Finite Math

FINITE MATH 8

FiniteMath

FiniteMath

Supplyversus demand

Supplyanddemand are concepts that require the application of linearequations to solve. Supply refers to the quantity of goods orservices that producers provide on the market at a select periodwhile the demand refers to the capability and willingness of thetarget population to purchase the supplied goods or services.

Alinear equation normally comprises of two unknowns that vary as oneof them changes. In demand and supply, applications of forming andsolving the equations aids in finding the values of the changingvariables, which are the products on the market and also theirrespective prices. Most importantly, they vitally aid inascertaining the equilibrium position in the market to facilitatesound decision making. In applying this concept, the equations arereferred to as functions.

Linearequation mathematical solutions are the best illustrations forunderstanding both the demand concepts in economics. Hence,understanding the solution to linear equations provide the capacityfor one to solve economic problems entailing demand and supply. Whilethe equations can help solve supply and demand equations, linearequations can also help derive the producer and consumer surplusbecause they are directly affected by the level of both in themarket. The demand curve is downward sloping while the supply curveis upward sloping because the former is inversely proportional toprice while the latter is directly proportional to price. Thus, thesame way mathematicians can solve linear equation problems by simplylocating their point of intersection, so can economists identify apoint of equilibrium by simply locating the point of intersectionbetween the demand and supply curves.

Before,illustrating the mathematical application in demand and supplyfunctions, an illustration of linear equations and how they can besolved through the echelon methods will be the best point to start. A linear equation is simply a straight line when plotted on a graph.It presented in the form:

Y=mx+ c (m is the gradient of the line and c is the y-intercept)(Lial,Greenwell, &amp Ritchey, 2012)

Hence,an example of a linear equations is y= 5x-2 or y=-3x+3. The firstequation has a positive gradient, therefore, representing the supplycurve, while the second equation has a negative gradient, therefore,representing a demand curve.

Usingthe Echelon method to solve the linear system:

Y=5x–2 ………………………….. (I)

Y=-3x + 3 ……………………… (ii)

Theechelon solution

Multiplythe second equation with 4

Y=5x – 2

Y=-3x + 3

Y= 5x – 2)3

Y=-3x+ 3)5

3y= 15x -6-iii

5y= -15x +15……….iv

8y= 9

Y= 9/8

Y=1.125

1.125=-3x + 3

X= 1.875/3

X= 0.625 or 5/8

Applicationof the concept in demand and supply

Thesolution to a linear equation is the same tool that an economistsuses to know the price and quantity that is identical for the goodssupplied and the goods demanded. Now that the price of the commodityinfluences demand and supply, both functions are equated to get theboth the price and quantity. In respect to their gradients, Equation(i) above represents a hypothetical supply function and equation (ii)a demand function. In the equation above, the market equilibriumpoint of both equations (which in this case represent supply andeconomic functions) is:

Supply: P= 2Q – 2

Demand: P= -0.5Q + 3

Theequation indicated below illustrates the equilibrium position to the above linear functions:

2Q– 2 = -0.5Q + 3

2.5Q= 5

Q= 2 units

P= 2 (2) -2

P= 2 dollars or any other unit of currency

Thus,the equilibrium price and quantity is represented by coordinates (2,2)

Example:

TheDepartment of State is intends to hire 300 technicians per year ifthe minimum wage is $7000 and 250 technician per year if the averageminimum wage is $8000. However, only 150 qualified technicians arewilling to take up jobs in the state department if the minimum wagedrops to $6000 and 250 if the minimum wage is $6500. What is theaverage minimum wage and number of technicians willing to take upjobs in the Department of State?

Demandfunction:

M= 8000 – 7000 = -20

250– 300

p-7000 = – 20 (q -300)

p=-20q + 13000

Supplyfunction:

M=6500 – 6000 = 5

250-150

P-6000 = 5 (q – 150)

P-6000= 5q – 750

P=5q +5250

Thewage level and number of technicians who can join the department areequal at equilibrium. Thus,

25q= 7750

q=310

p=5 (310) + 5250

p=6800

Prepresents the equilibrium minimum wage of $6800 and q represents thenumber of technicians that the department of state can hire per year.

Inreal life people use the term demand to refer to how much of aproduct can sell on the market and supply to refer to the actualproducts on the market in the given period of time.

Reference

Lial,M. L., Greenwell, R. N., &amp Ritchey, N. P. (2012). Finitemathematics(10th ed.). Boston, MA: Pearson Education.