Here is the question and answer. Can you explain the steps of the answer?

1- (15 marks) Both population and the workforce grow at the rate of m = 1% per year ina closed economy. Consumption is C= 0.5(1-7)Y, where t is the tax rate on income and Y is total output. The per-worker production function is y = 8 k, where y is output per worker and is the capital-labour ratio. The deprecation rate of capital is 9% per year. Suppose now that there are no government purchases and the tax rate on income is 0. a. * Find expressions for national saving per worker and the steady-state level of investment per worker as functions of the capital-labour ratio, . In the steady state, what are the values of the capital-labour ratio, output per worker, consumption per worker, and investment per worker. (5 marks) b. According to the neoclassical growth model, how would an increase in population growth affects consumption per worker in the long-run (that is, in the steady state)? Explain c. Suppose that the government purchases goods each year and pays for these purchases using taxes on income. The government runs a balanced budget in each period and the tax rate on income is t = 0.5. Repeat part (a). (5 marks) Answer: First, derive saving per worker as sy = y-c - g =[10.5(1-f4] 8k? =0.5(1 N8k =4(1Dk a. When f= 0, sy = 4 (1 0)k = 4k = national saving per worker Investment per worker = (n + d)k = .1k In steady state, sy =(n + d)k, so Ak =0.1k, or 40k? = k, so 1600k =F, so k = 1600. Since k= 1600, y=8 x 1600 = 320, c= 0.5 (1 0) 320 = 160, and (1 + d)k=0.1 x 1600 = 160 = investment per worker |