1. Let's track the capital stock, GDP, and rental rate of capital in the simplest Solow economy, one rigged to speed up the process of getting to steady state: Y = KY2 s=20%, 6 = 30%, K, = 0.1 So we're starting off with 0.1 units of capital (much lower than the steady state level of capital, as you'll see), and 30% of K vanishes each yearthat high depreciation rate will speed up the convergence to the steady state. Starting off with such a poor simulated economy offers us a chance to evaluate the theory that a country can be trapped in poverty solely due to past poverty. Remember the key equation of Solow, which comes in a number of guises: Kipn=(1-0)K+ I, Notice that it's just the capital accounting equation, with the single assumption that the annual depreciation rate is fixed! Sometimes you can get a lot of mileage out of an accounting definition: Next period's capital is the capital that hasn't worn out plus the new capital you've added. (a) Report K, Y, for t=0, 1, 2, 3, 4, 5, and separately report K* and Y*, the steady-state values of both. (b) Also, report the annual growth rate of GDP for each of these years-in percent of course. (c) Report the mathematical function MPK, the marginal product of capital, given the assumptions of this model. To be clear, report dY(K)/dK. (d) Report the numerical value of MPK for each of those time periods, 0 to 5. Is it rising over time, falling over time, staying the same, or can't you tell? (e) Draw a simple graph with K on the x-axis and MPK (the actual function, for these given parameter values) on the Y-axis. Draw the curve of the MPK function; feel free to hand-draw and include a screenshot, no need for fancy graphics. (f) On the same graph, plot the values of K and MPK for periods 0-5 and the steady state. (g) Are the dots for (f) on the line you drew in (e), or are the above or below that line? (h) Does the path of (f) look like a movement along a demand curve or a movement of the demand curve? (i) Does the path of (f) look like a movement along a supply curve or a movement of the supply curve? (j) Put it together: \"This looks like a movement of a -~ curve along a fixed . curve.\" (k) The MPK is truly a \"rental rate of capital,\" because in a market that rented physical capital, a voluntary renter would have to be compensated for the annual depreciation. This is thus a \"gross rental rate\" (gross of depreciation). In a typical efficient financial market, capital investors get paid net of depreciation, so financial investors get paid MPK - 4 per unit of capital. With a little algebra, you can find that in the Solow model, when the exponent on capital is , the steady state gross rental rate is \"f (Maybe remember that as \"ads\