hw_6_5.py

from matplotlib.backends.backend_pdf import PdfPages
%matplotlib inline
def inverse_supply(quantity):
    '''Inverse supply function $p_s = {\sqrt{q_s} }$, where quantity is inputed and price is output'''
    return (math.sqrt(quantity))

def inverse_supply_with_tax(quantity):
    '''Inverse supply function with the tax added $p_s = {\sqrt{q_s} } + 2$, where quantity is inputed and price is output'''
    return inverse_supply(quantity) + 2

def inverse_demand(quantity):
    '''Inverse demand function $p_d = 100e^{-q_d}$, where quantity is inputed and price is output'''
    return 100 * math.pow(math.e, (0 - quantity))

def calculate_equilibrium(supply_func, demand_func):
    '''Loops through quantity values for supply and demand and finds where the two functions intersect within 0.0001 '''
    equilibrium = 0.0001

    p_s = supply_func(equilibrium)
    p_d = demand_func(equilibrium)

    while abs(p_s - p_d) > 0.0001 and equilibrium < 100:
        p_s = supply_func(equilibrium)
        p_d = demand_func(equilibrium)
        
        equilibrium += 0.0001
    return equilibrium

def build_line(func, X):
    '''build a list of y values based on x values for a given function'''
    y = []
    for point in X:
        y.append(func(point))

    return y

def fill_consumer_surplus(X, equilibrium_w_tax):
    x_below_equilibrium = [point for point in X if point <= equilibrium_w_tax]
    y_below_equilibrium = []
    y_above_equilibrium = []
    
    for point in x_below_equilibrium:
        y_below_equilibrium.append(inverse_demand(point))
        y_above_equilibrium.append(inverse_demand(equilibrium_w_tax))

    plt.fill_between(x_below_equilibrium, y_below_equilibrium, y_above_equilibrium, step="pre", color = "c", alpha=0.4, label='CS') # fill in area for consumer surplus

def fill_producer_surplus(X, equilibrium_w_tax):
    x_below_equilibrium = [point for point in X if point <= equilibrium_w_tax]
    y_below_equilibrium = []
    y_above_equilibrium = []
    
    for point in x_below_equilibrium:
        y_below_equilibrium.append(inverse_supply(point))
        y_above_equilibrium.append(inverse_supply(equilibrium_w_tax))

    plt.fill_between(x_below_equilibrium, y_below_equilibrium, y_above_equilibrium, step="pre", color = "orange", alpha=0.4, label='PS') # fill in area for consumer surplus

def fill_dead_weight(X, equilibrium_w_tax, equilibrium):
    x_below_equilibrium = [equilibrium_w_tax]
    for point in X:
        if point >= equilibrium_w_tax and point <= equilibrium:
            x_below_equilibrium.append(point)
    x_below_equilibrium.append(equilibrium)
            
    y_below_equilibrium = []
    y_above_equilibrium = []
    
    for point in x_below_equilibrium:
        y_below_equilibrium.append(inverse_demand(point))
        y_above_equilibrium.append(inverse_supply(point))

    plt.fill_between(x_below_equilibrium, y_below_equilibrium, y_above_equilibrium, step="pre", color = "green", alpha=0.4, label='DW') # fill in area for consumer surplus

# Starting point 
def q5():
    equilibrium_w_tax = calculate_equilibrium(inverse_supply_with_tax, inverse_demand) # Get equilibrium with tax
    equilibrium = calculate_equilibrium(inverse_supply, inverse_demand) # get standard equilibrium
    
    demand_integral = si.quad(inverse_demand,0,equilibrium_w_tax) # get area under the inverse demand function
    supply_integral = si.quad(inverse_supply,0,equilibrium) # get area under the inverse supply function

    area_below_curves = equilibrium_w_tax * inverse_demand(equilibrium_w_tax)

    demand_integral[0] - area_below_curves

    consum_sur = demand_integral[0] - area_below_curves
    producer_sur = area_below_curves - supply_integral[0]

    fig = plt.figure()

    x = []
    value = 2
    while value <= 4: # generate list of values for x to be used in generating lines. 
        x.append(value)
        value += 0.05 # each value in line is separated by 0.05
    
    y = build_line(inverse_demand, x)   # build y values for inverse demand then plot
    plt.plot(x, y, color='blue', label='Inverse Demand')

    y = build_line(inverse_supply, x) # build y values for inverse supply then plot
    plt.plot(x, y, color='black', label='Inverse Supply')

    y = build_line(inverse_supply_with_tax, x) # build y values for inverse supply w/tax then plot 
    plt.plot(x, y, color='red', label='Inverse Supply with Tax')
    
    plt.plot(equilibrium, inverse_supply(equilibrium), 'o', color='red') # plot equilibrium point w/o tax
    plt.plot(equilibrium_w_tax, inverse_supply_with_tax(equilibrium_w_tax), 'o', color='black') # plot equilibrium point w/ tax
    plt.plot(equilibrium_w_tax, inverse_supply(equilibrium_w_tax), 'o', color='black')
    
    gov_revenue = equilibrium_w_tax * (inverse_supply_with_tax(equilibrium_w_tax) - inverse_supply(equilibrium_w_tax))
    dead = (0.5 * (inverse_supply_with_tax(equilibrium_w_tax) - inverse_supply(equilibrium_w_tax))) * (equilibrium - equilibrium_w_tax) # calculate the dead weight loss

    fill_consumer_surplus(x, equilibrium_w_tax)
    fill_producer_surplus(x, equilibrium_w_tax)
    fill_dead_weight(x, equilibrium_w_tax, equilibrium)
    
    plt.fill_between([2, equilibrium_w_tax], [inverse_supply_with_tax(equilibrium_w_tax), inverse_supply_with_tax(equilibrium_w_tax)], [inverse_supply(equilibrium_w_tax), inverse_supply(equilibrium_w_tax)], step="pre", color = "purple", alpha=0.4, label='Gov Revenue') # fill in area for consumer surplus

    plt.xlabel = "Quantity"
    plt.ylabel = "Price"
    plt.legend()
    plt.show()

    pp = PdfPages(outputfolder + "//dboland_q5.pdf")
    
    fig.savefig(pp, format='pdf')

    pp.close()
    
    print("consumer surplus:",consum_sur)
    print("producer surplus:",producer_sur)
    print("government revenue:",gov_revenue)
    print("deadweight loss:",dead)