Basic Theory

Production Possibilities and Revenue Maximization 
This is the first module I designed and so bear with it.  I got better over time.  Indeed, there are two worksheets here and I actually started with the second sheet on the PPF and the revenue maximum.  At first, this was a number exercise only.  Students could see the PPF data and see how the rate of product transformation (RPT) was the difference in Butter between two adjacent values divided by the change in Guns.  They could then look at the revenue at each point on the PPF and see were the the revenue is maximized.  By varying the price of Guns, they should see not just that maximal revenue changes, but that the point on the PPF that yields maximal revenue also changes.  They should be able to "predict" which point yields the revenue maximum based on a comparison of the RPT and the price of Guns.  The other worksheet, the first one, is very simple.  It shows an isorevenue line that is lower than the maximal one in addition to showing the maximal one.  Students can change the revenue and see how the line moves.  Big deal, right?  The point is that students should be able to identify the direction of increasing revenue by seeing how the PPF crosses the isorevenue line.  If done in class, it would be useful to draw a PPF that is convex to the origin with a suboptimal isorevenue line crossing it and having the students predict the direction of increasing revenue. 

Consumer Choice and Comparative Statics
There are five worksheets here.  The tabs for these may not all be immediately visible, so you need to make a point to show the students the arrows at the lower left of the worksheets, so they can navigate from one sheet to another.  The first of these is constructed like the first worksheet for the PPF example, to demonstrate a feasible but non-optimal solution and ask what it takes to improve the situation.  The second sheet shows all the comparative statics possible in one diagram.  Incidentally the utility function is in the Stone-Geary class: U(X,Y) = (X + A)(Y + B).  The students don't have to know this.  The third sheet shows comparative statics with respect to Income.  Both an income-consumption curve and an Engel curve are drawn and it must be emphasized that the graph on the left is in consumption space while the graph on the right has income explicitly, on the y-axis.  I've always had trouble showing how the Engel curve was constructed from the income-consumption curve and the budget lines.  This approach doesn't help with the constructions but it does show that these are two alternative representations of the same choice.  The next worksheet does the analogous comparative statics for a change in the price of X.  The final worksheet does income and substitution effects.  For these last three sheets, the approach is quite traditional.  I'd appreciate getting feedback on whether the animation is helpful over traditional textbook presentations. 

Elasticity
Two of the three sheets are devoted to the linear expenditure system.  The first of these shows a bar graph with expenditure on each of four commodities and a pie graph with the associated expenditure shares.  Comparative statics can be done with respect to each of the prices and income too.  Students should be asked whether pairs of goods are substitutes or complements, whether goods are price elastic or price inelastic, and whether they are inferior, necessities, or superior goods.   The second sheet compares the Engel curve to the line from the origin through the optimum for each of the four goods.  One commodity is inferior, one exhibits no income effects, one is normal but with an income elasticity less than one, and one has an income elasticity greater than one.  The students should be able to identify these.  The third sheet contrasts linear and unitary elastic demand.  Revenue rectangles are drawn for each.  Students should be able to identify where the linear demand curve is elastic and where it is inelastic.  The should conjecture about the point of unitary demand elasticity on the linear demand curve. 

Productivity Relationships in the Short Run
Both sheets are devoted to short run productivity relationship with a single variable input, labor.  The first sheet illustrates a typical convex-concave short run production function.  The student can select a particular point on the curve.  The graph also includes the line from the origin to that point as well as the tangent line.  Below this graph is a second graph with the average and marginal product curves.  The student should be able to see how the average and marginal product is determined in the first graph and make predictions about the shape of the second graph.  The second sheet has a tabular/numerical representation of the same relationships.  Part of the table is left unfilled and it is for the student to determine how to complete the tables.  One can vary productivity parameter values so that each student gets their own distinctive sheet.

Cost Relationships in the Short Run
The setup is like the previous productivity relationships setup.  There are two sheets.  The first shows the relationships in graphical form.  The second has the relationship in tabular form.  There are again cells to fill in on the second sheet.  The table has more columns than before and there is more to fill in.  The thought is that the students would have learned the general approach from the productivity exercise and so it can be amplified, here, for the cost exercise.  

