Solution

for x in range(1,11):
    quantity = DemandEquation.subs(p,x)
    elast = abs(elasticity(x,x+1,DemandEquation.subs(p,x),DemandEquation.subs(p,x+1)))
    plt.plot(demandQ,prices)
    drawRevenue(x,quantity)
    print("The elasticity at this point is "+str(elast))
    plt.show()

Now let’s take a closer look at how elasticity and revenue are related.

for x in range(1,11):
    quantity = DemandEquation.subs(p,x)
    elast = abs(elasticity(x,x+1,DemandEquation.subs(p,x),DemandEquation.subs(p,x+1)))
    revenue = quantity*x
    print("At price "+str(x)+" elasticity is "+str(elast)+" and the revenue is "+str(revenue)+".")

Something interesting to notice is that at the farthest ends (price = 1 and price=10), the elasticity is at its lowest and its highest, and also the revenue is at it’s lowest for both. Let’s graph these.

elast = [abs(elasticity(x,x+1,DemandEquation.subs(p,x),DemandEquation.subs(p,x+1))) for x in range(1,11)]
revenue = [DemandEquation.subs(p,x)*x for x in range(1,11)]
prices = [x for x in range(1,11)]
plt.plot(prices,revenue)
plt.show()
plt.plot(elast,revenue)
plt.show()

This graph shows us the important relationship between elasticity and revenue. When elasticity is unit elastic (equal to 1), we have the highest revenue. Also when elasticity is low, if we increase price we increase revenue. This makes sense because the growth in price is greater than the loss in quantity. When elasticity is high, we benefit from reducing prices because we have higher growth in quantity, which makes up for the loss in price. These apply to all cases of demand, not just this particular one.

Now, a question to consider. Would producers be better off if all of a sudden they could make twice as much product at every level? You might guess that they would be, but it depends on the way supply and demand are.