Linear and Non Linear Equation for Economics

Dr. Ananda Sabil Hussein

Demand and Supply

Deman and Supply

Q = quantity

P = price

The demand function is the negative relationship between P and Q which P rises so Q decreases. The demand equation is:

Example

Sketch a graph of demand function

Hence, or otherwise, determine the value ofP when Q = 9Q when P = 10

Market Equilibrium Analysis (Related to Taxes and Subsidy)

The demand and supply functions of a good are given by

Where P, Qd and Qs denote the price, quantity demanded and quantity supplied respectively.

Determine the equilibrium price and quantity

Determine the effect on the market equilibrium if the government decides to impose a fixed tax of $5 on each good.

National Income Determination

Y= C+S

C = consumption

Y = Income

S = Saving

Y = C+I+G

The income that households have to spend on consumer goods is no longer Y but rather Y – T (income less tax) is called disposable income Yd.

 

Given that G = 20 ; I = 35

Calculate the equilibrium level of national income!

The simplest non linear function is known as a quadratic and takes the form

Given the supply and demand functions

Calculate the equilibrium price and quantity.

Total cost function, TC, relates to the production costs to the level of output, Q. Total cost consist of two types elements, fixed cost and variable cost.

TC = FC + (VC) Q.

The profit function is denoted by the Greek letter π and is defined to be the difference between total revenue, TR, and total cost, TC.

Π = TR – TC

If fixed costs are 4, variable costs per unit are 1 and the demand function is

Obtain an expression for π in terms of Q.

For what values of Q does the firm break even?

What is the maximum profit?

Solution:We begin by obtaining expressions for the Total Cost and Total Revenue.

Hence the profit is given by

Break even point is illustratedTR = TC

The number of quantity is even point. Therefore break even point is happening in the 4 unit of quantity. The basic rules of maximum profit is MR = MC

Practice

Given the quadratic supply and demand functions

Determine the equilibrium price and quantity