## Wolfram Demonstrations Project: "Short-Run Cost Curves"

To use this simulation, you must download and install the Mathematica Viewer. Although this software is free, it is a sizable download. This activity is therefore optional.

This simulation shows how Total and Marginal Cost curves interrelate and lead a firm to its profit maximization production point.

Once you have downloaded the software to your desktop, open the simulation and read the instructions. Unlike previous simulations, this one has two panels to analyze: The left panel shows the Total Cost (TC) curve, and the right panel shows the Marginal Cost (MC) curve.

The lettered sliders correspond to the following variables:

a = the slope of the TC curve

= the slope of the MC curve = the rate of change of the slope of TC

c = Average Variable Cost

d = Fixed Costs

Experiment with changing these variables and note how changes affect the break even point and the shutdown point.

These curves are the backbone of a firm's production decisions. All that needs to be added is a Total Revenue curve. As you know, if a firm takes its selling price from the market, its Total Revenue curve (left panel) is a straight line originating at the origin with a slope of 1. The Marginal Revenue curve (right panel) is a horizontal line running from the y-axis, originating at Price. Recall that, with a price taker, P = MR = AR. From this simulation, you can examine various points where MC would equal MR and determine if the firm would be profitable.

Set all sliders to their mid position (= 77 and = 5400) and imagine a Marginal Revenue of $90. What can you tell from the graphs? You would see that the firm is profitable and produces about 625 units. In other words, MC and MR intersect at the point (625, 90) because that is where MC = MR. Looking now at the left panel, you can see that to make 625 units, the total cost is about$50,000 and total revenue ($90 times 625 units) is$56,250 – a tidy economic profit!

Explore the model. Set the variables at different rates, set the market price, and see how that affects the cost curves and profits.

Any rational firm will choose to produce only at the point of MC = MR.