Equilibrium in a single market model, Managerial Economics

Equilibrium in a single market model

A single market model has three variables: the quantity demanded of the commodity (Qd), the quantity supplied of the commodity (Qs) and the price of the commodity (P).  equilibrium is assumed to hold in the market when the quantity demanded (Qd) = Quantity Supplied (Qs) .  It is assumed that both Qd and Qs are functions.  A function such as y = f (x) expresses a relationship between two variables x and y such that for each value of x there exists one and only one value of y.  Qd is assumed to be a decreasing linear function of P which implies that as P increases, Qd decreases and Vice Versa.  Qs on the other hand is assumed to be an increasing linear function of P which implies that as P increases, so does Qs.

Mathematically, this can be expressed as follows:

Qd = Qs

Qd = a - bP where a,b > 0. ............................(i)

Qs = -c + dp where c,d >0. ...........................(ii)

Both the Qd and Qs functions in this case are linear and can be expressed graphically as follows:

850_one market model.png

Once the model has been constructed it can be solved.

At equilibrium,

Qd = Qs

\a - bP = -c + dP

2342_Untitled.png = a + c

        b + d

To find the equilibrium quantity 2007_supply.png, we can substitute into either function (i) or (ii).

Substituting 2342_Untitled.png into equation (i) we obtain:

2007_supply.png = a - b (a+c) = a (b+d) - b (a+c) = ad -bc

              b + d                 b + d             b + d

Taking a numerical example, assume the following demand and supply functions:

2342_Untitled.png = 100 - 2P

Qs = 40 + 4P

At equilibrium, Qd = Qs

100 - 22342_Untitled.png = 40 + 42342_Untitled.png

              62342_Untitled.png = 60

            2342_Untitled.png = 10

Substituting P = 10, in either equation.

Qd = 100 - 2 (10) = 100 - 20 = 80 = Qs

A single market model may contain a quadratic function instead of a linear function.  A quadratic function is one which involves the square of a variable as the highest power.  The key difference between a quadratic function and a linear one is that the quadratic function will yield two solution values.

 

In general, a quadratic equation takes the following form:

ax2 + bx + c = 0 where a ¹ 0.

Its two roots can be obtained from the following quadratic formula:

X1, X2 = -b + ( b2 - 4ac)

                        2a

Given the following market model:

Qd = 3 - P2

2 = 6P - 4

At equilibrium:

3 - P2 = 6P - 4

P2 + 6P - 7 = 0

Substituting in the quadratic formula:

a =1, b = 6, c = -7

= - 6 +Ö 62 - 4 (1 x - 7)

                2 x 1

1000_supply1.png

P = 1 or -7 (ignoring -7 since price cannot be negative)

2342_Untitled.png = 1

Substituting 2342_Untitled.png = 1 into either equation:

Qd = 3 - (1)2 = 2 = Qs

2007_supply.png = 2

Posted Date: 11/27/2012 7:07:41 AM | Location : United States







Related Discussions:- Equilibrium in a single market model, Assignment Help, Ask Question on Equilibrium in a single market model, Get Answer, Expert's Help, Equilibrium in a single market model Discussions

Write discussion on Equilibrium in a single market model
Your posts are moderated
Related Questions
Q. Show the Fixed Proportion Production Function? A fixed proportion production function is one in that technology needs a fixed combination of inputs, say labour and capital,

A MATHEMATICAL APPROACH TO REVENUE AND COST FUNCTIONS Recall that TR = P x Q This implies that P(AR) = TR                                     Q For example, assuming

with the of evidence comprehensively discuss the market structure in the south African mobile telecommunications industry

Calculate point elasticity of demand for demand function Q=10-2p for decrease in price from Rs. 3 to 2

What is the goal of a firm?

State the difficulties in the measurement of profit.

Using the CD data estimate a quadratic cost function. Test the hypothesis that there is diminishing marginal cost. Be sure to state what critical value you are using. Then, using t

Factors affecting the long run trend of the Terms of Trade for developing countries Most Third World countries have been faced by a fall in their terms of trade over the long

FACTORS RESPONSIBLE FOR WAGE DIFFERENTIALS BETWEEN OCCUPATIONS The major cause is demand and supply for the particular labour concerned, but other causes could be: i.

Explaination of the Marris Model