a) Consider the Solow growth model where Y=F(K,L) . Y is output, K is capital stock and L is the work force. Derive the steady state equilibrium condition of this model if depreciation rate is zero, s is the savings rate , and n is the labour force growth rate, and draw the diagram showing the equilibrium [10 marks] b) Singapore in the 1980s experienced a large inflow of labour . Assume this is one off increase in L (A one period increase in stock of labour). Analyse the impact of this change in the short run and the long run on output per worker. growth of output per worker and capital labour ratio and illustrate the impact on steady state equilibrium in a diagram. [10 marks] c) Assume F(K)=K^1/3L^2/3 ,s is 12% and n is 3% . Specify the production function and find how much capital per worker will change over time starting from k=4 . What is the steady state value of k?[10 marks]

a) In the Solow growth model, the steady-state equilibrium condition occurs when the capital stock per worker (k) remains constant over time. This happens when the investment per worker (sY) is equal to the depreciation per worker (δk), where δ is the depreciation rate.<br /><br />The equation for investment per worker is sY, and the equation for depreciation per worker is δk. Setting these two equal to each other, we get:<br /><br />sY = δk<br /><br />To find the steady-state value of k, we can rearrange the equation:<br /><br />k = sY/δ<br /><br />This equation represents the level of capital per worker at which the economy is in steady-state equilibrium.<br /><br />b) In the short run, the one-off increase in labor will lead to a decrease in output per worker, as the capital stock per worker remains constant. This is because the additional workers will have to share the same amount of capital, resulting in lower productivity.<br /><br />In the long run, however, the economy will adjust to the new steady-state equilibrium. As the capital stock per worker increases due to the higher savings rate (s), output per worker will also increase. The growth rate of output per worker will eventually return to the original steady-state level, which is determined by the production function and the parameters of the model.<br /><br />The impact of the one-off increase in labor on the capital-labor ratio can be illustrated in a diagram. Initially, the capital-labor ratio will decrease due to the increase in labor. However, as the economy adjusts to the new steady-state equilibrium, the capital-labor ratio will increase back to its original level.<br /><br />c) Given the production function F(K) = K^(1/3)L^(2/3), we can substitute the values of s and n into the steady-state condition to find the steady-state value of k.<br /><br />sY = δk<br /><br />K^(1/3)L^(2/3) = δk<br /><br />k = (K^(1/3)L^(2/3))/δ<br /><br />To find how much capital per worker will change over time starting from k=4, we can use the equation for the change in capital per worker:<br /><br />Δk/k = (sY/δ) - n<br /><br />Substituting the given values, we get:<br /><br />Δk/k = (0.12 * K^(1/3)L^(2/3))/δ - 0.03<br /><br />Solving this equation will give us the change in capital per worker over time.