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Econ425 Economics of Public Expenditures Fall 2014 homework 1




Question;Homework 1.;Econ 425 Economics of Public Expenditures;Fall 2014;Problem 1;Consumer wants to maximize happiness given by utility;function u(c1, c2) =?1 log c1 +?2 log c2. His/her;income is M and the prices of goods 1 and 2 are p1, p2.;(a) Write down the problem of the consumer.;(b) Write down the Lagrangian for the problem.;(c) Write down the first order necessary conditions (FOCs);for c;?;1, c?;2,??.;(d) Use FOCs to find optimal c;?;1, c?;2 as functions of p1, p2, M. Hint: Use FOC for c1 to solve;for c1 in;terms of? and FOC for c2 to solve for c2 in terms of?;plug these into the budget constraint, solve;the resulting equation for? and finally plug it back into;the expressions for c1, c2.;Problem 2;Consider an endowment economy with two consumers - Tom Hanks;and Wilson, and two goods - coconuts;and fish. Denote by c;TH, cW, fTH, fW the consumption of coconuts and fish by Tom;Hanks an Wilson;respectively. Assume that their utility functions are;U;TH(c;TH, fTH) = B log c;TH + log f;TH;U;W (c;W, fW) = B log c;W + log f;W;Tom Hanks an Wilson don?t have money, but they do have;endowments of coconuts and fish which we denote;by e;TH;c, eW;c, eTH;f, eW;f.;(a) Suppose that prices of fish pf and coconuts pc are;determined by competitive markets. Write down;the consumer?s problem for Tom Hanks and the consumer?s;problem for Wilson.;(b) Let Mi denote the total value of endowments of the;consumer i (where i can be TH or W). Write the;expression for Mi using pc, pf, ei;c, ei;f. Write down the optimal choices c;i?, fi?;in terms of pc, pf, ei;c, ei;f, B.;Do not use Lagrangeans, just adapt the results from Problem;1(d) appropriately.;(c) Use c;TH?, cW?, fTH?, fW?;from part (b) to write the expression for the total demand;for coconuts, and;the total demand for fish in this economy.;(d) Draw supply-demand diagrams showing the market for;coconuts and the market for fish. Label the;equilibrium prices p;?;c and p;?;f. Hint: Be particularly careful about the shape of the;supply curve!;(e) Suppose now that there is a government that needs Gf;fish. To obtain Gf government imposes lump;sum tax T on each consumer, and uses this revenue to;purchase fish in the market for fish. Write the;problem of consumer i in the presence of government.;(f) Write down the budget constraint of the government.;(g) Write down the market clearing conditions for the two;markets in the presence of government.;(h) Consider the market clearing condition for fish. Suppose;that p;?;c;is fixed at 1, how does the presence;of government affect equilibrium price p;?;f;? Show this effect in the supply-demand diagram for the fish;market.;1Problem 3;Go to the webpage of Economic Report of the President; and;click on the link for year 2014. Obtain Population from;Table B11. Obtain Federal government receipts;outlays, surplus/deficit, debt and GDP from Table B19.;Remove row called ?Transition quarter? from B-19 and;construct the following time series;1. total federal receipts as % of GDP;2. total federal outlays as % of GDP;3. federal surplus/deficit as % of GDP;4. gross federal debt as % of GDP;5. gross federal debt per capita;Then create the following charts;1. A line chart with receipts and with outlays as % of GDP;(both time series plotted together);2. A line chart with deficit as % of GDP;3. A line chart with debt as % of GDP;4. A line with debt per capita;Find who was president in US in which years since 1945;whether he was Republican or Democrat, and add;this information to your charts (draw vertical lines;separating presidents). Here is an example to give you;the idea what your charts should look like (this chart;however shows different time series than those you;should plot).;Comment briefly the four charts that you have obtained (at;least three observations about each chart).;Submit only charts and comments, do not print out tables!;2


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