Monte Carlo Simulation

This page has been left emptied for a while. It was hard for me to find a good example for this page since Monte Carlo Simulation is a very broad field. What example would be appropriate for this site? It is not an easy question. However, due to great demand on this topic, I have decided to put up a "Mickey Mouse" version of Monte Carlo Simulation. Please note that this example make a lot of loose assumptions which may or may not reflected the real world scenario.

What is a Monte Carlo Simulation? Well, think about it as a computation process that utilized random numbers to derive an outcome(s). So instead of having fixed inputs, probability distributions are assigned to some or all of the inputs. This will generate a probability

distribution for the output after the simulation is ran.

Here is an example. A firm that sells product X under a pure/perfect competition market* wants to know the probability distribution for the profit of this product and the probability that the firm will loss money when marketing it.

The equation for the profit is: TP = TR - TC = (Q*P) - (Q*VC+FC)

Assumption:

The average profit for this investment is $29,546 as shown on cells G25 after 50,000 iteration is ran. The probability that the profit of the investment turns out to be negative (loss money) is 22.28% as shown on cell C24. The probability distribution of the profit > X is display on column F and G. For example, there is 65% of chance that the profit will be greater than $12,481. The probability distribution is quite normal as shown on the figure. The mean is also very close to the median. This is due to the probability distribution that we assigned to the variables.

What is a Monte Carlo Simulation? Well, think about it as a computation process that utilized random numbers to derive an outcome(s). So instead of having fixed inputs, probability distributions are assigned to some or all of the inputs. This will generate a probability

distribution for the output after the simulation is ran.

Here is an example. A firm that sells product X under a pure/perfect competition market* wants to know the probability distribution for the profit of this product and the probability that the firm will loss money when marketing it.

The equation for the profit is: TP = TR - TC = (Q*P) - (Q*VC+FC)

Assumption:

- The Quantity Demanded (Q) flucturates between 8,000 and 12,000 units and is uniformly distributed.
- Variable Cost (VC) is normally distributed (with mean = 7, Sd = 2) truncated on both sides (with a minimum of 7 / 2 and a maximum of 10).

- Market Price (P) is normally distributed (with mean = 10, Sd = 3) truncated on the left-hand side (with a minimum of 1).

- Fixed Cost (FC) is $5,000.

- Under perfect competition market, the firm does not have the influence to affect the price of this product - the firm takes the market price as a given, dP/dQ = 0.

The average profit for this investment is $29,546 as shown on cells G25 after 50,000 iteration is ran. The probability that the profit of the investment turns out to be negative (loss money) is 22.28% as shown on cell C24. The probability distribution of the profit > X is display on column F and G. For example, there is 65% of chance that the profit will be greater than $12,481. The probability distribution is quite normal as shown on the figure. The mean is also very close to the median. This is due to the probability distribution that we assigned to the variables.

Figure 1.

Figure 2.

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