Functions in business and economics
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Transcript of Functions in business and economics
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FUNCTIONS IN BUSINESS AND
ECONOMICSApplications
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Functions
Y – dependent variable RevenueCost of productionProfit
X – independent variableGoods/merchandize manufacturedGoods/merchandize soldTicket sales
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Functions
Function of one variable
Example: Profit from sales of tickets (as a retail seller)
Function of two or more variables
y- Human development indexx- Life Expectancy, w – purchasing power of money, z - Literacy
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Demand Function
Demand function describes consumer behavior in relation
to the price of goods. the quantity y of goods a consumer is
willing to buy at price x
What are your common observations about the behavior of consumers in relation to price of goods?
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Demand Function
Case 1 Negative slopey - price
x- demand
Slope (m, rate of change) is negative
An increase in price results in a decrease in demand
A decrease in price results in an increase in demand
x- demand
y - priceCase 2 Constant slope
Slope (m, rate of change) is constant
An increase/decrease in demand does not affect price
A change in demand leaves price unchanged
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Demand Function
Case 3 Undefined slope
y- price
x demand
Slope m is undefined
Quantity demanded is not affected by priceThe rise and fall in price does not affect demand
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Demand function
Case 4 Increasing slope
y- price
x demand
Slope is increasing
The demand for the product increases when the price increases
An increase in price encourages consumption of the good/merchandize
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Demand Function
Mathematical Model for Demand Function Point-Slope form
Slope-Intercept form General form
ExampleFind the equation of the line that has the slope of 6 and which passes through the point ( 4, 7)𝑦−7=6 (𝑥−4 )
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Demand Function
Find the equation of the line with slope -5 and is equal to 3 when x = 0.
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Demand Function applicationA business sells 20,000 units each month at a price of 100php each. It is projected that monthly sales will increase by 2,500 units for each 2.50php reduction in price.a. Construct the demand equation.
?(20,000, 100)
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Demand FunctionApplication
𝑦−100=−11000
(𝑥−20,000 )How do you transform it to slope-intercept form?
How do you transform it to general form
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Demand Function Application
b. What is the highest price to be paid for this commodity?How would the graph look like?
How do you interpret mathematically the question?
x - demand
y- price(0 , 𝑦 )
𝑦−100=−11000
(𝑥−20,000 )
𝑦−100=−11000
(0−20,000 )
𝑦=120
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Demand Function Application
c. What is the highest quantity demanded for this product?
y- price
x - demand
0,x 𝑦−100=−11000
(𝑥−20,000 )
0−100=−11000
(𝑥−20,000 )
𝑥=120,000
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Demand Function Application
d. How many units will be bought if the price is 80php per unit?
What is x when y is 80php?
Equation in slope intercept form
Solve for x 𝑥=40,000𝑢𝑛𝑖𝑡𝑠
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Demand Function Application
e. What is the price per unit if 25,000 units were demanded?
What is y when x is 25,000 units?
Equation in slope intercept form
Solve for y 𝑦=95 h𝑝 𝑝
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Demand Function Application
f. Sketch the graph of the demand equation
𝑦=120−𝑥1000
x -demand
y price
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Supply Function
Case 1 Positive slope
x – quantity supplied
y price
Slope is positive
As price increases, the supply for the product increases
As price decreases, the supply for the product decreases.
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Supply Function
Case 2 Constant Supply
y price
x – quantity supplied
Slope is constant
The price stays the same regardless of the amount of supplyThe quantity of supply does not affect the price
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Supply Function
Case 3 Slope is undefined
y price
x – quantity supplied
Slope is undefined
Quantity supplied is constant, is not affected by the price
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Supply Function
Case 4 Negative Slope, Decreasing supply
x – quantity supplied
y priceSlope is negative As the price
decreases, supply increases A price decrease is an incentive to produce more
Meron bang ganitong pangyayari in real business situations?
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Supply Function
Yes!