How big is your island?
Development of current technology is going to depend heavily on how many people you can put on this island. When the occasional backyard tinkerer who comes up with a new product, it takes lots of money to turn that invention into a product. Every widespread technological innovation in history has happened in an environment where it is economically viable to sell it. This is true for commercial and military products.
Consider the following example with plastics:
Sam, the inventor comes up with a new plastic thingy that will solve everyone's problems. Money at this point hasn't mattered. However, to create the tooling to pressure inject the plastic costs 1,000,000 ISK. If the market for the plastic thingy is only 1000 people (because there's only 1000 people to be sold to) then each thingy will cost at least 1000 ISK to make up just the tooling costs. This doesn't include materials, admin overhead, marketing or a healthy profit for any investors, so the cost per thingy will be at least 2000 ISK. That product just isn't worth it.
However, if there 100 million people in the plastic thingy market then the tooling costs per person are 1 ISK per thingy. The very high one-time costs just disappear when spread across large markets.
(This also explains why China is such a huge draw for large multinationals. For the longest time there was no market in China but now there are tens of millions of newly middle-class people who want goods and services. Markets that size are just too big to ignore.)
Real numbers please
Consider how large the market must be to support modern semiconductor manufacturers who spent many hundreds of billions in capital investments in the last five years. And that's just one small section of the larger economy.
Market size has a huge impact on how much technological innovation can be afforded and in what area that innovation happens.