## Problem Description

In this demand analysis assignment using SAS, we are tasked with constructing a demand model for Maa mustard oil, considering several influential factors. These include per capita Net State Domestic Product (NSDP), the price of the product, the price of competing products, promotional expenditure, and the month of operation. To accomplish this, we employ Multiple Regression analysis and utilize the SAS statistical software.

**Question 1:** Factors Affecting the Demand Function for Maa Mustard Oil

To construct a demand model for Maa mustard oil, it's imperative to comprehend the influential factors that affect this demand. Here is an in-depth look at these variables:

**Per Capita NSDP (Net State Domestic Product):**Per capita NSDP directly influences income elasticity of demand, which gauges how the quantity demanded reacts to changes in consumer income. This is calculated by dividing the percentage change in quantity demanded by the percentage change in per capita income.**Price of the Product:**The price of Maa mustard oil plays a pivotal role in determining the price elasticity of demand, which reveals how alterations in the product's price affect the quantity demanded. It is obtained by dividing the percentage change in quantity demanded by the percentage change in the price of the product.**Price of Competitors' Product:**The price of competitors' products influences cross elasticity of demand, which assesses how changes in the price of one product affect the quantity demanded of another. Cross elasticity of demand is computed by dividing the percentage change in quantity demanded by the percentage change in the price of competitors' products.**Promotional Expenditure:**The amount spent on advertisements and promotions has a significant impact on the quantity demanded. An increase in promotional expenditure is likely to lead to an upsurge in the quantity demanded.**Month of Operation:**The month of operation plays a crucial role in shaping the demand for Maa Mustard oil. For instance, sales may surge during festival months. To account for this, each month is considered a dummy variable, with March as the reference month to circumvent the dummy variable trap.

The Multiple Regression output from SAS displays an R-squared value of 0.8298.

Parameter Estimates | ||||||
---|---|---|---|---|---|---|

Variable | Label | DF | Parameter Estimate | Standard Error | t Value | Pr > |t| |

Intercept | Intercept | 1 | 3934.25479 | 1893.36143 | 2.08 | 0.0445 |

own_price | Price of product | 1 | -121.15405 | 41.64890 | -2.91 | 0.0060 |

compe_price | Price of competitors product | 1 | 113.48792 | 36.81224 | 3.08 | 0.0038 |

inc_per_capita | Per capita NSDP | 1 | -0.31301 | 0.13842 | -2.26 | 0.0295 |

pro_exp | Promotional Expenditure | 1 | 7.98640 | 1.15801 | 6.90 | <.0001 |

dummy 1 | April | 1 | 655.01454 | 419.70257 | 1.56 | 0.1269 |

dummy 2 | May | 1 | 459.80601 | 423.61763 | 1.09 | 0.2846 |

dummy 3 | June | 1 | 793.62186 | 420.13834 | 1.89 | 0.0665 |

dummy 4 | July | 1 | 577.62617 | 436.75206 | 1.32 | 0.1939 |

dummy 5 | August | 1 | 648.42500 | 450.54716 | 1.44 | 0.1583 |

dummy 6 | September | 1 | 53.65763 | 462.74373 | 0.12 | 0.9083 |

dummy 7 | October | 1 | 283.71817 | 458.39384 | 0.62 | 0.5396 |

dummy 8 | November | 1 | -565.54508 | 455.83485 | -1.24 | 0.2223 |

dummy 9 | December | 1 | -794.68160 | 437.51052 | -1.82 | 0.0772 |

dummy 10 | January | 1 | 392.61141 | 440.69225 | 0.89 | 0.3786 |

dummy 11 | February | 1 | -16.89403 | 434.26288 | -0.04 | 0.9692 |

**Table 1:** Multiple regression output from SAS

**Question 2:** Analyzing the Estimated Demand Function and Elasticities

The estimated demand function for Maa mustard oil is as follows:

demand.Maa=3934.25479−121.15405×own.price+113.48792×compe.price−0.31301×inc.per.capita+7.98640×pro.exp+S

Here's a detailed examination of the model:

- The intercept, represented by 0β0, signifies the expected demand when all explanatory variables are held constant, which amounts to 3,934 rupees.
- The coefficient of own.priceown.price (1β1) suggests an inverse relationship, aligning with the law of demand. It implies that a unit increase in the price of Maa mustard oil will lead to a 121.15 unit decrease in quantity demanded.
- The coefficient 2β2 indicates that the price of competitive products has a positive impact on the quantity of Maa mustard oil demanded, with a unit increase in compe.pricecompe.price leading to a 113.49 unit increase in quantity demanded.
- 3β3 highlights that inc.per.capitainc.per.capita (income) negatively influences the quantity of Maa mustard oil demanded. A unit increase in inc.per.capitainc.per.capita results in a 0.31 unit decrease in quantity demanded, implying that Maa mustard oil is an inferior product.
- The coefficient 4β4 for pro.exppro.exp (promotional expenditure) suggests that a unit increase in promotional expenditure leads to a 7.99 unit increase in quantity demanded, indicating a positive impact.

