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*, x2*)? What is going on at this point?
Let f(x1, x
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 function depends only on the total amount of output
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.
Use the Lagrange multiplier technique to find the amounts of x1 and x2 that
maximize the consumers uti
Chiang/Wainwright: Fundamental Methods of Mathematical Economics
1. Find the stationary values of the following (check whether they are relative
maxima or minima or inflection points), assuming the domain to be the set of
all real n
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 , and
(c)Check the second-order condition for minimum
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 holdings held by the public, i.e, C and the reserves held by
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(x).
0 ?O\~(n0mio.,\g -. \(r. ao-HMX +OZXL+ -n