Supply and Demand: equilibrium, comparative statics, effect of a tax, and simple dynamics
There are again five worksheets here so the students should be made aware to find them all.  I've stuck with linear supply and demand.  A mathematically inclined student could solve for the equilibrium on pencil and paper given the parameter values.   On the first sheet, labeled Comparative Statics, the general student should play with the buttons for a while and then begin to make predictions about how the equilibrium will change based on a change in the particular parameter value.  As a particular application, I have the effect of a unit tax.  The next three worksheets are devoted to that.  Students (at least the ones I teach) are generally confused on the question of whether the tax shifts the demand curve or the supply curve, so there are two sheets, one from the perspective of the buyer, the other from that of the seller.  In both of these, I've allowed the tax rate to be negative and the students need to be able to identify a negative tax as a subsidy. There is also a sheet for the Welfare  analysis.  The last sheet does a Cobweb model of price dynamics.  I know most folks don't teach this stuff anymore, but it is visually striking and can be used as an entry point into the question of how markets come to equilibrium and do they get there? Students should be able to identify convergent dynamics, cycles, and explosive dynamics.  They can vary slopes of supply and demand to see their effect on the dynamics.   

Price Ceilings and Floors, binding or inert?
This is my favorite module, not because of the complexity but rather because of the visualization.  There is a very simple device to indicate the price control binds.  The horizontal line at the value of the control gets solid and thicker indicating the distortion the control creates.  When the control is inert, there is no thick horizontal line and the equilibrium is as in the absence of the control.  The interesting economics, of course, is discussing how the market re-equilibrates when the control binds. There are two worksheets here, one for ceilings, the other for floors.

Monopoly Pricing, Welfare, and 3rd Degree Price Discrimination
There are five worksheets here.  The one labeled Basic model might look a tad unusual.  One of my pet peeves with textbook presentations on this topic is that they rarely draw marginal revenue as negative.  But, of course, marginal revenue is negative in the region where demand is inelastic.  This representation makes that explicit.  Students should vary each parameter and note whether the change affects the monopoly price or not.  The next sheet does a welfare analysis.  It allows students to see how the welfare results change as the demand elasticity changes, holding the monopoly solution constant.  The students should get the idea that the distortion is not so great if the firm has little market power.  The sheet on price caps, which is next, is meant to contrast with the price ceilings sheet in the previous module.  Students need to understand that when the cap binds, lowering the cap actually raises output, since output is demand determined.  This model has been mentioned in the context of the California energy crisis.  The last two sheets are on 3rd degree price discrimination.  I'm not entirely happy with them, because the graphs look cluttered.  Markups in the two markets are represented by vertical line segments.  Students should be able to see without difficulty that the markup in the more elastic market is lower.  In the first of these sheets the more elastic market is also a smaller market.  Marginal cost can be either downward sloping, constant, or upward sloping.  Students should see how the effect on the larger market of serving this smaller market depends on the slope of marginal cost.  The last sheet is representation of Viner's model of dumping as international price discrimination, where the domestic price is higher than the world price.  Students should identify how much the domestic firm produces for export, as well as how the markups compare on the two markets.   

Dynamic Examples

Interest and Discounting
I created this module because I felt students need an intuitive feel for discounting before doing other dynamic models.  There are three worksheet.  The first consider a model with a one period loan that must be refinanced in full for another period and then again, until the load is ultimately paid off.  The payoff is plotted against the period in which the payoff occurs and the student can do comparative statics on this with respect to the interest rate.  The plot looks more "curvy" as the interest rate increases, indicating the exponential growth entailed in compound interest and how the growth rate increases with an increase in the interest rate.  The second and third sheets are devoted to a model where the loan is paid of gradually over time, where the payments are flat when measured in current values.  The sheet calculates the per period payment based on the principal, the interest rate and the term of the loan.  There is a graph that contrasts the per period payment when measure in current value, on the one hand, and when measured in discounted present value, on the other hand.  The student should not that the disparity between the two increase with the period and with the interest rate.  The third sheet plots the amount of the loan paid off, measured in discounted value, and the value of the loan left unpaid, measured in current value.  The student should get the feel that for a typical loan at typical interest rates, most of the loan is paid of near the end.  In the beginning, payments are substantially interest, rather than principal.  

