The Design and Use of a Macroeconomics Simulation Using Maple Software: A Pilot Study Developments in Business Simulation and Experiential Learning, Volume 33, 2006 THE DESIGN AND USE OF A MACROECONOMICS SIMULATION USING MAPLE SOFTWARE: A PILOT STUDY Hal W. Snarr NC A&T State University hwsnarr@ncat.edu Steven C. Gold Rochester Institute of Technology stevengold@cob.rit.edu ABSTRACT The mathematical models used in intermediate macroeconomics have become increasingly more sophisticated and challenging for students to learn. This paper demonstrates how mathematics software, such as Maple, can be used to design a simulation as a pedagogical aid. The paper proceeds by developing a system of equations to model the economy, simulating the system with Maple, and illustrating the impacts of fiscal and monetary policy changes. A pilot test of the simulation was performed to see if higher levels of mathematical rigor could be introduced in a principles course. The results indicate that symbolic mathematics software can be an effective teaching and student learning tool. INTRODUCTION The mathematical models used in macroeconomic analysis have become increasingly sophisticated at the intermediate and advanced levels (Blanchard, 2000; Azaroadis, 1993; and Romer, 1996); and teaching these courses are becoming more challenging. Technologies such as spreadsheet programs, textbook tutorials and electronic blackboards have been used as pedagogical aids and found to be helpful (Fair, 1990; King and McConnell, 1991; Smith and Smith, 1988; Adams and Kroch, 1989; and Gillette, 1994). But more is needed. A study by Allgood, et. al. (2004), published in the American Economic Review, show that student ratings of teaching effectiveness and interest in economics courses are relatively low compared with other fields. For the past 20 years there has been a growing body of literature in economics education espousing the problems with using lecture or “chalk and talk” as the primary teaching pedagogy (Allgood, et.al. 2004; Simkins 1999). Wetzstein (1988) suggests that instructors at the principles level consider new teaching techniques to increase proficiency in economics by stimulating the student’s imagination and interest in the subject matter. He believes that recent developments in teaching – programmed learning, television, and computer-aided instruction –“stifles students’ imagination, contribute to a dependent learning style, and fail to stimulate interest in the subject matter.” Rishi (1998) argues that traditional teaching methods in economics fail to give students the context they need to support critical thinking and problem solving skills. Bartlett and King (1990) identify two major reasons why economics instruction at all levels is not as effective as it could be: (1) economics instructors do not understand how students learn, and (2) economics is not taught as a science. According to Bloom (1971), students need to master definitions and basic facts before they can progress to more complex, causal relationships. Once these prerequisites are satisfied students can then tackle complex relationships represented by a system of equations. Bartlett and King (1990) suggest the best approach to learning economics at all levels is not through memorizing the text and “regurgitating lectures” so that students can pass multiple choice exams. They claim that the key to learning economics is by teaching economics as a science. Teaching economics as a science includes computer simulations, statistical analysis and performing experiments. Schmidt (2003) reported that the use of simulations to teach economics is gaining in popularity and support as an effective pedagogical approach. A primary advantage of a simulation is that it can perform mathematical manipulations quickly, so more complex models can be demonstrated in a short period of time. As examples, Cameron (1997) reported success in using an interactive simulation to teach introductory and intermediate macroeconomics; and Motahar (1994) reported success in using a simulation to teach modeling in microeconomics. The claimed advantages of the simulation included improvement in student performance, retention, and attitude. Three factors accounted for the reported success in the Motahar (1994) study. First, students could see an improvement in their performance as they work with the simulation. Second, there is a complementary relationship between the outcome of the simulation and what is being explained in class. Third, continual feedback from the simulation provided reinforcement of economic concepts. 