Econ 102 Summer 2, 2007: Steady State Analysis of an Ant Economy, Assignments of Economics

Download Econ 102 Summer 2, 2007: Steady State Analysis of an Ant Economy and more Assignments Economics in PDF only on Docsity! Econ 102, Summer 2, 2007, Nirav Mehta Take an economy of ants where there is one CRS ant farm using Cobb-Douglas technology, Yt = ztK 1 2 t N 1 2 t . Ants have utility U(ct) = log(ct). Since ants are genetically predisposed to saving a certain fraction of their incomes, they save a constant fraction, s, of their gross income. The ant population grows exogenously according to Pt+1 = Pt(1 + ρ), and the law of motion for capital is Kt+1 = Kt(1− δ) + It. 1. Write the explicit form of the per ant production function, yt = f(kt). 2. In words, what is a steady state in per ant capital? Why are we looking for a steady state in terms of per ant values, instead of aggregate values? 3. Fix zt = z, so technology remains constant. Say ants save half of what their gross income. What is the steady state level of per ant capital? What is steady state consumption, ct? 4. What are the effects of increases in z and ρ on steady state levels of per ant output, consumption, and capital? How about on the growth rates for per ant and aggregate values? Show your answer both analytically and graphically. (graphically for steady state per ant capital, analytically for everything else) 5. Take the per ant law of motion for capital. Does per ant capital grow faster when we have higher or lower initial capital? 6. Now take some lazy grasshoppers who save only .1 of their gross income. Would you rather be an ant or a grasshopper, holding everything else equal? 7. Let’s go back to dealing with ants. Now say there is ant government spending, which is a constant fraction of output. Ants still save a constant fraction s of their gross income. How does this change the levels of steady state per ant output and consumption, and the growth rates of per ant and aggregate values? 1