EXERCÍCIOSDEMICRONOWOLFRAM

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Computer Assisted Learning(CAL) in Economics by using Mathematica

andInternet Resources on Economics

By Masaru UzawaOtaru University of Commerce

1. Introduction

1.1 How to learn EconomicsIt is well known that there are many approaches to learn and teach the elementaryeconomics (microeconomics and macroeconomics). In section 3, you will find that in Great Britain and U.S.A. many people andinstitutions are struggle for increase computational means to proceed economiceducation.Followings are some approaches that help learner of economics hitherto:(1) to read a text for several times,(2) to draw graphs or make figures from data by yourself,(3) to attend the class and ask your teacher the point,(4) to attend the seminar in small size and make discussion on the issue points,(5) to attend the interested group in small size for reading the text in depth,(6) to solve the computational examples by substituting the assigned values,(7) to analyze the problem in the model framework,(8) to use computer for getting the essence of the economics,and so on.

Also, there are many approaches to use of computer. I pick up here threeapproaches. The first is to make the computer programs to solve your economic problem.The second is to use the economic simulation programs which are programmed by theauthorized programmers. The third is to use the spread sheet programs and/or theeconometric analysis programs including the statistical ones for your economicproblems.

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1.2 Three types of SoftwareThere are three types of software of economics. The first type of software can affordthe same contents of the textbook on the display of the personal computer. There aremany software in this first type category such as Cliffs StudyWare for ECONOMICS(1993), WinEcon4.0(1996) explained later in section 3.5, and the accompaniedsoftware to Stiglitz,J., Economics(W.W. Norton & Company, 1993). They are highlyevaluated and have large learning effectiveness for the students because the softwareare made of the multimedia tools. The second type of software is the economic simulation program for the students.There are many software, too. I only pick up the software of Prof. Lovell(1995,1996)explained later in 3.9. They are very interested in and are helpful to the learnersof economics. The third type of software can help learners to understand economics by usingsimulation and/or estimating the economic relationships on the actual data. Of course,the second type of software have this character in common. There are many softwarewhich covers programs of the introductory economics to econometric tools foreconomics.In this note, we present the applicability of Mathematica to economic analysis andtalk about the learning economics via Internet and the availability of researchresource on the Web. In section 2, we get the Cournot equilibrium and the Stackelbergequilibrium in duopoly by using Mathematica. In section 3, we pick up the resourcesfor students of learning economics and researchers.

2. Application of Mathematica to Duopoly Theory --- Cournot and Stackelberg equilibria ---

Mathematica was developed by Wolfram for solving the scientific problems. NowMathematica has been updated by Wolfram Research, Inc. and are used by researchesin other fields.Varian[1993] edited 17 examples of Mathematica applications to economic and financialproblems. Asari, Kubo, Ishibashi and Yamashita[1995,1997] have published papers andbooks with many graph representations by using Mathematica. Kobayashi[1996] publishedbook to learn microeconomics with the aids of graphical Mathematica.

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In this section, we want to get the Cournot equilibrium and the Stackelbergequilibriuim in duopoly by using Mathematica. As for Cournot model and Stakelbergmodel you may consult with such a book as Friedman[1983]. See also Kon, Uzawa andYamamoto[1992], Okuno and Suzumura[1988], and Umehara and Hsiao[1997].

2.1 Cournot-Nash equilibrium in Duopoly model

There are two firms(firm 1 and firm 2) that produce the same quality of good.Each firm's object is to maximize her profit subject to given other firm's quantity.Each firm knows that both her profit and other's profit depend on her own quantityand other's quantity as well. In game theory, this is the game in which each player(firm1 and firm2) uses quantity as strategy. Cournot found the Nash equilibrium concept in his book published in 1838.For this reason the Cournot equilibrium is often called as the Cournot-Nashequilibrium.

The output pair (q1C,q2C) is said to Cournot-Nash equilibrium if the followingconditions are satisfied: (1) Firm 1's output q1C maximizes her profit when firm 2's output is q2C, and (2) Firm 2's output q2C maximizes her profit when firm 1's output is q1C.

In other words, firm 1's output q1C is the best reply for firm 2's output q2C,and firm 2's output q2C is the best reply for firm 1's output q1C.

Both firms produce the same good and they confront with the following marketdemand curve(inverse demand function);

p = a - b(q1 + q2)

where, p is market price, q1 and q2 denote firm 1's output and firm 2's output,respectively. a and b are positive parameters. We can do the following exercises by using Mathematica. You can get the smoothed graphics under the Motif mode of Mathematica.

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When you exert Mathematica on your platform, you can see the following prompt:

In[1]:=

You may input the market demand curve as follows:

In[1]:= p = a - b (q1+q2)

Then you can see in the screen:

Out[1]= a - b (q1 + q2)

You can omit "Out[.]= " by putting semicolon[;] in the end of input.The space between b and (q1 + q2) means the product operation of both itemsin Mathematica. Now we consider the case where two firms have identical cost function.In particular, marginal cost equals average cost, say, m.