253 mailto:hwsnarr@ncat.edu mailto:stevengold@cob.rit.edu Developments in Business Simulation and Experiential Learning, Volume 33, 2006 Robinson and Davis (1999) argue that the use of statistical programs and simulations are particularly useful supporting technologies for courses using advanced mathematical model. An excellent example is the application of Maple software by Boyd (1998) to help students understand complex economic systems. Maple software, published by Maplesoft (www.maplesoft.com), is a mathematical programming tool for problem-solving, data visualization, and technical authoring. Boyd (1998) provides a detailed discussion of how he has incorporated Maple into his courses. He combined traditional lecture periods with weekly Maple computer laboratory sessions and found that a majority of the students had a positive experience with Maple because it allowed them to focus on the economic interpretation of the models and less on the tedious task of solving the system. The negative experiences associated with Maple were mostly a result of the speed and memory limitations of the computers in the laboratories, an issue that is no longer a problem in most college computer laboratories with current hardware. The purpose of this paper is to extend the work done by Boyd (1998) and show how Maple software can be used to create a simulation model like the one shown in the appendix to illustrate the impacts of monetary and fiscal policies. But it is argued that Maple is not a magic box of answers. In order to use it effectively students must first master economics terminology and thoroughly understand the basic economic theories behind the model. The paper will show that, if implemented correctly, a tool like Maple can be an effective pedagogical approach. The paper proceeds by first constructing the aggregate demand and supply model used in traditional courses in macroeconomic principles. Second, Maple software is used to create a simulation model to solve and graphically display the system. Third, two fiscal policy applications using the Maple simulation are given as examples of how the simulation works. The simulation graphs the effects of changes in fiscal policies, calculating the resulting GDP growth, inflation rates, trade balance, government budget deficits, and the policy multiplier. The paper concludes with a discussion of student perceptions of the simulation and future pedagogical research. AGGREGATE EXPENDITURE SCHEDULE AND DEMAND EQUILIBRIUM We begin with the basic building blocks of the traditional aggregate demand model, i.e. the aggregate expenditure (AE) schedule is AE C I G X M= + + + − (1) AE Y= where: C = consumer expenditures I = business and new home investment expenditures G = government expenditures X –M = net exports. The general form of the consumption function is C A mpc DI= + ⋅ (2) where: A = autonomous level of consumption mpc = marginal propensity to consume DI = disposable income. Baumol and Blinder (2005) discuss four consumption function shifters, consumer wealth (W), price level (PL), real interest rate (r) and future income expectations (Y ). Because these parallel shifters essentially increase or decrease the intercept A, the autonomous consumption (A) is further defined as follows: e eA W PL Y u r= − + − ⋅ (3) where: W = wealth PL = price level eY = income expectations u r⋅ = interest rate sensitivity parameter (u) times the interest rate (r) Any factor that changes autonomous consumer spending can be included in equation 3. The final component of the traditional AE schedule is disposable income (DI), which is income less taxes net of government transfers (T). If t is the percentage of income paid in taxes, then disposable income is (1 )DI t Y= − ⋅ (4) Substituting equations 2, 3, and 4 into 1 we get the expanded form of AE. [ ] { }(1 )eAE I G X M W PL Y u r mpc t Y= + + − + − + − ⋅ + ⋅ − ⋅ (5) Equation (5) is just a line whose intercept and slope are the expressions in the [ ] and { }, respectively. The values for the AE constants (shift parameters: I, G, X, M, W, PL, Ye, u r⋅ ), and the AE slope parameters (mpc, t) can be set to any value with the Maple Software and graphed. To illustrate, the solid black line in Figure 1 is the graph of the AE schedule, equation 5, with an intercept