Firm Demand Model (return to Monte Carlo
Application)
The firm demand is described by the equation below:
Firm Demand (FD) = Total Industry Demand (TID)*Market Share (MS) = TID *RD/N
FD = TID*RD/N
where TID =
130249.2813+132.2283Quarter-358.6135(Avg.Price)+0.2634(Avg.Advertising)
and RD =
16.13-16.44PREL+0.7796AREL+0.5334RD1
Below are descriptions of the three types are variables that
contribute to the Model: Variables
involving uncertainty, Forecast variables, and Decision variables.
Variables
Involving Uncertainty
In the above model, the variables involving uncertainty include the Average Price and Average Advertising.
Average Price - Summary Measures
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Count |
19.000 |
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Mean |
93325.789 |
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Median |
93400.000 |
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Standard deviation |
9828.045 |
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Minimum |
76800.000 |
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Maximum |
108570.000 |
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Range |
31770.000 |
Average Advertising - Summary Measures
|
Count |
19.000 |
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Mean |
377.784 |
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Median |
378.900 |
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Standard deviation |
6.103 |
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Minimum |
365.000 |
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Maximum |
387.500 |
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Range |
22.500 |
From the above tables, it is evident that since
the mean and median for both average price and average advertising are almost
equal. So, for both these variables, we will use the normal distribution.
Here are the assumptions:
Assumptions: Average Price
Normal distribution with parameters:
Mean = 378
Standard Deviation = 6.103
Assumptions: Average Advertising
Normal Distribution with parameters:
Mean = 93326
Standard Deviation = 9828
Forecast
Variables
The next step is to identify the variables that
are being forecasted. In this case, we are forecasting Firm Demand (FD) and
Market Share (MS).
Decision
Variables
We chose the Firm's price and Firm's
advertising as our decision variables. We chose the following values for these
variables:
Firm Price = $366
Advertising = $115000
Model Used For Simulation (To access the spreadsheet model, please click here)
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Model for forecasting Firm Demand |
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Inputs |
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Outputs |
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Quarter # |
20 |
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Total Industry Demand |
21920.01 |
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Estimates for industry (for Quarter 20) |
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Relative Demand |
1.221271 |
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Market Share |
0.122127 |
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Estimated Average Price |
378 |
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Firm Demand |
2677.028 |
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Estimated Average Advertising |
93326 |
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Number of firms |
10 |
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Firm Decisions (for Quarter 20) |
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Price |
366 |
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Advertising |
115000 |
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Historical data for quarter 19 |
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Firm Demand |
3000 |
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Total Industry Demand |
32850 |
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