impact the steady state capital stock per worker and the dynamics of adjustment (Hint: plot time on the horizontal axis and capital stock per worker on the vertical axis.).
2. Explain how output, consumption and real wages per worker will respond to the permanent increase in the labor force.

Solutions

Expert Solution

The above diagram shows the Solow Model steady state growth model. In the model above, the initial steady state in the economy occurs at point E1 where the level of break even investment in the economy is equal to the rate at which capital is added in the economy or rate of investment which is equal to savings in the model. At this steady state level, K1* represents the steady state level of capital per worker and y1* represents the steady state level of output per worker in the economy.

A one time increase in labor force growth rate in the economy will shift the line of break even investment upwards and thus new steady state equilibrium occurs at point E2 where the level of steady state capital per worker has decreased to k2* and the level of output per worker has reduced to y2*. Both the parameters fall because at the initial steady state level, savings or addition to the new capital stock is less than rate at which capital is being used represented by depreciation and labor force growth rate. This will reduce the level of capital per worker in the economy and reduction in capital per worker will reduce the level of output per worker in the economy.

b.Increase in the labor force will reduce output in the economy and consumption in the economy as depicted in the diagram above. Increase in the labor supply in the labor market will also reduce real wages per worker in the labor market.

Rahul Sunny answered 1 year ago

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