value of 1600 and a slope less than one. The “demand-side” equilibrium occurs when real GDP (Y) equals aggregate expenditure (AE). Thus we have the familiar demand side equilibrium relationship. (6) The dashed line shown in Figure 1 is the graph of equation (6), showing the equilibrium level of real GDP is $6300 billion in this illustration. If one of the shift parameters with a positive one coefficient increases, the AE schedule shifts 254 http://www.maplesoft.com/ Developments in Business Simulation and Experiential Learning, Volume 33, 2006 Figure 1 The Aggregate Expenditure Schedule 0 1000 2000 3000 4000 5000 6000 7000 8000 0 80 0 16 00 24 00 32 00 40 00 48 00 56 00 64 00 72 00 80 00 88 00 real GPD (in billions) A E 1 (1 )PL I G X M W Y u r mpc t Y= + + − + + − ⋅ − − ⋅ − ⋅ (7) 255 [ ] { }e AD Figure 2 The AD Curve PL 3000 2300 3800 6300 real GDP (in billions of dollars) upward increasing real GDP. On the other hand just the opposite would be true if a shift parameter with a negative one coefficient increases. If the mpc increases or t is cut, AE gets steeper raising real GDP. DERIVING THE AGGREGATE DEMAND CURVE We obtain the aggregate demand (AD) curve when we solve equation (5) explicitly for PL after we impose the equilibrium condition, equation 6, thatY . Replacing and AE with Y and simplifying yields the general form of the AD curve: (See equation 7) AE= Y AD The term in brackets [ ] is the intercept term while the expression in the { } represents the slope of the AD curve. The aggregate demand equation can be illustrated graphically with Maple Software, as shown in Figure 2. For our example, suppose the price level is increased from $2300 to $3000. Since PL enters the intercept of equation (5) with a negative one coefficient, an increase in PL means the intercept of equation (5) decreases. This results in a downward shift of the AE schedule shown in Figure 1 and the slide along the AD curve shown in Figure 2. In this Developments in Business Simulation and Experiential Learning, Volume 33, 2006 case, aggregate expenditures decline decreases from $6300 to $3800 billion. The Aggregate Supply C The construction of the AS curve is si counterpart. The simulation model allow satisfy both Keynesian and Classical sc The slope of the AS curve is generical which ranges between zero and infinit Blinder (2005) discuss six major AS curv include the money wage rate (w), prices production ( p ), supply-side taxes (τ ) productivity (z), labor (L), and capital (K) this model, the aggregate supply schedule [ ]PL w p z K Lτ= + + − − − + β where: β = slope of the line, ranging from ze The AS curve shows the relationship betw price level and the value of goods and nation’s businesses are willing to produce period of time, holding all of the AS constant. THE AD-AS EQUILIR In this section, Maple is used to solv equations 7 and 8 simultaneously, plot th same diagram, and perform fiscal policy an Figure 3 The AD-AS Equilibrium and real GDP urve mpler than its AD s the AS curve to hools of thought. ly defined asβ , y. Baumol and e shifters, which of other inputs to , technology and . Consistent with is specified as: ASY⋅ (8) ro to infinity. een each possible services that the during a specified curve’s shifters IUM e the AD and AS e equations in the alysis. The impact of an increase in government spending from $500 to $600 is evaluated using Maple Software and shown in Figure 3. Aggregate demand increases, raising both the price level and real GDP. Initially, the equilibrium price level and real GDP were about, 760 and 1910, respectively. After the increase in government spending, the price level and real GDP rose to about 810 and 2060, respectively. In this example, the government spending multiplier (change in Y divided by the change in government spending) was 1.46, yielding an economic growth rate (percent change in Y) of 7.63%, and an inflation rate (percent change in price) of 6.73%. THE AD-AS SIMULATION MODEL This section discusses how an instructor can use the AD-AS simulation code in Maple to illustrate fiscal policy analysis. But this is not a replacement for having the students learn and understand the theory behind the equations. Student are not shown the simulation result until they can do equilibrium analysis using equations (7) and (8) with paper and pencil. The Maple simulation graphs the initial and final AS and AD curves; plots the corresponding equilibria; and reports the resulting economic growth and inflation rates, the trade and budget deficits, and the policy multiplier. The simulation captures student attention and is a catalyst for class discussion of the impacts of fiscal and monetary policies. GOVERNMENT SPENIDNG EXAMPLE The simulation starts with the definition of the initial and final conditions (the only difference between the final and 256 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 ec Budge initial conditions is the chan the beginning of the Maple appendix. Suppose we are happens when the governm to G . executed, the students are as price and output by looking anticipating the affect on t model. 