Using the marginal cost and marginal benefit model.

Economic Naturalist 6.1 asks, "When recycling is left to private market forces, why are so many more aluminum beverage containers recycled than glass ones?" The response has to do with the relationship between the price which companies will pay for aluminum versus glass and the marginal cost of gathering discarded glass and aluminum containers. It is the case that the aluminum in an aluminum container is worth more on the market than the glass in a glass container. It is also the case that the additional (or marginal) cost of finding and gathering in one more glass container is no less than the marginal cost of gathering in an additional aluminum container. Thus it is clear that it is in the best interest of those who gather containers for recycling to gather aluminum in preference to glass.

Exploration: Using Marginal Cost and Marginal Revenue to determine optimal levels of productive activity.

Take a few minutes to explore the window above. Underlying this model is the notion that most people will pick up containers for two reasons: first to clean up the area and second to gain some money from selling the containers. In some cases they keep the money from selling and in others they collect on behalf of their favorite charity. In a few other cases the selling price of the containers is irrelevant – they are working solely to clean up the area. However, in all cases people will work so that the profit from collecting bottles is maximized, whether that profit is money in their pocket, money to their favorite charity, or measured in the non-monetary "profit" of having the largest area cleaned for the time and effort spent.

Now, to the model: Notice that in the left-hand graph we have the Marginal Cost and the Price. In this case we are going to work with the situation where marginal cost can be expressed in dollar terms (gas, bags, time spent, etc.) and the price is the selling price of the containers. (Remember that the same logic can be used to work with non-monetary costs and benefits.) In the right hand graph we have the Total Cost and Total Revenue associated with the left-hand graph. The objective here is to decide how many containers we are going to gather in order to maximize our profit; the difference between total revenue and total cost.

Notice that as we begin the price is $25 and the optimal quantity is 300 containers (in the left-hand graph). This results in total revenue of $7,500 ($25X300=$7,500) and total costs of $3,000, leaving a profit of $4,500. Use the mouse to adjust the quantity either up or down (use the magenta triangle slider and move it to the left for quantity down and to the right for quantity up) in the left-hand graph and notice what happens to the profit in the right-hand graph. No matter which way you go, if you move away from the quantity at which Marginal Cost is equal to Marginal Revenue (in this case Marginal Revenue is the same as Price), profit will fall. There is a powerful truth here: Profit will always maximize at a point where Marginal Revenue and Marginal Cost are equal. In the interest of completeness, note that while Price is equal to Marginal Revenue in this case, it is not always so – more on that in later chapters!

1. For the moment let's concentrate on bottles. If the selling price is $25, how many will be gathered? Suppose the price rose to $35?
   
   
2. Suppose we now concentrate on aluminum cans. If the selling price is $25 how many will be gathered? Suppose the price fell to $20?
   
   
3. Now to the interesting question: Suppose you can gather either glass bottles OR aluminum cans (or both). If the selling price for bottles is $25 and the selling price for cans is $35, how many of each would you gather?
   
   

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Exercise picked up from the 2e Economics textbook.