The kind of innovation that helps improve the economy could do so by improving the efficiency of production, the quality of goods and services, and the availability (access) of goods and services.
Before saying a quick word about those three areas, it is important to note that innovation by itself is not always sufficient to sustain durable economic growth and development. The eventual adoption of promising innovations by a broad range of firms and households is important. In an economy where markets are competitive, investments are being made in physical and human capital, and regulatory frameworks are supportive/not distortionary, the potential for innovation to drive economic prosperity is strongest.
Efficiency of Production
Economic theory has this part somewhat pinned down. Producing goods and services requires three things – capital (machines, factories, computers, offices), labor, and the combination of capital and labor. This combination of capital and labor is what economists call total factor productivity, and it depends on the ingenuity and know-how used in the production process. Two firms can be given the same inputs (capital and labor), but one firm might do a much better job in making something useful with what it has than the other. That firm is the more innovative firm. The more innovative the firm, the more productive it is with its resources.
Note that productivity can improve by being innovative in your approach to your production process (like, switching to an assembly line set-up on the factory floor or thinking of a new kind of business process that improves productivity) or in the technology embedded in the capital you use (faster computer processors, more capable software, etc.).
There are two major implications of productivity-enhancing innovations. The first is that the more efficient firm can charge a lower price (especially true if competition is strong) which is good for consumers. The second implication is that it can improve profitability, allowing the firms to invest more/hire more workers and scale up.
A major concern here is around automation. This is a big concern of our time that I briefly talked about in another answer (). The short jist is that the more machines can do, the more time we have to do other stuff. What other stuff can we do? Innovate!
As a side note, innovations in the delivery of public services also improve efficiency in the government sector, which is usually the largest sector of any economy.
Quality of Goods and Services
In addition to impacting the relationship between the inputs and outputs to production (efficiency and productivity), innovation can improve the quality of goods and services. A major example here is in health care. Over the last century, very important scientific breakthroughs have led to dramatic improvements in the quality of care (think of the imaging capabilities that radiologists use, the difference in treatment you’d get for a broken hip in the 1960s vs. today), despite a worsening of productivity in health care industries related to spending and volume (there are some majorthat are useful to understand but not necessary to discuss here). Other examples include faster internet (improved communication time and faster logistics) and improved learning and educational techniques.
Access to Goods and Services
Innovations can also be centered around reaching hard-to-reach geographies, making previously expensive goods or services available to more people, or sharing information broadly. With digital platforms, free online courses from the best universities in the world can be accessible to people who previously had no pathway to attend those universities themselves, for example. This spreads information and hopefully develops human capital where it may not have otherwise had an opportunity. Similarly,can improve health care for a wider range of people which helps the economy through lower health care costs, more capable people (healthier people can be more productive workers), and a reduction in travel time and congestion if you usually drive or take the bus to the doctor’s office. Another example of wider access is e-commerce along with wider distribution networks. These are just some examples. Other innovations can expand access beyond the internet and digital platforms, but that is where the biggest impact is possible in terms of access.