algebra ...............

Suppose the per worker production function in an economy is given by the following: y = k\" where y is production per worker, and k is physical capital per worker. This function links the amount of capital an average worker can use to the income this person can earn in an economy. Assume for simplicity that human capital and natural resources input remain constant and is not included in the function. At the same time, the capital stock gets old through wear and tear, which is a cost to the economy. The depreciation cost of the capital is incurred at a constant rate and is equal to y = 0.4k The Solow-Swan growth model [1956} in the economic growth literature posits that the accumulation of capital per worker in an economy should proceed until the rate of depreciation of capital is as high as the income produced by it. {a} At what level of capital will the income of a worker be the same as depreciation of capital? Show all your steps in finding the answer. [6 marks] (b) Draw a graph with production per worker (y) in the vertical axis and capital per worker (it) on the horizontal axis. Then illustrate the two equations on the graph. showing clearly the point where they meet. [7 marks) (c) A friend of yours argues that since production is income and depreciation is cost, then the best position for an economy (and hence the workers) is when the difference between income and cost is growing at the fastest rate. Explain in detail whether you agree or not. 1-! ___l._s