## FIGURE 55 Elastic impact block

The block has three inputs: the base series (the series that you will measure both before a change in another variable and after), the impact series (the variable that is changing), and the elasticity factor. Keep in mind that price elasticities of demand are normally negative. See Figure 5-5, "Elastic impact block."

Using the block is straightforward: connect the variable that changes (such as a price, tax rate, or other policy variable) to the "impact" port. Connect the elasticity (which could be a constant or a changing variable) to the "elasticity" port. Finally, connect the base series variable to the "in" and "out" ports.

In such a system, for example, the base series of "sales" will increase by 5% when the impact series of "price" drops by 10%, if the elasticity is set at -0.050.

We have incorporated the blocks in the Economics Toolbox described above into an example model, which will illustrate a Simulink economics model and also how these various blocks work.

### Purpose of the Model

The purpose of this model is to simulate sales in a market before and after a policy change that affects the price of the goods or service in question. This problem is a fundamental one in both theoretical microeconomics and applied economics, and is faced by policymakers in government as well as business leaders every day.

For this model we assume that sales are determined by income and price.83 We will simulate the effect on sales as income changes over time and as tax policy changes affect the price of the goods or services.

### Top-Level View of Model

The overview of the model shows the constants on the left: initial income and two growth variables. We would normally use only one growth variable, but for this example we include two to illustrate the use of both constant and varying growth blocks. See Figure 5-6, "Example business economics model."

The large subsystem to the right of the constants is the base case income subsystem, which takes the income and growth variables and calculates income for each period. The policy change and impact subsystem takes the income variable, and within the subsystem takes the policy variable (a tax rate) and an elasticity parameter, and calculates sales before and after the policy change. The last subsystem takes the variables in and saves them properly.

These individual subsystems are illustrated in Figure 5-7, "Base income subsystem," Figure 5-8, "Policy change subsystem," and Figure 5-9, "Income and sales subsystem."

Running the Example Model

### Master Simulation Callback

We run the model using the master simulation callback that was described in Chapter 3, "MATLAB and Simulink Design Guidelines" at "A Master Simulation Callback" on page 52.

That callback script initializes the model, loads the variables, runs the simulation, and graphs the output. The key output is the projection of sales before and after the policy change. A graphical illustration of this is produced by the callback and illustrated in Figure 5-10, "Sales projection with policy change."

83 See "Estimating Demand Schedules" on page 98 for a discussion of demand schedules. For this simulation model we assume that we have already properly modeled the demand for the particular good or service and obtained a price elasticity of demand as well as a relationship between income and demand. We are making further simplifying assumptions that the relative price in a demand function is captured by the after-tax price in this model and that the fundamental price and income relationships do not change during the simulation time period.

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