**Further analysis:
**

The coefficients of the dummy variables are listed in the table. These coefficients represent the expected differences in the quantity of Maa mustard oil demanded in comparison to March, which serves as the reference category. Notably, the negative coefficients for December and February imply higher demand during these months than the base month, March.

**Elasticities of demand:
**

- The price elasticity of demand for own.priceown.price is -0.85452, implying that an increase in the price of Maa mustard oil will lead to a decrease in quantity demanded. Specifically, a 1% change in price results in an 0.85% decline in quantity demanded.
- The cross elasticity of demand for compe.pricecompe.price is 0.90649, indicating that an increase in the price of competitive products triggers a higher demand for Maa Mustard Oil. Consumers tend to seek substitutes for more expensive products, leading to a 0.91% increase in quantity demanded for a 1% change in the price of competitive products.
- The income elasticity of demand for inc.per.capitainc.per.capita is -0.16570, suggesting that an increase in consumers' income decreases the demand for Maa mustard oil. This indicates that Maa mustard oil is an inferior product, as consumers shift to better-packaged and pricier alternatives when their income rises. A 1% change in consumers' income leads to a 0.17% decline in quantity demanded.
- The advertising elasticity of demand for pro.exppro.exp is 0.71099, signifying that an increase in advertising expenditure boosts the quantity of Maa mustard oil demanded.

**Question 3: **Impact of Price Changes on Total Revenue

The price elasticity of demand, with a value of -0.85452, indicates inelastic demand. In an inelastic scenario, total revenue increases as price rises and decreases as price falls. This underscores the direct relationship between price and total revenue.

**Question 4:** Optimal Pricing Scenarios

**Scenario 1: **Incorporating the effect of October, with the remaining dummy variables removed.

- Optimum Price: 99.79 rupees
- Quantity: 12,090.12
- Total Revenue: 1,206,489 rupees

**Scenario 2: **The price of the competitive product increases by 6%.

- Optimum Price: 102.86 rupees
- Quantity: 12,461.7
- Total Revenue: 1,281,789 rupees

In both scenarios, the company benefits from raising its price due to the inelastic demand, resulting in increased total revenue.

**Question 5:** Price and Total Revenue Scenarios

**Scenario 1:** Price elasticity of -0.85452

Price | Quantity Demanded | Total Revenue |
---|---|---|

50.00 | 18,122.54 | 906,126.88 |

55.00 | 17,516.77 | 963,422.20 |

60.00 | 16,911.00 | 1,014,659.82 |

65.00 | 16,305.23 | 1,059,839.74 |

70.00 | 15,699.46 | 1,098,961.96 |

75.00 | 15,093.69 | 1,132,026.47 |

80.00 | 14,487.92 | 1,159,033.28 |

85.00 | 13,882.15 | 1,179,982.39 |

90.00 | 13,276.38 | 1,194,873.80 |

95.00 | 12,670.61 | 1,203,707.50 |

100.00 | 12,064.84 | 1,206,483.50 |

105.00 | 11,459.06 | 1,203,201.80 |

110.00 | 10,853.29 | 1,193,862.40 |

115.00 | 10,247.52 | 1,178,465.29 |

120.00 | 9,641.75 | 1,156,189.68 |

125.00 | 9,035.98 | 1,129,497.97 |

130.00 | 8,430.21 | 1,092,538.56 |

**Table 2: **Price and Total Revenue Scenarios - Scenario 1

**Scenario 2:** Price elasticity of -0.85452

Price | Quantity Demanded | Total Revenue |
---|---|---|

50.00 | 18,865.70 | 943,284.88 |

55.00 | 18,259.93 | 1,004,296.00 |

60.00 | 17,654.16 | 1,059,249.42 |

65.00 | 17,048.39 | 1,108,145.14 |

70.00 | 16,442.62 | 1,150,983.16 |

75.00 | 15,836.85 | 1,187,763.47 |

80.00 | 15,231.08 | 1,218,486.08 |

85.00 | 14,625.31 | 1,243,150.99 |

90.00 | 14,019.54 | 1,261,758.20 |

95.00 | 13,413.77 | 1,274,307.70 |

100.00 | 12,808.00 | 1,280,799.50 |

105.00 | 12,202.22 | 1,281,233.60 |

110.00 | 11,596.45 | 1,275,610.00 |

115.00 | 10,990.68 | 1,263,928.69 |

120.00 | 10,384.91 | 1,246,189.68 |

125.00 | 9,779.14 | 1,222,392.97 |

130.00 | 9,173.37 | 1,192,538.56 |

**Table 3:** Price and Total Revenue Scenarios - Scenario 2

In conclusion, the price at which total revenue is maximized differs between the scenarios: 99.79 rupees in Scenario 1 and 102.86 rupees in Scenario 2. Both scenarios underscore the critical role of price elasticity in determining optimal pricing strategies.