0 500G = 1 600= Figure 4 displays the simulation. Both the price The model reports that econo are 7.6 and 6.4 percent, re remained at –$100, while the 189.47 to $142.11, a 25 per spending multiplier suggest government is associated with TAX CUT Next we analyze the e instead of an increase in g example it is assumed the g percent to 0 30t = 1 25t = Figure 5 shows the simulation when the tax rate level and real GDP increase Maple output is calculated by in the equilibrium level of re Figure 6 Keynesian Equilibrium Analysis: Increased G := on_growth 7.633587790 := inflation .003001741389 := t_Deficit 0 562.133456 := Budget_Deficit 1 543.212346 := Trade_Deficit 0 -100 := Trade_Deficit 1 -100 := Multiplier G 2.702629660 ge in G), which are listed near simulation code located in the interested in finding out what ent increases spending from Before the simulation is ked to predict the impacts on at equations (7) and (8) and he equilibrium in the AD-AS actual output of the Maple level and real GDP increase. mic growth and inflation rates spectively. The trade deficit budget deficit decreased from cent decline. The government s that each dollar spent by a $1.75 increase in real GDP. EXAMPLE ffect of a cut in the tax rate overnment spending. In this overnment cuts tax rates from percent. actual output of the Maple is cut. Again, both the price . The multiplier listed in the taking the ratio of the change al GDP and the corresponding change in taxes. According to the Maple output in Figure 5, each dollar decrease in taxes resulted in a $3 increase in real GDP. Notice that budget deficit is also included and decreased from 189.47 to $123.81. These results serve as an excellent source of classroom discussion as to the factors that contribute to this result. THE KEYNESIAN EQUILIBRIUM MODEL Because the Keynesian school believes the AS curve is elastic, the slope of the AS curve can be flattened by changing the beta coefficients from 0.2β = to 0.00001β = . Figure 6 replicates the government spending example above, but this time the AS curve is relatively elastic. According to Figure 6, real GDP increases substantially, while inflation is approximately zero. The government spending multiplier is $2.70 and the budget deficit fell 3.5 percent as a result of the shift in AD. Similar findings result when the tax rate is cut instead. Therefore, according to Keynesian economics, fiscal policy (increased government spending and/or tax cuts) leads to higher real GDP with no appreciable increase in prices (zero inflation). THE CLASSICAL ECONOMICS EQUILIBRIUM The Classical school of economics believes the AS curve is inelastic. This is achieved with the Maple 257 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 simulation code by simply making the AS curve steeper. In the previous examples the slopes of the AS curves were 0.2β = and 0.00001β = , in this example we set 100β = . Figure 7 replicates the tax cut example above only this econ_gro Budget_Defici Trade econ_gro Budget_Defici Trad Figure 4 Increased Government Spending := wth 7.633587809 := inflation 6.383657855 := t 0 189.4736842 := Budget_Deficit 1 142.1052633 := _Deficit 0 -100 := Trade_Deficit 1 -100 := Multiplier G 1.754385970 wth :t 0 e_D Figure 5 Demand-side Tax Cuts := 8.571428563 := inflation 7.167935791 = 189.4736842 := Budget_Deficit 1 123.8095238 := eficit -100 := Trade_Deficit -100 258 0 1 := Multiplier T -2.999999997 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 B time the AS curve is Figure 7, inflation incr essentially constant. T $1 cut in taxes results i GDP. The budget d percent. Similar find spending is increased Classical School of ma higher prices (inflation GDP. EVALUATIO The Maple simula University to determi increased (i.e. using models) in the non-hon taught during