- Common Pool Resource Problem
- Limits to Growth
- Success to Successful
Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died.
mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it.
F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model.
Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”.
Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1.
Assignment 3 – Complex Systems
Ryan Salvaggio - 43668070
The Model
This model conceptualizes the effects on a real-estate market-model utilizing agent based modelling. This model utilizes basic economic principles of supply and demand.
The model bases itself on two Agents - one being ‘Customers’ of the real estate market model, whilst the other being the Real estate itself, coined 'Houses'.
Consumers (Demand)
The Agent population, ‘Consumers’ specifies the total amount of people whom can potentially become buyers within the market. This is limited to 30 for conceptual purposes. The Agent ‘Consumer’ exists in two states, either being an ‘Active Customer’ (Active) or an ‘Inactive Customer’ (Inactive). The transition from Inactive to Active occurs upon the basis that the ‘Budget’ of the Consumer meets the desired price of the marketplace, this is specified through the variable ‘Budget’ defining the probability that this transition will occur – this is adjustable by the user indicating a highly resistive or by accepting the market. ‘Budget’s probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.
Upon transitioning into an active state an ‘Active consumer’ will attempt to find the closest ‘For sale household’, this is represented and carried out through the ‘Enter’ action. Upon finding a household the consumer and house will both return to their respected inactive state thus repeating the process.
Demand – ‘Count of active customers – demand’ is then calculated by a count of Consumers transitioned and currently in the Active state. A high demand would be indicative through a high ‘Budget’ responsiveness whilst a low demand would be indicative of a low ‘Budget’ responsiveness. The increase in Price and hence supply of household thus reduces demand and vise versa.
House (Supply)
The Agent population, ‘Houses’ specifies the total amount of households that can potentially become for sale within the market. This is limited to 112 for conceptual purposes. The Agent ‘House’ exists in two states, either being ‘For Sale’ (Active) or ‘Not for Sale’ (Inactive). The transition from Inactive to Active occurs upon the basis that the ‘Motivation to Sell’ of the House is satisfied, this satisfaction is specified by a set probability that this transition will occur – this is adjustable by the user indicating a highly responsive or restricted house market. ‘Motivation to sell’ probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.
Upon transitioning into an active state a ‘For Sale’ house will wait for an ‘Active Customer’ ‘this is represented and carried out through the ‘Search’ action. Upon completion of the action both states become inactive and the process continues.
Supply – ‘Count of houses for sale –supply’ is then calculated by a count of Houses ‘For Sale’ that are currently in the active state. Ultimately a high Motivation to sell would sharply increase supply, whilst a low motivation would have the adverse effects.
Movement Speed
Movement speed – describes the base movement rate of Consumers. This variable describes the transition into the ‘Inactive’ state of a consumer, ultimately when a household is found and purchased. Movement speed affects both demand and supply in the sense that the transitioning of stages is quickened and more responsive. (Indicated by a more rigid demand and supply curve).
Market Price
In economics Price is a linear function (straight line) of the proportion of houses for sale (positive slope), and also a linear function of the proportion of buyers (negative slope).Therefore , the variable ‘Market Price’ is calculated by 10 * the portion of ‘House’ in the active state (which is the supply) over the portion of ‘Consumers’ in the active state (which is the demand) Ultimately this presents the economic principles that as Supply is directly related to Price and demand is inversely related to Price.
Note
Each simulation (with the same settings) will present a different and unique simulation. I have set a Random Boolean to the active component that randomizes the amount of Customers or houses that begin in their active state. The probability is only 0.008 but is useful in describing the effects on the market from various position’s and seeing unique models.
References
https://www.youtube.com/watch?v=ynuoZQbqeUg - Your First ABM/Part II
https://insightmaker.com/insight/35714/Foraging-Model
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