Consider the basic Solow growth model with the following aggregate Cobb-Douglas production function:Y=AKL^{(1- )}, whereis a parameter and satisfies 0< <1;A>0is exogenous and measures productivity.Acan potentially change over time, and if it does, it changes permanently. Denote the saving rate bys, 0<s<1, and capital depreciation rate by, 0<<1.

a) Using the aggregate production function above, derive the expression for output per worker,y=Y/L, as a function of capital per worker,k=K/L, and the level of technology,A.That is, derive the production function in terms of per-worker quantities.

b)Solve for the steady state level of capital per workerk* and steady state level of output per workery*. How does each of these steady state variables change with depreciation rate? Saving rates? Illustrate your answerswith graphical analysis.

c) Derive the expression for steady-state consumption per worker as a function of steady-state capital per worker. Find the condition that characterizes the golden rule level of steady-state capital per worker. Solve fork*_gold. Find the associated golden-rule level of saving rates_gold.

d) Suppose that a country starts with some positive level of productivityA_1.Suppose that due to a major technological advancement the level of productivity permanently rises to a new higher levelA₂>A₁. Using your answers to part (b) explain how this change will affect the steady state level of capital per worker and output per worker. Also, illustrate these effects using the graphical analysis.