the Spri Fall 2004 semester non evaluations scores prio high in the 2004 seme Table 1), the hypoth mathematics could b principles course in evaluations of course ef According to the Table 1, the 25 student course slightly lower t course—a difference o row in the table). The Figure 7: Classical Equilibrium Analysis: Demand-side Tax Cuts := econ_growth .04485425252 := inflation 8.036602915 := udget_Deficit 0 -47.4743450 := Budget_Deficit 1 -122.7261400 := Trade_Deficit 0 -100 := Trade_Deficit 1 -100 := Multiplier T -.008991014766 relatively inelastic. According to eases substantially while real GDP is he tax cut multiplier suggests that a n less than a one cent increase in real eficit ballooned, increasing by 160 ings result when the government instead. Therefore, according to croeconomics, fiscal policy leads to ) with no noticeable increase in real N AND ASSESSMENT tion was tested at NC A&T State ne if the level of rigor could be more sophisticated mathematical ors macroeconomic principles course ng 2005 semester, compared to the -honors course. Since the teaching r to using the simulation were very ster (4.7 out of a 5 point scale – see esis was that a higher level of e introduced into the non-honors 2005 without lowering student fectiveness. course evaluations summarized in s in the Spring 2005 course rated the han the 22 students in the Fall 2004 f 0.1 on a 5 point scale (see the last variance for the spring 2005 course was slightly higher as well, 0.5 and 0.4 respectively. However, according to the last column of Table 1, the differences in course evaluations were all insignificant. Specifically, the t-stat corresponding to the difference (or gain) in course evaluations, located in the last row of Table 1, was –0.51. With any reasonable level of significance, this t-stat suggests that there was an insignificant change in overall course evaluations. But because the spring 2005 class was taught at a significantly higher level of rigor—the fall course was taught at the traditional level—one would have expected a significant drop in course evaluations, especially at the principles level. The fact that course evaluations showed no statistically significant difference, support the hypothesis that a higher level of mathematics could be introduced without lowering the course evaluations, owing to the use of the Maple simulation. Table 2 compares the gain in the overall course evaluations relative to course evaluation gains made by other macro principles sections, the Department, the School and the University. Column (iv) reports the difference-n- differences while column (vi) reports the corresponding t- statistics. The only significant difference-n-difference is the one that compares the instructor’s gain (an insignificant loss in this case) to the gains posted by all other macro principles instructors within the department. This value, 0.2c iµ µ∆ −∆ = − , suggests the drop in the instructor’s course evaluations was significantly lower than the gains posted by the other macro principles courses. The other difference-n-difference values were all insignificant. In this case, the decrease may be a result of the course being taught 259 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 number of students commented that the simulation allowed them to focus more on the “analysis” and less on the “math” or the “memorization of the curve shifts” in the aggregate consumption and AD-AS models. Furthermore, according to the instructor, student responses on essay test questions improved dramatically as a result of using the simulations in class. Students were able to answer essay questions with a higher of degree accuracy and breadth. at a more rigorous level. The current survey instrument used by the University does not ask students to rate the difficulty of the course or compare the amount of non- reading assignments required by the course relative to other courses they have taken are currently taking on campus. Students are also not asked what their approximate grades are in the class. Had this survey instrument addressed these issues, we could have possibly identified the reasons for the relative fall in the instructor’s overall course evaluations compared to the other macroeconomic sections. Given the statistically insignificant change in the instructor’s own overall course evaluation, the increased rigor, the mostly positive comments in the simulation survey, and the instructor’s