In[2]:= c1=m q1

Out[2]= m q1

In[3]:= c2=m q2

Out[3]= m q2

Amount of sales(revenue for firm) is the product of price and quantity produced.So we can define that the profit equals revenue minus cost.You can get profit for firm 1(profit1) by following manner:

In[4]:= profit1=p q1 - c1

Out[4]= -(m q1) + q1 (a - b (q1 + q2))

Please use "Simplify" to get the simplest expression.

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In[5]:= Simplify[profit1]

Or you may also use:

In[5]:= Simplify[%]

Out[5]= q1 (a - m - b q1 - bq2)

The "%" means the latest content, namely, profit1.As for profit for firm 2(profit2) you can get the result by the same manner.

In[6]:= profit2=p q2 - c2

Out[6]= -(m q2) + q2 (a - b (q1 + q2))

Now we want to find the quantity that maximizes her profit given other firm'squantity. This relationship is called by Cournot's reaction function, or thebest response function in the game theory.

In[7]:= foc ={D[profit1,q1]==0, D[profit2,q2]==0}

Out[7]= {a - m - b q1 - b (q1 + q2) == 0, a - m - b q2 - b (q1 + q2) == 0}

Expression of "D[profit1,q1]==0" means the partial derivative of profit1 withrespect to output q1. It is the first order condition of profit maximizationfor firm 1. The "foc" express both conditions of profit maximization for two firms.

In[8]:=D[profit1,{q1,2}]

Out[8]= - 2 b

Expression of "D[profit1,{q1,2}]" means the twice partial derivatives ofprofit1 with respect to output q1. Its value is negative because b is positiveby assumption.

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The profit function of firm 1(profit1) is the concave function of output q1.We have the profit curve to be convex to the top.The second order condition for maximization is satisfied in this case.The same is true for the condition of firm 2.

In[9]:= r1=Solve[foc [[1]],q1][[1]]

a - m - b q2Out[9]= {q1 -> ------------} 2 b

In[10]:= r2=Solve[foc [[2]],q2][[1]]

a - m - b q1Out[10]= {q2 -> ------------} 2 b

Expression of "Solve[foc [[1]],q1]" shows you the output q1 which solves thefirst part of foc, namely, D[profit1,q1]==0. In effect, we get q1 from the expressionof "a - m - b q1 - b (q1 + q2) == 0".Please notice that [[1]] attached to the above expression can eliminate the redundant"{}" from the output expression.

You can get r1 for firm 1's reaction function and r2 for firm 2'sreaction function, respectively. We define new functions such as reaction1[a,b,m] and reaction2[a,b,m] asfollows;

In[11]:= reaction1[a_,b_,m]:=(a - m - b q2)/(2 b)

In[12]:= reaction1[a,b,m]

a - m - b q2Out[12]= ------------ 2 b

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In[13]:= reaction2[a_,b_,m_]:=(a - m -b q1)/(2 b)


a - m - b q1Out[14]= ------------ 2 b

You can see the reaction curve, namely, the graphic representation of thereaction function.The cross point of the both reaction curves means the Cournot-Nashequilibrium because you may check the equilibrium Condition (1) and (2) for the point.

In[15]:= qc=Solve[foc,{q1,q2}][[1]]

a - m a - mOut[15]= {q1 -> -----, q2 -> -----} 3 b 3 b

You can get the Cournot-Nash equilibrium as follows:

a - m a - m q1 = -----, q2 = ----- 3 b 3 b

We define the Cournot-Nash equilibrium output for both firms as Q1C[a,b,m] andQ2C[a,b,m], respectively:

In[16]:= Q1C[a_,b_,m_]:=(a - m)/(3 b)

In[17]:= Q1C[a,b,m]

a - mOut[17]= ----- 3 b

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In[18]:= Q2C[a_,b_,m_]:=(a - m)/(3 b)

In[19]:= Q2C[a,b,m]

a - mOut[19]= ----- 3 b

You see the Cournot-Nash equilibrium price of PC[a,b,m]):

In[20]:= PC[a_,b_,m_]:=Simplify[a - b (Q1C[a,b,m]+Q2C[a,b,m])]

In[21]:= PC[a,b,m]

a + 2 mOut[21]= ------- 3

We finally get the Cournot-Nash equilibrium profits for both firms aspai1C[a,b,m] and pai2C[a,b,m], respectively:

In[22]:= pai1C[a_,b_,m_]:=Simplify[(PC[a,b,m]-m) Q1C[a,b,m]]

In[23]:= pai1C[a,b,m]

2 (a - m)Out[23]= -------- 9 b

In[24]:= pai2C[a_,b_,m_]:=Simplify[(PC[a,b,m]-m) Q2C[a,b,m]]

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In[25]:= pai2C[a,b,m]

2 (a - m)Out[25]= -------- 9 b

Here we collect the Cournot equilibrium(CournotEquilibrium) and the associatedprofits for both firms(CournotProfits) as follows:

In[26]:= CournotEquilibrium={Q1C[a,b,m],Q2C[a,b,m],PC[a,b,m]}

a - m a - m a + 2 mOut[26]= {-----, -----, -------} 3 b 3 b 3

In[27]:= CournotProfits={pai1C[a,b,m],pai2C[a,b,m]}

2 2 (a - m) (a - m)Out[27]= {--------, --------} 9 b 9 b

2.2 Graphical representation of Cournot equilibrium

It is easy to show the graphical representation of reaction curves by usingMathematica. You may fix all values of parameters, in particular,

a=25, b=1, m=1

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In[28]:= a=25;b=1;m=1;

In[29]:= RE1=D[profit1,q1]

Out[29]= 24 - 2 q1 -q2

In[30]:= RE2=D[profit2,q2]

Out[30]= 24 - q1 -2 q2

Expression of "RE1 and RE2" shows the marginal profit(= marginal revenue -marginal cost) for both firms. Marginal revenue means the increment(positive or negative) of revenue whenfirm can sell one more unit of output. Marginal cost means the increment ofcost when firm can make one more unit of output. The locus of the points which are equal to zero marginal profit shows thereaction curve for the firm. You may get the result by using Mathematica.

In[31]:= GrRE1=ContourPlot[RE1,{q1,0,24},{q2,0,24}, Contours->{0}, ContourShading->False, FrameLabel->{q1,q2}]

Out[31]= -ContourGraphics-

You can see the reaction curve(in this case, linear segment) for firm 1in Figure 1. You may obtain the reaction curve(in this case, linear segment, too)for firm 2 in Figure 2(See the Figures in Appendix).

In[32]:= GrRE2=ContourPlot[RE2,{q1,0,24},{q2,0,24}, Contours->{0}, ContourShading->False, FrameLabel->{q1,q2}]


Good messages help you understand the graphical representation.Now we posit the ""C" on the cross of the two reaction curves to representthe Cournot-Nash equilibrium.

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You can easily obtain the coordinates of the crossing point of two reactioncurves.

In[33]:= Q1C[a,b,m]

Out[33]= {8}

In[34]:= Q2C[a,b,m]

Out[34]= {8}

In this case, the output pair of Cournot-Nash equilibrium is {{8,8}.You may input the following manner to get representation of "C".

In[35]:= tC=Show[Graphics[Text[C,{8+0.5,8+0.5}]]]

Out[35]= -Graphics-

You can see the "C" a little bit right-upward way to the cross point of tworeaction curves(See the Figure 3 in the Appendix).

In[36]:= tReaction1=Show[Graphics[Text[Firm 1's Reaction Curve,{6,23}]]]

Out[36]= -Graphics-

In[37]:= tReaction2=Show[Graphics[Text[Firm 2's Reaction Curve,{20,3}]]]

Out[37]= -Graphics-

Now we can show you the graphical representation of Cournot-Nash equilibrium.

In[38]:= GrCournotE=Show[GrRE1,GrRE2,tC,tReaction1,tReaction2, PlotLabel->Cournot Equilibrium]

Out[38]= -Graphics-

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You can see the graph of two crossing reaction curves in the Figure 3(See theFigure 3 in the Appendix). Next, we show you the isoquant through the Cournot-Nash equilibrium, C.The isoquant of firm 1 is defined to be the output pair,{q1,q2}, that keepsthe firm 1's profit constant. The same definition applies to the isoquant of firm2. You can obtain the isoquant of firm 1 by using Mathematica following ways.Here we use the option value of 50 as PlotPoints because the default value of25 shows you the non-smoothed graph of lines.

In[39]:= ISO1C=ContourPlot[profit1,{q1,0,24},{q2,0,24}, Contours->{pai1C[a,b,m]},ContourShading->False, PlotPoints-> 50, FrameLabel->{q1,q2}]


In[40]:= ISO2C=ContourPlot[profit2,{q1,0,24},{q2,0,24}, Contours->{pai2C[a,b,m]},ContourShading->False, PlotPoints-> 50, FrameLabel->{q1,q2}]


We represent the reaction curves and the isoquant of firm 1 on the same screen.The gradient of the isoquant of firm 1, D[profit1,q1], takes value of zero onthe point of the firm 1's reaction curve. The same is true. The gradient of the isoquant of firm 2, D[profit2,q2], takesvalue of infinity on the point of the firm 2's reaction curve.

In[41]:= GrCournotISO=Show[Graphics[GrRE1,GrRE2,tC,tReaction1, tReaction2, ISO1C,ISO2C]

Out[41]= -Graphics-

Please compare the Figure 4 with default value of 25 as PlotPoints with Figure5 with option value of 50(See the Figures in Appendix). Two profit levels of isoquantare the same, that is, 64 for both firms.

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Please note that the lower the isoquant of firm 1, the more profit for firm 1.Also you can see that the lefter the isoquant of firm 2, the more profit forfirm 2. The output pairs that are in the region enclosed by two isoquants through theCournot-Nash equilibrium are preferred by both firms because they can get more profitthan profit in the Cournot-Nash equilibrium, respectively. For example, if they produce at the output pair,{6,6}, then they get profit of72=(13-1)*6 ,respectively, because the price for this case is 13=25-(6+6).Namely, if they could cooperate to produce the output pair,{6,6}, then theycould get the profit pair,{72,72}. Here you are position to consider the situation.If your opponent firm produces 6 output, then you can get more profit by producing9 output instead of the cooperated 6 output. You can check this at once. Suppose firm 2 produces 6 output. Now we rewrite the firm 1's profit as rijun1. ["rijun" means profit in Japanese.]

In[42]:= rijun1=profit1/.q2->6

Out[42]= (18 - q1) q1

This is the profit for firm 1. Now you can get the output that maximizes his profit defined in Out[42].The first order condition for profit maximization is the following:

In[44]:= D[rijun1,q1]==0

Out[44]= 18 - 2 q1 == 0

To solve for q1 of above equation you may use Solve operation of Mathematica.

In[45]:= Solve[%,q1][[1]]

Out[45]= {q1 -> 9}

You can get 9 output that maximized firm 1's profit if the firm 2 produces6 output.

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The second order condition for profit maximization is satisfied in the following:

In[46]:= D[rijun1,{q1,2}]

Out[46]= -2

In[47]:= rijun1/.q1->9

Out[47]= 81

You can see that firm 1 gets 81 profit by producing 9 output with deviationfrom producing of 6 output. The profit of 81 is larger than the cooperated profitof 72. In this case the firm 2's profit, rijun2, is obtained as follows:

In[48]:= rijun2=profit2/.q1->9

Out[48]= (15 - q2) q2

In[49]:= rijun2/.q2-> 6

Out[49]= 54

The profit of 54 is accrued by firm 2.

In summary, if two firms cooperate by producing the output pair,{6,6}, thenthey get the profit pair,{72,72}. However, if the opponent firm keep the cooperationby producing 6 output, then you can get 81 of the profit pair,{81,54} by producing9 output with deviation from the cooperated 6 output. There is no incentives to keep the cooperative agreement. However, if both firmsdeviate from the cooperative agreement, then they may be only the Courot-Nashequilibrium and get the profit pair,{64,64}. This situation is the same as "Prisoner's Dilemma" in the game theory.

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One shot game can support no cooperative solution. If we consider the super games(the infinitely repeated games), we have the FolkTheorem in which the cooperative solutions are supported by the strategy in non-cooperative framework. See Friedman[1983].

2.3 The Stackelberg equilibrium in Duopoly

We call firm A to be "Follower" if she chooses the strategy that is the bestresponse to other firm B's strategy.Also we call firm C to be "Leader"" if she knows that the other firm D is "Follower".Therefore the Leader knows the Follower's reaction function or curve.

Stackelberg considered such a case in duopoly.Let us suppose that firm 1 is the Leader and firm 2 is the Follower.We will find the Stackelberg equilibrium S1.

For that purpose let us regime the parameters(a, b, and m).In Mathematica, we can do it as follows:

In[50]:= Clear[a,b,m];

Let us recall firm 1's profit(profit1), again.

In[51]:= Simplify[profit1]

Out[51]= q1 (a - m - b q1 - b q2)

Please note that the parameters(a,b, and m) are resumed.Since firm 1 is the Leader by assumption, she knows the firm 2's reaction functionor curve. Let us recall the firm 2's reaction function as follows:

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a - m - b q1Out[52]= ------------ 2 b

You can substitute this value as q2 in the expression of firm 1's profit1.In Mathematica, you may input the following manner, where the profit1S1 means thefirm 1's profit when she is the Leader.

In[53]:= profit1S1=profit1/.q2->reaction2[a,b,m]

a - m - b q1Out[53]= -(m q1) + q1 (a - b (q1 + ------------)) 2 b

In[54]:= Simplify[profit1S1]

q1 (a - m - b q1)Out[54]= ----------------- 2

You can get the simplified expression of profit1S1.Both conditions of profit maximization for two firms are as follows. Please note that the second order condition for profit maximization is satisfiedfor both firms.

In[55]:= focS1={D[profit1S1,q1]==0, foc [[2]]}

b q1 a - m - b q1Out[55]= {a - m - ---- - b (q1 + ------------) == 0, 2 2 b

a - m - b q2 - b (q1 + q2) == 0}

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To solve for q1 and q2 from above equations, you may use Solve function inMathematica.

In[56]:= S1=Solve[focS1,{q1,q2}][[1]]

a - m a - mOut[56]= {q2 -> -----, q1 -> -----} 4 b 2 b

Now let us define the Stackelberg equilibrium output as follows:

In[57]:= Q1S1[a_,b_,m_]:=Evaluate[Simplify[q1/.S1]]

In[58]:= Q1S1[a,b,m]

a - mOut[58]= ----- 2 b

In[59]:= Q2S1[a_,b_,m_]:=Evaluate[Simplify[q2/.S1]]

In[60]:= Q2S1[a,b,m]

a - mOut[60]= ----- 4 b

Following is the price level at the Stackelberg equilibrium.

In[61]:= pS1[a_,b_,m_]:=Simplify[a-b (Q1S1[a,b,m]+Q2S1[a,b,m])]

In[62]:= pS1[a,b,m]

a + 3 mOut[62]= ------- 4

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The profits of both firms are obtained as follows, respectively.

In[63]:= pai1S1[a_,b_,m_]:=Simplify[(pS1[a,b,m]-m) Q1S1[a,b,m]]

In[64]:= pai1S1[a,b,m]

2 (a - m)Out[64]= -------- 8 b

In[65]:= pai2S1[a_,b_,m_]:=Simplify[(pS1[a,b,m]-m) Q2S1[a,b,m]]

In[66]:= pai2S1[a,b,m]

2 (a - m)Out[66]= -------- 16 b

In summary, you have the Stackelberg equilibrium.

In[67]:=StackelbergS1Equilibrium={Q1S1[a,b,m],Q2S1[a,b,m],PS1[a,b,m]}

a - m a - m a + 3 mOut[67]= { ----- , ----- , ------- } 2 b 4 b 4

In[68]:= StackelbergS1Profits{pai1S1[a,b,m],pai2S1[a,b,m]}

2 2 (a - m) (a - m)Out[68]= { -------- , -------- } 8 b 16 b

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2.4 Graphical representation of the Stackelberg equilibrium

The firm 1's profit is maximized at the Stackelberg equilibrium S1 while the pointS1 is on the firm 2's reaction curve where firm 1 is the Leader and firm 2 is theFollower. In other words, firm 1's isoprofit curve is tangent to firm 2's reactioncurve. To see the case, you have to make some arrangement.

Let us fix the parameters(a,b, and m) to compare the Cournot-Nash equilibriumwith the Stackelberg equilibrium in the graphical representation. Now suppose that

a=25,b=1, and m=1.

In[69]:= a=25;b=1;m=1;

You can get the Stackelberg equilibrium as follows:

In[70]:=StackelbergS1Equilibrium

Out[70]= {12, 6, 7 }

From the above expression you can see that firm 1 produces 12 output, firm 2produces 6 output, and the price level is 7 at the Stackelberg equilibrium.

In[71]:=StackelbergS1Profits

Out[71]= {72, 36}

Also you can see that profit of "Leader" firm 1 is 72 while profit of "Follower"firm 2 is 36. Now you can get firm 1's isoprofit curve in which she gets 72 profit.

In[72]:= ISO1S1=ContourPlot[profit1,{q1,0,24},{q2,0,24}, Contours->{pai1S1[a,b,m]}, ContourShading->False, PlotPoints-> 50, FrameLabel->{q1,q2}]

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Also you can get firm 2's isoprofit curve in which she gets 36 profit.

In[73]:= ISO2S1=ContourPlot[profit1,{q1,0,24},{q2,0,24}, Contours->{pai2S1[a,b,m]}, ContourShading->False, PlotPoints-> 50, FrameLabel->{q1,q2}]


Now you are position to express the Stackelberg equilibrium S1.

In[74]:= tStackelbergS1=Show[Graphics[Text[S1,{Q1S1[a,b,m]+0.5, Q2S1[a,b,m]+0.5}]]]

Out[74]= -Graphics-

You may overlap the Stakelberg equilibrium onto the graph of Cournot-Nashequilibrium.

In[75]:= GrStackelberg=Show[GrRE1,GrRE2,tC,tReaction1,tReaction2, ISO1S1, ISO2S1,tStackelbergS1]

Out[75]= -Graphics-

You can get the Figure 6(See the Figure in Appendix). From this Figure, you havemore information concerning the relationships between the Cournot-Nash equilibriumand Stackelberg equilibrium. It is more preferable for firm 1 as Leader in the Stackelberg equilibrium ofprofit 72 than the Cournot-Nash equilibrium of profit 64. It is evident from the fact that the lower isoprofit curve, the more profit forfirm 1. On the other hand, it is more preferable for firm 2 as Follower in the Cournot-Nash equilibrium of profit 64 than the Stackelberg equilibrium of profit 36.

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You can also compare the outputs in both equilibria, C and S1.The sum of the outputs at the Cournot-Nash equilibrium is 8+8=16.The sum of the outputs at the Stackelberg equilibrium is 12+6=18.

The price level at the Cournot-Nash equilibrium(25-(8+8)=9) is higher than theone at the Stackelberg equilibrium(25-(12+6)=7).

2.5 Concluding remarks of this section

You can get the Cournot-Nash equilibrium and the Stackelberg equilibrium in theduopolymodel by using Mathematica. By the combination of several operations you may see thegraphical representation of duopoly theory.

You can easily understand the essence of principles of economics by usingMathematica. You are free from the complicated computation such as differentiation.Of course you need some sort of knowledge of introductory economics. I think it is more profitable to use Mathematica to teach elementary economics.Computer Assisted Learning(CAL) in Economics is on.

3. Computer Assisted Learning in Economics by using Internet and theavailability of Research Resources on the Net.

You can easily get a couple of software of CAL in economics, discussion papersa large volume of economic data if you can access the Internet such as WorldWide Web(WWW) and ftp. Here I will introduce some useful resources because of limited space.

3.1 General and almost exhaustive introduction by Bill Goffe on Internet

The file by Bill Goffe on the Internet is very useful to researchers and firstlearners of economics. It is general and almost exhaustive introduction toInternet concerning economic resources.

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Resources for Economists on the Internet, Vol. 2, No. 3, May, 1997

This file is constantly updated almost every 3 months. The latest version is uploadedin May 27, 1997. Total contents have 41 chapters(about 425 KB in ASCCI format) andare available from the following site. You may access the following URL(UniformResource Locator):

http://econwpa.wustl.edu/EconFAQ/EconFAQ.html

3.2 Software guide for economicsEconomics Software Guide, Alphabetical Listing, is uploaded in:

http://www.ilrt.bris.ac.uk/ctiecon/alphalst.htm

This list is managed by the Computers in Teaching Initiative, CTI Centre forEconomics, the University of Bristol in Great Britain. This is the alphabeticallisting. On the other hand, the categorical listing makes you good introduction tosoftware. The its URL is :

http://www.ilrt.bris.ac.uk/ctiecon/catalog.htm

3.3 NetEcThis server has been managed by the MIDAS service of Manchester Computing and hasseveral mirror sites such as Washington University and Hitotsubashi University.

URL: http://netec.mcc.ac.uk/NetEc.html

The object of NetEc is to proceed to economic research and communications throughthe electric means and following 7 activities are conducted by volunteers.

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(1)Information on printed working papers on BibEc, URL: http://netec.mcc.ac.uk/BibEc.html(2)Data about electronic working papers on WoPEc,URL: http://netec.mcc.ac.uk/WoPEc.html(3)Code for Economics and Econometrics on CodEc,URL: http://netec.mcc.ac.uk/CodEc.html(4)World Wide Web resources in Economics on WebEc,URL: http://netec.mcc.ac.uk/WebEc.html(5)Select Resources in Business Administration BizEc,URL: http://netec.mcc.ac.uk/BizEc.html(6)Home Page Papers in Economics on HoPEc,URL: http://netec.mcc.ac.uk/HoPEc.html(7)Jokes about economists and economics on JokEc.URL: http://netec.mcc.ac.uk/JokEc.html

3.4 Resources on Economics and EducationWebEc(World Wide Web Resources in Economics) opens the site of Economics and Teaching.Please get start the following site or mirror site:

URL: http://www.helsinki.fi/WebEc/webeca.html

URL: http://netec.ier.hit-u.ac.jp/WebEc/weveca.html

Each site provides you several approaches to teaching economics for students.

EcEdWeb(the Economic Education Website) is the another good Web site for teachingeconomics. This site is managed by Mary Lynn Reiser, Jim Dick, and Kim Sosin(Univeristyof Nebraska, Omaha).

URL: http://ecedweb.unomaha.edu/home2.htm

In particular, for Economic Resources for College Teachers, you may consult thefollowing site:

URL: http://ecedweb.unomaha.edu/teach-ec2.htm

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Also you may find it interesting in the following site of Economic Resources for K-12Teachers:

URL: http://ecedweb.unomaha.edu/teach2.htm

These sites are good starting points to learn economics by students as well asteachers.

3.5 Introduction to Economics software (WinEcon 4.0TLTP(Teaching and Learning Technology Programme) Economics Consortium has beenestablished to promote Teaching and Learning through modern technology productivelyand efficiently. Under these projects, 8 universities in Great Britain has beendeveloped Computer Based Learning(CBL) software, WinEcon(tm), version 4.0 in February1996 and version 4.1 in 1997. The WinEcon has been evaluated. See the review of John Sloman ,EconomicJournal(September 1995), Vol. 105, No.432, pp.1327-1346.

URL: http://www.ilrt.bris.ac.uk/ctiecon/tltp.htm URL: http://sosig.ac.uk/winecon/product/intro.htm

The EinEcon can help learners to learn economics and it is very convenientinteractive program of teaching students for economics at the undergraduate levels.The contents have 25 chapters including all items such as introductory economics,microeconomics, macroeconomics, an introductory mathematics and statistics.

3.6 Educational software for Experimental Economics

The ESL(Economic Science Laboratory), the University of Arizona, USA, has usedthe experimental economic technology to teach economics, financial problems, andaccounting. The ESL find it very valuable approaches and effective ways of teaching.The ESL also developed the following programs:

URL: http://www.econlab.arizona.edu/eslsoft.html

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(1)MICRO Monop(MONOP.EXE)By using this program you can have experience of the simulation in which you are themonopolist.

(2)MICRO Call(HAND.EXE)By using this program you may exert classroom experiment such as a uniform price,or "call" auction.

(3)ESL Double Auction(ESLDA143.EXE)By using this program you can learn theories of supply and demand and equilibriumin the network.

(4)Voluntary Contribution Mechanism(VCM110.EXE)By using this program you can have experience of the investment decision betweenprivate good and public good under the give resources. Because the yield from theinvestment of public good is accrued by all member of this game, you can have a strongincentives for Free Rider.

(5)Normal Form Game(NFG2.EXE)By using this 2 person game you can learn several concepts in game theory.

3.8 Game Theory and the Experimental EconomicsProf. Roth (University of Pittsburgh) opens his Web homepage(Al Roth's game theoryand experimental economics page) in which there are several resources such as GameTheory, Bargaining Theory, Matching Game, Experimental Economics and ComputationalEconomics.

URL: http://www.pitt.edu/~alroth.html

As for Experimental Economics, he links to 26 Web homepages.Prof. Saijo(Osaka University)'s Web home page contains the experiments in Japan.

URL: http://www.iser.osaka-u.ac.jp/~saijo/index-e.html

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He is a leading scholar in this field in Japan and also encourages young researchersin Japan in addition to his own contribution to Experimental Economics.

3.8 Experimental Economics and the Letter (Classroom Expernomics)Expernomics is the new word made from the hybrid of Experiment and Economics.Classroom Expernomics can offer the Experimental economists in the classroom.The letter has been published in every Spring and Autumn in electric means by GregDelemeester(Marietta College) and John Neral(Frostburgh State University) fromSpring 1992.

URL: http://www.marietta.edu/~delemeeg/expernom.html

3.9 Computer Assisted Learning(CAL) in Economics programs developed by Economists(1)Michael C. Lovell[1990, 1995]"EconoLand", 1990, 1995 Version 6.0This is a simulation program of Macroeconomics available on Windows95.The program covers very large variety of situations in simulation.It is very useful and operational because its graphical representations are veryhelpful.

(2)Michael C. Lovell [1986,1996],"Let's Play Oligopoly", Version 9.1By using this program you can learn the oligopoly theory. More than 2 and less than8 firms can compete each to maximize her profit.This program runs on MS-DOS(PC-DOS) in IBM PC or DOS/V compatible machine.

Prof. Lovell has used his programs in Wesleyan University, USA. He suggested stronglyto me to use his programs (1) and (2). I think they are very interesting programs.He also has interested in my program (3).

(3)My CAL Program in EconomicsUzawa[1990][1992][1995][1996]have developed many CAL programs in Economics by usingseveral Basic Languages. The CAL programs in Economics are uploaded in Internet. ItsURL is as follows:

http://www.res.otaru-uc.ac.jp/~uzawa/cal-econ.html

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These 19 programs consist of 9 programs of Microeconomics, 4 programs ofMacroeconomics, 4 programs of Industrial Organization, and 2 programs of Game Theory .Each of these programs can be run on MS-DOS(PC-DOS) mode of IBM PC or DOS/V compatibles.You can use these programs under the written consent of non-commercial use but I retainthe copyright of these programs. To be Continued

References:Asari, Kubo, Ishibashi, and Yamashita[1995],"Mathematica-de keizaigaku (Learning Economics by using Mathematica)," (1)-(6)Keizai Seminar(Economic Seminar),(Nihon Hyouronsha,Tokyo),Nos.485-491June-December,1995, (in Japanese).

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Asari, Kubo, Ishibashi, and Yamashita[1997],"Hajimeyou Keizaigaku-no tameno Mathematica pasokon-ni yoru suushiki-shori(Getting Started in Mathematica for Learning Economics: Mathematica aided by Personal Computer,(Nihon Hyouronsha, Tokyo),1997,(in Japanese).

Hsiao nad Umehara[1997], Pasokon-de gehmu-no riron(Thery of Games aided by Personal Computer),(Nihon Hyouronsha, Tokyo), 1997 (in Japanese).

Uzawa[1990][1992][1995][1996],"Pasokon-no konpyuta gurafikkusu wo riyoushita keizaigaku gakushu-no puroguramu(On the BASIC Programs of Learning Economics by Using Microcomputer Graphics)" (1),(2),(3),and (4), The Economic Review (Otaru University of Commerce), Vol.41, No.2 (1990), pp.25-72., Vol.42, No.4 (1992), pp.15-45., Vol.45, No.3 (1995), pp.83-107, and Vol.46, Nos.2-3 (1996), pp.43-67, (in Japanese).

Uzawa1996,"Mathematica-wo mochiite Cournot-kinko-to Stackelberg-kinko-wo motomeru(Find the Cournot and Stakelberg equilibria by using Mathematica" Suushiki shorigengo Mathematica-wo riyoushita suuri moderu-no kaiseki (Mathematical Analysis of Several models by using Mathematica, Tokutei kenkyu houkokusho(Research Report(Otaru University of Commerce),(1994- 1995), pp.35-56 (in Japanese)

Okada[1996], Gehmu riron(Game Theory), (Yuhikaku, Kyoto), 1996 (in Japanese).

Okuno and Suzumura[1988],Mikuro-keizaigaku(Microeconomics), Vol.II,(Iwanami Shoten, Tokyo), 1988 (in Japanese).

Cournot(Translated by Nakayama)[1982],Tomi-no riron-no suugakuteki genri-ni- kansuru kenkyu(Researches into The Mathematical Princeples of The Theory of Wealth,(Nihon Hyouronsha, Tokyo), 1982, Chapter 7 (in Japanese). Original French version was published in 1838 as Recherches sur les principes mathematiques de la theorie des richesses. Gray and Glynn(Translated by Sakakibara)[1992],Mathematica biginah gaido(The Beginner's Guide to Mathematica),(Toppan, Tokyo), 1992 (in Japanese).

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Kobayashi[1996],Mathematica-niyoru Mikuro-keizaigaku sutadei gaido(Study guide to Nishimura's Microeconomics by using Mathematica),(Tohyo Keizai shinpohsha, Tokyo), 1996 (in Japanese).

Kon, Uzawa, and Yamamoto[1992],Kihon Gendai Keizaigaku(Basic Contemporary Economics,(Chuo-Keizai-sha, Tokyo), 1992 (in Japanese).

Wakabayashi1996,"Otaru shouka daigaku joho shori sentah pisces-deno Mathematica-no riyou-ho(How to use Mathematica in pisces, The Information Center of Otaru University of Commerce), Suushiki shorigengo Mathematica- wo riyoushita suuri moderu-no kaiseki (Mathematical Analysis of Several models by using Mathematica, Tokutei kenkyu houkokusho(Research Report (Otaru University of Commerce),(1994-1995), pp.1-33 (in Japanese)

Bill Goffe "Resources for Economists on the Internet," Vol. 2, No. 3, May, 1997 URL: http://econwpa.wustl.edu/EconFAQ/EconFAQ.html

Dixit[1979]A Model of Duopoly Suggesting a Theory of Entry Barriers, Bell Journal of Economics, Vol.10, No.1(Spring 1979), pp.20-32.

Friedman[1983] Oligopoly,(Cambridge University Press,1983), pp.58-59

Huang and Crooke(eds)[1977],Mathematics and Mathematica for Economists, (Includes diskette), Blackwell Publishers, Oxford, 1977

Stiglitz[1993] Economics,(W.W. Norton & Company, 1993)

Varian(ed.)[1993] Economic and Financial Modeling with Mathematica,(Includes diskette), TELOS, Springer-Verlag, New York, 1993.

Wolfram[1988] Mathematica: A System for Doing Mathematics by Computer, Wolfram Research Inc., Addison-Wesley Publishing Company, New York, 1988. Japanese version was published in 1992 by Addison-Wesley Publishers Japan and Toppan.

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[Summary]Computer Assisted Learning(CAL) in Economics by using Mathematica and InternetResources on Economics By Masaru Uzawa (Otaru University of Commerce)

Abstract: In this paper we talk about CAL in Economics by using Mathematica andInternet Resources on Economics. In section 2, we can use Mathematica to obtain theCournot Equilibrium and Stackelberg Equilibrium. Both computational operations andgraphical representations in Mathematica can be done so easily. We can understandthe oligopoly theory by using Mathematica. In section 3, we can pick up the InternetResources on Economics. Several interested URL(Uniform Resource Locator) are shown.Please try it. You will find it very interesting and useful.

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Figure 1. The Firm 1's Reaction Curve

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Figure 2. The Firm 2's Reaction Curve

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Figure 3. The Cournot-Nash Equilibrium

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Figure 4. The Cournot-Nash Equilibrium and the IsoProfit Curve (PlotPoints=25(default))

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Figure 5. The Cournot-Nash Equilibrium and the IsoProfit Curve

(PlotPoints=50)

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Figure 6. The Cournot-Nash Equilibrium

and the Stackelberg Equilibrium

[End of File: ec98e2.doc]

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