In this problem, we will work through a supply$-$and$-$demand model to better understand when cost$-$saving gains are passed on to consumers in the form of lower prices. We will consider two different versions of a market for widgets: one in which demand is elastic and one in which demand is inelastic. We will consider an outward shift in the supply curve in both markets. Initially, our supply equation is

$q_0^S=100+4p$

Cost$-$saving gains $($as a result of$,$ say, technological innovation$)$ shift supply outward to

$q_1^S=150+4p$

Let's first take the market with inelastic demand. Here, we describe the relationship between the widget price and quantity demanded by the equation

$q_i^D=250-p$