assessment of improved student performance, the simulation is argued to have been effective, but more supporting research is needed. In addition to the course evaluations, the results of a separate student survey distributed in the spring 2005 course indicated that all but one of the non-honors students had a generally favorable experience with the simulation. A TABLE 1 Changes in Course Evaluations FALL 2004 Spring 2005 Difference Item fµ 2 fσ sµ 2 sσ µ∆ t The course syllabus was distributed at the beginning of the course 4.8 0.3 4.6 0.3 -0.2 -1.2 The course objectives were clearly explained at the beginning of the course 4.7 0.3 4.5 0.4 -0.2 -1.2 The course evaluation measures were presented in the course syllabus 4.8 0.3 4.6 0.3 -0.2 -1.2 The course was carefully planned 4.5 0.7 4.6 0.3 0.1 0.5 The course readings related to the course goals 4.6 0.6 4.7 0.2 0.1 0.5 The instructor met classes as scheduled 4.8 0.3 4.7 0.3 -0.1 -0.6 The instructor was well prepared for class 4.6 0.3 4.7 0.3 0.1 0.6 The instructor appropriately presented practical application of the course material 4.7 0.4 4.6 0.4 -0.1 -0.5 The instructor was knowledgeable about the subject matter 4.8 0.3 4.7 0.3 -0.1 -0.6 The instructor was organized in class 4.7 0.3 4.6 0.3 -0.1 -0.6 The instructor showed enthusiasm for the subject matter 4.8 0.3 4.7 0.3 -0.1 -0.6 The instructor communicated course material in a clear manner 4.6 0.6 4.5 0.4 -0.1 -0.5 The instructor used examples to clarify course subject matter 4.6 0.6 4.6 0.5 0 0.0 The instructor utilized teaching aids effectively 4.6 0.4 4.6 0.5 0 0.0 The instructor encouraged students to ask questions during class 4.6 0.6 4.6 0.4 0 0.0 The instructor provided feedback to students' questions 4.7 0.3 4.6 0.4 -0.1 -0.6 The instructor summarized the material effectively 4.6 0.6 4.4 0.4 -0.2 -1.0 The instructor used various teaching strategies for this course 4.6 0.4 4.4 0.8 -0.2 -0.9 The instructor maintained a positive instructor/student relationship in class 4.7 0.3 4.6 0.4 -0.1 -0.6 The instructor was available to provide assistance outside of class 4.7 0.4 4.6 0.4 -0.1 -0.5 The instructor promoted the development of thinking skills in the course 4.7 0.3 4.6 0.4 -0.1 -0.6 The instructor promoted the development of communication skills in the course 4.7 0.3 4.5 0.6 -0.2 -1.0 The grading system was fair 4.6 0.8 4.5 0.6 -0.1 -0.4 The methods used for evaluating my work were consistent 4.6 0.5 4.5 0.5 -0.1 -0.5 The instructor returned tests and graded assignments in a timely manner 4.6 0.4 4.5 0.5 -0.1 -0.5 The instructor provided feedback to regarding my progress during the course 4.6 0.6 4.5 0.6 -0.1 -0.4 The textbook(s) were useful to my understanding of the course content 4.3 0.9 4.3 1.1 0 0.0 Course and Section Overall Rating 4.7 0.4 4.6 0.5 -0.1 -0.5 260 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 TABLE 2 Course Comparison to Other Units in the University Difference Difference-n-Difference (i) (ii) (iii) (iv) (v) (vi) µ∆ 2σ ∆ t ∆ c iµ µ∆ − ∆ 2σ ∆∆ t ∆∆ Course and Section Overall Rating -0.1 0.04 -0.51 - - - Course (regardless of section) 0.1 0.08 0.35 -0.2 0.01 -2.82 Department 0.0 0.08 0.00 -0.1 0.01 -1.20 School -0.1 0.08 -0.36 0.0 0.01 0.00 University 0.0 0.07 0.00 -0.1 0.01 -1.25 CONCLUSIONS AND FUTURE RESEARCH Principles students are not accustomed to seeing equations with more than two variables. The general forms of the AD and AS curves, equations (7) and (8), have 12 and 9 variables, respectively. Students that are challenged by math find it very difficult to learn economics. As a consequence many studies on economics education find that at an early stage in their education, students become turned- off to economics. Simulation technology with software like Maple offers more than just a new way of doing things. Rather, it has the possibility of changing significantly the way economics is taught and how students learn by engaging them in a way not possible with other pedagogical tools. Using the Maple simulation in the classroom allowed more mathematical rigor to be included in the course, similar to the honors sections, without a decline in student ratings of the course. Student feedback on a separate survey indicated the students enjoyed the simulation because it freed them from tedious mathematical manipulation, and made the economic models much easier to visualize than the traditional classroom lecture. By practicing with the simulation, students