"When we are able to cut our prices, that actually leads to an increase in earnings for drivers...
When we're able to drop those prices, earnings for drivers increase, and increase disproportionately to what we drop."Essentially, Peppitt is telling us that demand for rides on Uber is what economists term price elastic. When demand is elastic, that means that an increase in price will result in a more than proportional decrease in the quantity sold (e.g. a 10% increase in price might lead to a 20% decrease in quantity). The reverse is also true - a decrease in price will result in a more than proportional increase in the quantity sold (e.g. a 10% decrease in price might lead to a 20% increase in quantity).
When demand is elastic, decreasing your price will increase total revenue. This is because for a simple firm (like a taxi) total revenue is simply price multiplied by quantity. If price decreases, but quantity increases by a greater proportion, then total revenue will increase.
Here's where things get tricky, because firms don't operate in isolation. Elasticities have a strategic element, as we teach in ECON100. Uber might face elastic demand for rides when it lowers prices and other taxi firms don't match the price decrease. Taxi customers would suddenly find that Uber's rides are much cheaper than those of other taxi firms (they are already, but we won't worry about that for now). Many customers will switch to Uber, leading to a large increase in demand (relatively elastic demand). This is illustrated in the diagram below. When Uber lowers their price from P0 to P1, and no other firm matches the new price, then Uber faces the demand curve D1. Quantity increases by a lot, from Q0 to Q1. Total revenue, which is the rectangle under the price and to the left of the quantity, increases from P0*Q0 to P1*Q1 (it should be clear the rectangle of total revenue becomes larger).
However, if the other taxi firms also lower their prices, Uber doesn't have the same cost advantage. There will be some increase in customers overall (because prices are lower for customers from all firms), but Uber won't capture all of those new customers because the other firms are cheaper now too. That means that the quantity demanded from Uber will increase, but not by as much. In the diagram above, when Uber lowers their price from P0 to P1, and other firms also lower their prices, then Uber faces the demand curve D2. Quantity increases a little, from Q0 to Q2. Total revenue decreases from P0*Q0 to P1*Q2 (it should be clear the rectangle of total revenue becomes smaller).
To make matters worse, if marginal costs are increasing then not only does total revenue decrease, but profits for taxi drivers will decrease too (note that this is a possibility even if total revenue increases slightly). And we haven't even considered the distributional impacts (some Uber drivers might get lots more rides, while others get the same, depending on when they are available to drive, where they are located, and so on). So it's probably overly simplistic to assume that lower prices and more rides will make all Uber drivers better off. It certainly shouldn't attract more drivers to sign up for Uber.
So maybe Uber has other motives for lowering prices? Market penetration pricing perhaps? Or just good publicity to try and capture market share?