MATHEMATICAL ECONOMICS
PRACTICE PROBLEMS WEEK 10
1.
In the IS-LM model for a closed economy, let the goods and money markets be defined by:
Goods Market
Y=C+I+G
C = C(Y T)
I = I(r)
T = T(Y)
Money Mark
MATHEMATICAL ECONOMICS
PRACTICE PROBLEMS WEEK 6 continued
1.
Consider an economy with a labor market, an output market, and a numeraire
commodity. There are 1000 identical consumers and 100 identical
I)
U (I) = ln(I)
For example, a consumer has a utility function U(I)=In( I ), where I is
income, suppose that a consumer faces a probability p of experiencing a loss of L,
where L < I. Let B be the am
MATHEMATICAL ECONOMICS
PRACTICE PROBLEMS WEEK 9
1.
Consider the one-commodity market model:
Qd = a bP
Qs = -c + dP
Qd = Qs
Assume all parameters in the model are positive. Use Cramers Rule to solve fo
MATHEMATICAL ECONOMICS
PROBLEM SET 2
DUE: Wednesday, March 9, 2016
1.
Let the consumers utility function over goods X and Y be denoted U = U(X, Y).
a. Write down the total differential dU in terms of
1
Xiaoyi Yang, Chen Bian, Zihao Xu
ECON 2301
Stan McMillen
April 29th, 2016
Utility is a measure of customers preference among alternative products. Higher
utility is usually the primary determinant f
MATHEMATICAL ECONOMICS
PROBLEM SET 3
DUE: THURS., April 6, 2016
1.
(10 points) A firm is perfectly competitive in the output and capital markets, sells its output
at a market price of P, has the stric
Xiaoyi Yang, Chen Bian, Zihao Xu
ECON 2301
Stan McMillen
April 18th, 2016
The Demand for Insurance (First Draft)
Higher utility is usually the primary determinacies for individuals choice of
consumpti
MATHEMATICAL ECONOMICS
PRACTICE PROBLEMS WEEKS 7- 8
1.
Consider the national income model defined by the equations:
Y=C+I+G
C = a + b(Y T)
T = d + tY
Write this system of equations in matrix notation,
MATHEMATICAL ECONOMICS
WEEK 1-2 NOTES, Fall 2015
CHIANG, CHAPTER 2: ECONOMIC MODELS (CONTINUED)
HNIVARIATE VS. MDLTIVARIATE FUNCTIONS
0 A unrivariate function is a function ofa single variable, y = f(
1.
Let f(x1, x2) = 2x12 4x22 + 8x1x2 + 16x1 + 32x2. Find the values x1* and x2* that satisfy the
first order conditions. Do the second-order conditions for a maximum or a minimum hold at the
point (x1
1.
A monopolistic firm sells a single output in two segmented markets. In market 1, the
inverse demand function is P1 = 100 5Q1, and in market 2, the inverse demand
function is P2 = 120 2Q2. The cost
1. The total money supply M has two components: bank deposits D and cash holdings C,
which we assume to bear a constant ratio C/D=c, 0<c<1. The high-powered money H is
defined as the sum of cash holdi
Homework 10
April 20, 2017
Question 1 Given the cost function C=2a+2b which subjects
to the production constraint Q(a, b)=a0.5 b0.5 =10.
(a)Write down the Lagrangian function
(b)Solve for the a ,b , a
Chiang/Wainwright: Fundamental Methods of Mathematical Economics
CHAPTER 9
EXERCISE 9.2
1. Find the stationary values of the following (check whether they are relative
maxima or minima or inflection p
1.
A consumer has the utility function U(x1, x2) = x11/4x23/4. The price of good 1 is 10, the price of
good 2 is 20, and the consumers income is 200.
a.
Use the Lagrange multiplier technique to find t
ECON 2301-003: MATHEMATICAL ECONOMICS
PROBLEM SET 4
DUE: WEDNESDAY, April 27, 2016
1.
A monopolistic firm sells a single output in two segmented markets. In market 1, the
inverse demand function is P1