found it easier to understand complex mathematical systems and remember the economic theories. The evidence presented in this pilot study on the pedagogical effectiveness of the Maple simulation is largely tentative owing to the limited supporting data. More comprehensive course evaluation and simulation survey instruments are being constructed to more accurately measure teaching effectiveness of new technologies, and future research is needed to design a more formal testing scheme. REFERENCES Hall, Whitmire & Knight (1999) “Using Internet for Retail Access: Banks Found Lagging.” American Banker’s Journal of Retail Banking Services, Volume Twenty- One, Number One, Spring 1999, 51-55. Angrist, Joshua and Victor Lavy (1999) New Evidence on Classroom Computers and Pupil Learning National Bureau of Economic Research, Inc, NBER Working Papers: 7424. Azariadis, Costas (1993) Intertemporal Macroeconomics, 1st ed. Malden, MA: Blackwell Publishing. Baumol, William J. and Alan S. Blinder (2005) Economics: Principles and Policy, 9th ed. Mason, Ohio: South- Western. Blanchard, Oliver (2000) Macroeconomics. 2nd ed. Upper Saddle, NJ: Prentice Hall Bloom, Benjamin S., J. Thomas Hastings and George F. Madaus (1971) Handbook on Formative and Summative Evaluation of Student Learning, New York, NY: McGraw-Hill. Boyd, David W. (1998) “On the Use of Symbolic Computation in Undergraduate Microeconomics Instruction” Journal of Economic Education, v29, n3, Summer, 227-46. Cameron, Norman E. (1997) “Teaching Economics: Simulating Money Supply Creation in Class” Economic Enquiry, v35, n3, 686-693. Gillette, David H. (1994) “Hyperlecturing and Linkages,” American Economist v38, n2, Fall, 58-65. Motahar, Eshragh (1994) “Teaching Modeling and Simulation in Economics: A Pleasant Surprise” Journal of Economics Education, (fall) v25, n4, 335-342. Porter, Tod S. and Teresa M. Riley (1992) “CAI in Economics: What Happened to the Revolution?” Journal of Economic Education v23, n4, Fall, 374-378. Rishi, Meenakshi (1998) “Beyond Chalk and Talk” College Teaching, v46, n3 (June), 8756-7555. Robin L. Bartlett and Paul G. King (1990) “Economic Instruction: Teaching Economics as a Laboratory Science” The Journal of Economic Education, Vol. 21, No. 2., Spring, 181-193. Simkins, Scott P. (1999) “Promoting Active-Student Learning Using the World Wide Web In Economics Courses” Journal of Economics Education, Vol.30, n3, Summer, 278-291. Schmidt, Stephen J. (2003) “Active and Cooperative Learning Using Web-based Simulations” The Journal of Economic Education, Vol. 34, No. 2, 151-167. Wetzstein, Michael E. (1988) “An Organonic and Modern Problems Approach for Teaching Agricultural Economics Principles.” American Journal of Agricultural Economics v70, n1, February, 63-68. 261 Developments in Business Simulation and Experiential Learning, Volume 33, 2006 APPENDIX: The Maple © code for the simulation: restart: "****** AD initial and final conditions *****************": mpc := 0.9: W0 := 250: W1 := 250: X0 := 500: X1 := 500: M0 := 600: M1 := 600: t0 := 0.3: t1 := 0.3: G0 := 500: G1 := 600: Ye0 := 250: Ye1 := 250: I0 := 500: I1 := 500: "****** AS initial and final conditions *****************": beta := 0.1: w0 := 120: w1 := 120: p0 := 100: p1 := 100: T0 := 30: T1 := 30: z0 := 50: z1 := 50: K0 := 50: K1 := 50: L0 := 60: L1 := 60: "****** The general forms of the AD and AS curves *******": AD:=(W,Ye,X,M,t,G,In,Y)->W+Ye+In+G+X-M-(1-mpc*(1-t))*Y: AS:=(w,p,T,z,K,L,Y)->w+p+T-z-K-L+beta*Y: PD[0]:=AD(W0,Ye0,X0,M0,t0,G0,I0,Y); PS[0]:=AS(w0,p0,T0,z0,K0,L0,Y); PD[1]:=AD(W1,Ye1,X1,M1,t1,G1,I1,Y); PS[1]:=AS(w1,p1,T1,z1,K1,L1,Y); if beta > 99 then PS[0]:=-150000+100*Y: PS[1]:=PS[0]: fi: d:=1: if PD[0]=PD[1] then d:=0: fi: s:=1: if PS[0]=PS[1] then s:=0: fi: Y0:=solve(PD[0]-PS[0],Y); PL[0] :=AD(W0,Ye0,X0,M0,t0,G0,I0,Y0); Y1:=solve(PD[1]-PS[1],Y); PL[1] :=AD(W1,Ye1,X1,M1,t1,G1,I1,Y1); plot([PD[0], PS[0], PD[1]*d+PS[1]*s, [[Y0,PL[0]],[Y0, 0 ]], [[0, PL[0]],[Y0,PL[0]]], [[Y1,PL[1]],[Y1, 0 ]], [[0, PL[1]],[Y1,PL[1]]] ], Y=0..Y1*2, PL=0..PL[1]*2, color=[blue,blue,black,black,black,black,black], linestyle=[SOLID,SOLID,SOLID,DOT,DOT,DOT,DOT], thickness=[3,3,3,1,1,1,1], tickmarks=[4,4]); econ_growth:=(Y1-Y0)/Y0*100; inflation:=(PL[1]-PL[0])/PL[0]*100; T0:=t0*Y0: T1:=t1*Y1: Budget_Deficit[0]:=T0-G0; Budget_Deficit[1]:=T1-G1; Trade_Deficit[0]:=X0-M0; Trade_Deficit[1]:=X1-M1; if T0 <> T1 then c := t1*Y1 - t0*Y0: var:=T: fi: if G0 <> G1 then c := G1 - G0: var:=G: fi: if I0 <> I1 then c := I1-I0: var:=Inv: fi: Change[GDP]:=Y1-Y0; Change[var]:=c; Multiplier:=(Change[GDP])/c; 262 Table of Contents Volume 33, 2006 Learning Assurance Using Business Simulations Applications To Executive Management Education Team Teaching In An Integrated Business Course Using Critical Problem Based Learning Factors In An Integrated Undergraduate Business Curriculum: A Business Course Success Personality Type And Strategic Planning Business Games As Strategic Management Laboratories The Relationship Between Students' Success On A Simulation Exercise And Their Perception Of Its Effectiveness As A PBL Problem Forecasting Accuracy And Learning: The Key To Measuring Simulation Performance The Business Strategy Game: A Performance Review Of The New Online Edition Using The Socratic Method And Bloom's Taxonomy Of The Cognitive Domain To Enhance Online Discussion, Critical Thinking, And Student Learning Using Negotiation Exercises To Promote Critical Thinking Skills Effective Leadership Experiences For Management Majors In A Futures Class The Role Of Learning Versus Performance Orientations When Reacting To Negative Outcomes In Simulation Games Is Pay Inversion Ethical? A Three-Part Exercise Simulations And Experiential Exercises - Do They Result In Learning? Have We Figured It Out Yet? Examining Program Management In Business Simulations: Student And Faculty Views Validating Business Simulations: Do Simulations Exhibit Natural Market Structures? Characterizing Business Games Used In Distance Education Utilizing Games In A Graduate Level Instructional Game Course Employment Interview Preparation: Assessing The Writing-To-Learn Approach Simulations - Bridging From Thwarted Innovation To Disruptive Technology Creating An Authentic Cultural Lens Using Case Dialogue Learning By Fire: Reflections Of A First Time Online Instructor An International Internship With A Service-Learning Focus Learner Participation In The Online Learning Experience: Help Or Hindrance? Any Given Sunday: Intervention In Pursuit Of Simulation Team Parity Beginning With The End: Creating An Experiential Exercise From Assessment Criteria Simulating Life Cycles: Life Span As The Measure Of Performance In Business Gaming Simulations It's Puzzling: Communications, Competition, And Cooperation Balanced Scorecard Implementation For Strategy Management: Variation Of Manager Opinion In Real And Simulated Companies Cases And Business Games: The Perfect Match! Three-Attribute Interrelationships For Industry-Level Demand Equations Using A Web-Based Module To Teach Information Literacy Decision Support System For Demand Forecasting In Business Games The Invalidity Of Profit=F(Market Share) PIMS Validation Of Marketing Games Online Market Test Laboratory With The MINSIM* Program The Gas Mileage Game - A Policy Simulation Delivered Cost And Differentiation Applied To Threshold 3rd Ed. The Effect Of Team-Leadership Modes On Team Performance: A Preliminary Study The Design And Use Of A Macroeconomics Simulation Using Maple Software: A Pilot Study The Instructor's Toolbox: A Meaning-Centered Framework For The Social Construction Of Experiential Learning Incorporating Strategic Product-Mix Decisions Into Simulation Games: Modeling The 'Profitable-Product Death Spiral' Group Composition And Groupthink In A Business Game A Direct Approach To Teaching Business Ethics A Decision Support System For Planning Sales, Production, And Plant Addition With Manager: A Computer Simulation Polish - American Entrepreneurial Business Cooperation Workshop Utilizing The Income/Outcome Simulation Student Leader Training Exercise Student Preference To Mode Of Learning In Hong Kong Experiential Learning For Technology-Based And Management Programme In Hong Kong: A China Study Tour A Price Game With Product Differentiation In The Classroom Discrete Event Modeling In A New Transportation Simulation Supply-Side Modeling In A Total Enterprise Simulation The Quality Game Towards A Massive Multiplayer Online Business Simulation Making The Connection: Improving Virtual Team Performance Through Behavioral Assessment Profiling And Behavioral Cues Individual Learning Producing A Learning Organization: 'Playing Dice With Polar Bears' Narratology and Ludology: Competing Paradigms or Complementary Theories in Simulation Framework For Evaluating Internet Research Using Children's Games To Illustrate Strategy Concepts: Is Less Better?