22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁402P₁ - P₂, D₂ = 5P₁ - 2P₂ + 16, S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4.
22. Models of markets. Determine the equilibrium solution (D₁ = S₁, D2 = S₂) of the two-commodity market with linear model (D, S, P = demand, supply, price; index 1 = first commodity, index 2 = second commodity) D₁402P₁ - P₂, D₂ = 5P₁ - 2P₂ + 16, S₁ = 4P₁ P₂ + 4, S₂ = 3P₂ - 4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 22
Transcribed Image Text:17-21 MODELS OF NETWORKS
In Probs. 17-19, using Kirchhoff's laws (see Example 2)
and showing the details, find the currents:
17.
16 V
18.
to Probs. 11-14 and to some larger systems of your
choice.
19.
292
1₁
4Ω
4Ω
12 V
EV₁
W
192
32 V
292
13
11
√1₂
1292
1₂
R₁ Q
24 V
1₂
13
892
R₂
www
20. Wheatstone bridge. Show that if Rx/R3 = R₁/R₂ in
22. Models of markets. Determine the equilibrium
solution (D₁ = S₁, D2 = S₂) of the two-commodity
market with linear model (D, S, P = demand, supply,
price; index 1 = first commodity, index 2 = second
commodity)
D₁ = 402P₁ - P2,
D₂ = 5P₁ - 2P₂ + 16,
23. Balancing a chemical equation x₁C3H8 + x20₂-
x3CO₂ + x4H₂O means finding integer X1, X2, X3, X4
such that the numbers of atoms of carbon (C), hydrogen
(H), and oxygen (O) are the same on both sides of this
reaction, in which propane C3H8 and O₂ give carbon
dioxide and water. Find the smallest positive integers
X1,***, X4.
S₁ = 4P₁ P₂ + 4,
S₂ = 3P₂ - 4.
24. PROJECT. Elementary Matrices. The idea is that
elementary operations can be accomplished by matrix
multiplication. If A is an m X n matrix on which we
want to do an elementary operation, then there is a
matrix E such that EA is the new matrix after the
operation. Such an E is called an elementary matrix.
This idea can be helpful, for instance, in the design
of algorithms. (Computationally, it is generally prefer-
able to do row operations directly, rather than by
multiplication by E.)
(a) Show that the following are elementary matrices,
for interchanging Rows 2 and 3, for adding -5 times
the first row to the third, and for multiplying the fourth
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