(15 points) Assume a Solow economy with labor-augmenting technological progress, Cobb-Douglas production function that is constant returns to scale in capital and labor (Y = K?(EL)1??), and the share of capital costs in total income that equals 50%. Population growth equals 2%, growth in the efficiency of labor equals 2%, savings rate equals 30%, and the depreciation rate equals 1%.

(a) (5 points) Find consumption per effective worker in the steady state when the savings rate equals 30%.

(b) (5 points) Find consumption per effective worker in the golden rule steady state.

(c) (5 points) Assume that economy was in steady state with the savings rate of 30% and at some point in time increases savings rate permanently to the golden rule savings rate. On a ratio scale, draw the path of consumption per worker on the vertical axis against time on the horizontal axis.

4. (15 points) Assume a Solow economy with labor-augmenting technological progress, Cobb-Douglas production function that is constant returns to scale in capital and labor (Y = KO'(EL)1_"'), and the share of capital costs in total income that equals 50%. Population growth equals 2%, growth in the efficiency of labor equals 2%, savings rate equals 30%, and the depreciation rate equals 1%. (a) (5 points) Find consumption per effective worker in the steady state when the savings rate equals 30%. (b) (5 points) Find consumption per effective worker in the golden rule steady state. (c) (5 points) Assume that economy was in steady state with the savings rate of 30% and at some point in time increases savings rate permanently to the golden rule savings rate. On a ratio scale, draw the path of consumption per worker on the vertical axis against time on the horizontal axis