Now let’s reverse the first step we did to find the modified quantity equation.

import sympy
p = sympy.Symbol("p")
q = sympy.Symbol("q")
cTax = sympy.Symbol("cTax")
pTax = sympy.Symbol("pTax")

def eqSolve(eq1,eq2,tax):
    demandP = sympy.solve(eq1-q,p)[0]
    supplyP = sympy.solve(eq2-q,p)[0]
    demandP = demandP-cTax
    supplyP = supplyP+pTax

    demandQ = sympy.solve(demandP-p,q)[0]
    supplyQ = sympy.solve(supplyP-p,q)[0]
    print(demandQ)
    print(supplyQ)

eqSolve(10-p,2*p,2)

The final step is solving the system of equations. We are going to feed sympy the equations in a tuple. Tuples are very similar to arrays, but we don’t use brackets, instead we use parentheses. We will give the program a tuple that looks like this (equation1, equation 2, equation 3). The three equations we are using as follows. 1) demandP = supplyP, these prices are the same because we added the correcting terms of tax. 2) demandP = supplyQ, you can’t sell more than people buy or vice versa. 3) tax = cTax+pTax, the two taxes need to add up. Everything needs to be moved to one side, so our tuple is: (demandP-supplyP, demandQ-supplyQ,tax-cTax-pTax). We are going to need to also tell sympy what variables we want to solve for after the tuple. We specify q,p,cTax,pTax so that it solves the system.

import sympy
p = sympy.Symbol("p")
q = sympy.Symbol("q")
cTax = sympy.Symbol("cTax")
pTax = sympy.Symbol("pTax")

def eqSolve(eq1,eq2,tax):
    demandP = sympy.solve(eq1-q,p)[0]
    supplyP = sympy.solve(eq2-q,p)[0]
    demandP = demandP-cTax
    supplyP = supplyP+pTax

    demandQ = sympy.solve(demandP-p,q)[0]
    supplyQ = sympy.solve(supplyP-p,q)[0]

    return sympy.solve((demandP-supplyP, demandQ-supplyQ,tax-cTax-pTax), q,p,cTax,pTax)
eqSolve(10-p,2*p,2)

What we get back is something you haven’t seen in this course yet, a dictionary. I’m going to break away from the function for one second to explain a dictionary. Dictionaries have keys, and each key has a value associated with it. This value can be anything valid, like an integer, a string, or even an array.

To initiate a dictionary, you set a variable equal to something with this format: {key1: value1, key2:value2…keyN:valueN}. Let’s see an example.

music = {"Genre":"Rap","Artists":["Kanye West","Kendrick Lamar","J. Cole"],"Albums":10}
print(music)

To get the value for a key you do this:

print(music["Genre"])

And if we wanted to add one to the number of albums we could do this:

music["Albums"]+=1
print(music["Albums"])

Now that we know how dictionaries work, let’s get the value of quantity from our dictionary by using the key q.

import sympy
p = sympy.Symbol("p")
q = sympy.Symbol("q")
cTax = sympy.Symbol("cTax")
pTax = sympy.Symbol("pTax")

def eqSolve(eq1,eq2,tax):
    demandP = sympy.solve(eq1-q,p)[0]
    supplyP = sympy.solve(eq2-q,p)[0]
    demandP = demandP-cTax
    supplyP = supplyP+pTax

    demandQ = sympy.solve(demandP-p,q)[0]
    supplyQ = sympy.solve(supplyP-p,q)[0]

    return sympy.solve((demandP-supplyP, demandQ-supplyQ,tax-cTax-pTax), q,p,cTax,pTax)[q]
eqSolve(10-p,2*p,2)

We are only going to need the quantity because we can find both prices for consumers and producers based on their respective curves in our model.