Question Homework 1. Econ 425 Economics of Public Expenditures

02 Jun Question Homework 1. Econ 425 Economics of Public Expenditures

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 www.gpoaccess.gov/eop/download.html 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!

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