Numerical Demand,
Elasticity, Forecasting
Dr. Sanjib Jaypuria
SME, KIIT University
Calculate the 3-month moving average for April to December.
April: (100 + 120 + 95) / 3 = 105
May: (120 + 95 + 110) / 3 = 108.33
June: (95 + 110 + 130) / 3 = 111.67
July: (110 + 130 + 105) / 3 = 115
August: (130 + 105 + 125) / 3 = 120
September: (105 + 125 + 115) / 3 = 115
October: (125 + 115 + 140) / 3 = 126.67
November: (115 + 140 + 120) / 3 = 125
December: (140 + 120 + 135) / 3 = 131.67
Finding the Trend Equation:
To find the trend equation, we'll use linear regression. The equation of a
straight line is: Y = a + bX
where: Y is the dependent variable (total sales)
X is the independent variable (year)
a is the y-intercept
b is the slope
Mean of X (X̄ ) = (2001 + 2002 + 2003 + 2004 + 2005 + 2006 + 2007) / 7 = 2004
Mean of Y (Ȳ) = (1150 + 1020 + 3050 + 3000 + 950 + 3060 + 4030) / 7 = 2322.86
b = Σ((Xi - X̄ ) * (Yi - Ȳ)) / Σ((Xi - X̄ )^2)
b ≈ 490.43
a = Ȳ - b * X̄
Substituting the values, we get: a ≈ -978457.14
Therefore, the trend equation is: Y = -978457.14 + 490.43X
The trend equation indicates a positive linear relationship between
the year and total sales. The slope (490.43) suggests that, on
average, total sales increase by approximately 490 units per year.
Given:
•Demand function: Q = 0.70P + 0.45A
• Q = Quantity demanded
• P = Price per pair
• A = Advertisement cost per unit
•Current sales: 50,000 pairs
•Current price: ₹600 per pair
•New advertisement cost: ₹1 lakh
Step 1: Find the current advertisement cost (A)
We know that Q = 50,000 and P = 600. We can use the demand
function to find A.
50,000 = 0.70 * 600 + 0.45A 50,000 = 420 + 0.45A 0.45A =
49,580 A = 49,580 / 0.45 ≈ 110,177.78
Step 2: Calculate new quantity demanded (Q)
We are given the new advertisement cost, A = 1,00,000 (₹1
lakh). We also know the price, P = 600. We can use the demand
function to find the new quantity demanded.
Q = 0.70 * 600 + 0.45 * 1,00,000 Q = 420 + 45,000 Q = 45,420
Therefore, the new annual sales will be 45,420 pairs of shoes.
Revenue concepts are fundamental in economics, particularly in understanding how firms
generate income from selling goods and services. Here’s a breakdown of these concepts:
1. Total Revenue (TR)
Total Revenue is the total amount of money a firm receives from selling its product. It is
calculated as:
2. Average Revenue (AR)
Average Revenue is the revenue earned per unit of output sold. It is the total revenue
divided by the number of units sold.
3. Marginal Revenue (MR)
Marginal Revenue is the additional revenue that a firm earns by selling one more unit
of a product. It is calculated as:
4. Relation between TR, AR, MR, and Price Elasticity of Demand
Price elasticity of demand measures how responsive the quantity demanded is to a
change in price. The relationship between these revenue concepts and price elasticity is
crucial:
•Elastic Demand (|Elasticity| > 1):
• In this case, a decrease in price leads to a proportionally larger increase in quantity
demanded, which increases total revenue. Therefore, when demand is elastic, MR
is positive, and TR increases as price decreases.
•Inelastic Demand (|Elasticity| < 1):
• Here, a decrease in price leads to a proportionally smaller increase in quantity
demanded, which decreases total revenue. When demand is inelastic, MR is
negative, and TR decreases as price decreases.
•Unitary Elastic Demand (|Elasticity| = 1):
• At this point, a change in price leads to a proportional change in quantity
demanded, so total revenue remains constant. MR is zero when demand is unit
elastic.
Q1: Nitya Food has observed that the demand for his lunch package has been
significantly affected by the income level of residents in the neighborhood.
After conducting the study he found that the daily sale of its number of lunch
packages (Q) and average monthly income (I) are related as: Q=500+0.2I.
Find the income elasticity of the product if the income increases from
₹10,000 to ₹20,000.
Q2: QD = 20 + 4P and QS = 50 - 2P. Find out the equilibrium price and
quantity from the following demand and supply function.
Q3: If the demand function is given as 𝑃=120−1.5 𝑄P=120−1.5Q, find
the output (Q) and price per unit (P) where total revenue of this producer
is maximized.
Q4:
Q5: From the following demand function, Q=10,000+12Y (where Q is the quantity demand
for the commodity and Y is the income of the consumer per month), find out the
income elasticity of demand if income of the consumer is Rs. 40,000/- per month.
Q1
Q2
Q3
Q4:
Q5:
