How to Graph integrals?

Question

Researcher DSGE 2024-7-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2140776-how-to-graph-integrals

编辑： Researcher DSGE 2024-7-29

采纳的回答： Torsten

在 MATLAB Online 中打开

Hello everybody,

I'm trying to get this graph:

Using this code:

function res = fun(bs,gamma)

fun_ode = @(b,z)[(1-gamma)*z(1)/(z(2)-b);z(2)/(z(1)-b);z(1)];

z0=[1 1 0];

[B,Z] = ode45(fun_ode,[bs,0],z0);

res = bs - 0.5*(1+gamma*Z(end,3));

end

gamma = 0.3;

bs = 0.542

fun_ode = @(b,z)[(1-gamma)*z(1)/(z(2)-b);z(2)/(z(1)-b);z(1)];

z0=[1 1 0];

[B,Z] = ode45(fun_ode,[bs,0],z0);

hold on

plot(B,Z(:,1),'r')

plot(B,Z(:,2),'b')

hold off

grid on

Error using fplot>singleFplot (line 258)
Input must be a function or functions of a single variable.

Error in fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 218)
hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot>vectorizeFplot (line 218)
hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot (line 184)
hObj = vectorizeFplot(cax,fn,limits,extraOpts,args);

But I didn't get it. I would appreciate it if I could get the graph.

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Answer 1

Torsten 2024-7-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2140776-how-to-graph-integrals#answer_1491921

编辑：Torsten 2024-7-29

在 MATLAB Online 中打开

According to proposition 4, the red curve should be the inverse bidding function X and the blue curve should be the inverse bidding function Y for the given value of gamma.

gamma = 0.3;

bs0 = 0.3;

bs = fsolve(@(b)fun(b,gamma),bs0,optimset('Display','None'))

bs = 0.4509

fun_ode = @(b,z)[(1-gamma)*z(1)/(z(2)-b);z(2)/(z(1)-b);z(1)];

z0=[1 1 0];

[B,Z] = ode45(fun_ode,[bs,0],z0);

hold on

plot(B,Z(:,1),'r')

plot(B,Z(:,2),'b')

hold off

grid on

function res = fun(bs,gamma)

fun_ode = @(b,z)[(1-gamma)*z(1)/(z(2)-b);z(2)/(z(1)-b);z(1)];

z0=[1 1 0];

[B,Z] = ode45(fun_ode,[bs,0],z0);

res = bs - 0.5*(1+gamma*Z(end,3));

end

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Researcher DSGE 2024-7-29

Thanks a lot!

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Answer 2

Walter Roberson 2024-7-27

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2140776-how-to-graph-integrals#answer_1491451

b is not defined.

This is the same problem as you had for your previous iteration of this question (which you have deleted.) I pointed out the problem there.

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Walter Roberson 2024-7-29

在 MATLAB Online 中打开

syms v a

gamma=0.3;

b_hat=0.542;

fun = v/2;

B(v) = int(fun, v, 0, a)

B(v) =

fplot(B,[0 1])

Error using fplot>singleFplot (line 258)
Input must be a function or functions of a single variable.

Error in fplot>@(f)singleFplot(cax,{f},limits,extraOpts,args) (line 218)
hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot>vectorizeFplot (line 218)
hObj = cellfun(@(f) singleFplot(cax,{f},limits,extraOpts,args),fn{1},'UniformOutput',false);

Error in fplot (line 184)
hObj = vectorizeFplot(cax,fn,limits,extraOpts,args);

You are defining B to be a function of v. But you are integrating over v with definite integral bounds that are independent of v, so the result will be independent of v. As a result, B(v) is independent of v, and is instead dependent on the constant a

Torsten 2024-7-29

编辑：Torsten 2024-7-29

@Researcher DSGE

I don't understand the relation between your graphs and Proposition 4. What is v ? Why is b plotted as y-axis and not as x-axis for it seems to be the independent variable ?

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