Hello, @EconJohn!

What you can do is to create a `Graphics`

object (let's call it `p`

) before entering the loop, then superimpose the plots of each `k1`

over the previous one and store the result in `p`

, and then show the plot outside of the loop. Since your`k1`

s are defined as symbolic equalities, you will need to use the `rhs()`

(right-hand side of the equality) method inside the `plot()`

command.

Before writing the final version of the code, I would like to make a few observations: You don't need to define `v0`

and `beta`

as symbolic variables, since you later assign to `beta`

the value `0.6`

, which overwrites the effect of the `var()`

command, converting it into a numerical variable; similarly, you assign `v0 = log(k)`

, which overwrites the definition made by `var()`

(in this case, `v0`

IS automatically made a symbolic variable, since it is the logarithm of the symbolic variable `k`

.) For a similar reason, it is unnecessary to define `vk`

with `var()`

. Finally, you define but never use the `vk1`

variable.

Here is the code:

```
#Step1: Name variables
k,k1 = var('k,k1')
#Step2: Initialize your values
beta = 0.6
v0 = log(k)
cols = ['red', 'darkgreen', 'blue', 'magenta', 'yellowgreen']
p = Graphics()
#Step 3: The Loop to Obtain Policy function
for n in range(5):
vk = log(k-k1) + beta*v0(k=k1)
FOC = vk.diff(k1)
k1star = solve(FOC==0, k1)
print(n, k1star)
v0 = (vk).subs(k1=k1star[0].rhs())
p += plot(k1star[0].rhs(), color=cols[n], legend_label=str(k1star[0]))
p.show()
```

I have taken the liberty of defining a list `cols`

with some different colors in order to differentiate the plots. The instruction `p = Graphics()`

defines `p`

as an empty plot. Inside the loop, I have added the instruction

```
p += plot(k1star[0].rhs(), color=cols[n], legend_label=str(k1star[0]))
```

Remember that superimposing plots is equivalent to "adding" the plots, so this command generates a plot for every iteration and adds it to `p`

. I have used the $n$-th color in the `cols`

list. I have also added a label, indicating which color and formula correspond to which plot. The last line, `p.show()`

finally shows the plot.

I hope this helps! Please, let me know if you need some additional help.

Hello, @EconJohn! I am adding a solution below that plots the solutions you found. I am not 100% sure that this is what you want. Please, let me know if you require some different kind of plot.