4. Consider a Solow model with the production function y = Af(k) = W? where n = 0.03, and 6 = 0.07. The only missing piece that we need before we can find the steady state is S, which we generally have assumed is fixed and exogenous. A major critique of the Solow model is that saving is a byproduct of choices about consumption so it should NOT be treated as exogenous. Maybe we can improve the Solow model by explicitly modeling consumption. Let's try it. 1. Suppose C(k) = 0.6 + 0.5y = 0.6 + 0.5%. (What did we call the 0.5 in this equation in earlier chapters [a Chapter 3]?). If there is no government and the economy is closed the accounting identity for output per worker is y = c + i. Find an equation for the investment function, i(k)? ii. Find the non-zero steady state levels of k. There are two of them. (hint: the equation you get is nasty, so it might help to make a graph at a site like https:[[www.wolframalpha.com or just use that website to solve your equation once you have it set up.) iii. 5 = i/y. Is the savings rate in this model an increasing or decreasing function ofthe capital-labor ratio