A simple overlapping generations model with savings
I am envisioning doing this module in a computer lab where I can give the students immediate feedback, because there is a degree of complexity here that is not present in the modules above.  Perhaps the students can get good use of this module when done asynchronously, but they'd likely need more instructions than I have supplied.  I intend to do this module right after we have done basic consumer theory, so the students can see some of the complexity, but also the flavor, in thinking about the issues in dynamic terms.  The exercise, in effect, asks students to identify consumption paths as feasible but inefficient, efficient, or infeasible.  Since consumption paths are infinite-dimensional animals, I've reduced the set to those paths where consumption grows geometrically.  This reduces the class to two dimensions - the initial consumption and the growth rate.  Even for this restricted class, the analysis is not trivial.  I would break the exercise into three parts.  First, identify infeasible paths, where income becomes negative in finite time.  There are several ways this can be done.  Negative values show up in red and the screen is split in two so it should not be hard to see if displayed values become negative eventually.  Also, if the graph looks concave, that is a telling sign that the path is infeasible, even if it does not cross the axis.  The interesting case to look at is infeasible paths where income is positive for the first several hundred periods and where the income growth rate initially exceeds the consumption growth rate.  One can then scroll down rapidly and make a "number movie" having students focus on the two columns that are the income growth rate and the savings growth rate.  Students should figure out that these paths are declining.  And they cross right through the consumption growth rate, which is an indication that the economy will crash and burn.  Next, lower the initial period consumption enough to have a feasible growth path, but one that is inefficient (but not too much so).  Play the same type of number movie.  Students should see the same behavior initially but eventually the income and growth paths start to increase.  Thereafter they increase steadily and approach the exogenous growth rate of investment, g.  Then they should note in this case that the share of consumption eventually starts to decline and indeed becomes negligible. Finally, I'd have them conjecture on the shape of an approximately efficient path and have them find the initial consumption level (up to two decimal places) for an approximately efficient path, given a fixed consumption growth rate.  If this is done with groups of students for a fixed g, where each group gets its own consumption growth rate, then the results can be reported to the whole class as tracing out the efficient boundary of the economy.   

Hotelling model of resource extraction: solution and comparative dynamics
There are two sheets here.  The first does the model with linear demand, where it is optimal to exhaust in finite time. The second with isoelastic demand, where a complete closed form solution is straightforward and exhaustion occurs in infinite time.  First, students should get an intuitive explanation of the demand curve as a marginal social benefit curve.  Depending on your point of view, I'd drop all the baggage associated with income effects and the like and I wouldn't write any integrals down or draw any areas.  I'd simply say that if the area under demand is social benefit then price is the marginal social benefit.   With that, you can reason fairly simply about the optimality conditions for distributing the resource between two periods, when there is discounting.  (And I think discounting is where this gets harder for the students.)  The optimality (first order) conditions say that the discounted price should be the same in each period.  One can then convince the students that having chosen an initial period output, that in effect determines an entire output path to satisfy the optimality conditions.  That is what we plot.  Note that the discounted price equals the initial price.  Now the question is whether the initial period output is set properly.  On the first sheet, the students can in effect determine the solution to the transversality conditions by considering when output first becomes negative versus determining when the stock initially exhausts.  If the initial output is too low, output gets negative early and the stock never exhausts.  You can convince the students that leaving the stock in the ground forever is not optimal - nobody benefits from that.  If the stock exhausts too early, you can convince the students that there are future generations of demand that would benefit from having some of the stock to consume.  Working that through, the students should be convinced that an approximate optimal path has the output and stock going negative in the same period.  Then the students can find such paths by varying the initial output up or down accordingly.  The first sheet also has the monopoly solution, which generates more revenue but less social surplus.  One can discuss that the monopolist is initially more patient than the planner, and that has to do with how the elasticity varies along a linear demand curve. In the second sheet, the graph helps students get a feeling for how the time path of extraction changes with the discount factor.  This can help the students understand what patience and impatience means to an economist without having to stick to a two period model.