Currently installing solar panels on your house costs about $4-$5 a watt.
Imagine how the world would change if a miracle technology made it $0.50 per watt.
If you installed a 6 kW system on your house, it would cost you $3000, and it would provide about $1000-$1200 of electricity per year ( at 10cents per kW ). It would pay for itself in less than 3 years and then be generating free electricity.
Actually the price of electricity during the daylight hours would crash – in areas with high demand during peak daylight hours – the price runs around 15-20c/kWh, and nighttime rates are 4-5c/kWh.
We would probably turn off and mothball all the coal and nuclear plants in the country. Natural gas plants that now run at the peak of the day to provide power for peak demand – would instead run in the evening hours and in the wee morning light and be off during the day.
But soon we would turn many of those off permanently too, because it would be cost competitive for energy consumers to install batteries and use them for the dark hours instead of buying power from the grid.
Natural gas power generation would be relegated to fill-in power when there is a particularly cloudy day.
Turning off all the coal fired power plants, and most of the natural gas ones, would lead to vastly cleaner air for everyone.
In the developing world, there are many places that are powered by large dirty expensive diesel generators.
Many of these generators are off at night, or are unreliable, leaving people without power for hours every day. These would disappear and be replaced by much cheaper solar panels. Their power would become more reliable as more and more batteries are added, extending the availability of power to more night time hours.
Instead of being at the mercy of diesel shortage or generator breakdown, they would instead worry about dark skies running the batteries dead ( some places would retain the diesel for backup, but others would lose that because it would break and never be repaired ). But the lower overall cost of batteries and solar panels should lead to more power availability overall.
Back in the western world – power would be massively decentralized, and many long distance transmission lines would probably be dismantled. The utilities would shift entirely to middlemen, buying and selling power over very short distances from those with surplus to those with smaller battery banks or those experiencing short term high load, or those under a dark cloud.
It is likely you would not install solar panels to meet rare peak needs, so they would still occasionally want to buy a little extra from neighbors. Perhaps small collectives/city/neighborhood based “utilities” or co-ops would form to share and sell with members, and buy and sell to neighboring co-ops.