Suppose that you have the standard Solow model with both labor augmenting productivity growth and population growth. The production function is Cobb-Douglas. The law of motion of capital per efficiency unit of labor is given by

k=1[sAk+(1)k].t+1(1+z)(1+n)t t

(b) Create a file in a spreadsheet app of your choosing. Suppose that the level of productivity is fixed atA= 1. Suppose thats= 0.2and= 0.1. Suppose that = 1/3. Letz= 0.02andn= 0.01. Solve for a numeric value of the steady state capital stock per efficiency unit of labor.

(c)Suppose that the capital stock per worker initially sits in the steady state in period 1. Create a column of periodst= 1, 2, ..., 100. Create a column of capital per efficiency unit of labork.Assume the economy sits in the steady state in periods 1 through 9. in period 10, assume that there is an increase in the population growth rate from n= 0.01ton= 0.02. Use the law of motion of capital to calculate the values of capital stock per efficiency unit of labor in periods 10 through 100. Produce a plot showing the path of the capital stock per efficiency unit of labor from period 1 to period 100.

(d)Assume thatN1= 1andZ1= 1. Calculate the values ofNandZin periods 1 through 100. Use these values to create a series of capital stockper unit of workin periods 1 through 100. Take the natural log of the capital stock per unit of work and produce a plot showing the path of the capital stock per unit of work from period 1 to period 100.

e)How does the increase in the population growth rate affect the dynamic path of the capital stock per worker?