Can the market model (3,6) be rewritten in the format of (4.1)? Why? The two-commodity market model (3.12) can be written after eliminating the quantityvariables as a system of two linear equations, as in (3.13'),C₁₁P₁ +0₂ P₂ = -CoY₁P₁+Y/₂P₂ = -10where the parameters co and yo appear to the right of the equals sign. In general, a systemof m linear equations in a variables (x₁, x2,...,xn) can also be arranged into such aformat:411x1 +412x2 +421x1 +922x2 +...+ anxn=d₁+ azn*n=d₂(4.1)am 1x1 + am 2x2 ++amnxn = dmIn (4.1), the variable x₁ appears only within the leftmost column, and in general the vari-able x appears only in the jth column on the left side of the equals sign. The double-subscripted parameter symbol a;; represents the coefficient appearing in the ith equationand attached to the jth variable. For example, azi is the coefficient in the second equation,attached to the variable x₁. The parameter d; which is unattached to any variable, on theother hand, represents the constant term in the ith equation. For instance, di is the constantterm in the first equation. All subscripts are therefore keyed to the specific locations of thevariables and parameters in (4.1). Let the linear demand in the isolated market model be replaced by a quadratic demandfunction, while the supply function remains linear. Also, let us use numerical coefficientsrather than parameters. Then a model such as the following may emerge:Qd = QsQa=4 - p²Qs = 4P 1-(3.6)

Demand refers to the quantity of a product or service that consumers are willing and able to…

Let the linear demand in the isolated market model be replaced by a quadratic demand function, while the supply function remains linear. Also, let us use numerical coefficients rather than parameters. Then a model such as the following may emerge: Qd = Qx Qd=4-p² Q. 4P 1 (3.6)

Let the linear demand in the isolated market model be replaced by a quadratic demand function, while the supply function remains linear. Also, let us use numerical coefficients rather than parameters. Then a model such as the following may emerge: Qd = Qx Qd=4-p² Q. 4P 1 (3.6)

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

Can the market model (3,6) be rewritten in the format of (4.1)? Why?

The two-commodity market model (3.12) can be written after eliminating the quantity
variables as a system of two linear equations, as in (3.13'),
C₁₁P₁ +0₂ P₂ = -Co
Y₁P₁+Y/₂P₂ = -10
where the parameters co and yo appear to the right of the equals sign. In general, a system
of m linear equations in a variables (x₁, x2,...,xn) can also be arranged into such a
format:
411x1 +412x2 +
421x1 +922x2 +
...
+ anxn=d₁
+ azn*n=d₂
(4.1)
am 1x1 + am 2x2 +
+amnxn = dm
In (4.1), the variable x₁ appears only within the leftmost column, and in general the vari-
able x appears only in the jth column on the left side of the equals sign. The double-
subscripted parameter symbol a;; represents the coefficient appearing in the ith equation
and attached to the jth variable. For example, azi is the coefficient in the second equation,
attached to the variable x₁. The parameter d; which is unattached to any variable, on the
other hand, represents the constant term in the ith equation. For instance, di is the constant
term in the first equation. All subscripts are therefore keyed to the specific locations of the
variables and parameters in (4.1).

Let the linear demand in the isolated market model be replaced by a quadratic demand
function, while the supply function remains linear. Also, let us use numerical coefficients
rather than parameters. Then a model such as the following may emerge:
Qd = Qs
Qa=4 - p²
Qs = 4P 1
-
(3.6)

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