The year is 2013. There are N people on the planet. ½ of them ignore climate change and do not view it to be a serious threat. ½ of them fear climate change. Suppose that climate change will not take place for 10 years and the annual interest rate is r%. Those who fear climate change will be willing to pay $P in the year 2023 for a product that will protect them from climate change. If it costs your firm an irreversible payment of $F dollars now to invent this new product, and you are a risk neutral present discounted value profit maximizer, write down an equation such that you would choose to invent this product.