Undefined An (ISP) serves a population of 1m consumers. Each consumer would like to download a very large file from the internet, and may either access the internet during peak or non-peak times. At either time (peak or non-peak), the download takes N/1000 seconds to complete, where N is the number of consumers downloading the file at that same time. (For example, if 700, 000 consumers choose to download at the peak time and 300, 000 consumers choose to download it at the non-peak time, the download takes 700s during the peak time and 300s during the non-peak time.)

For each consumer, the inconvenience of downloading the file during the non-peak time is equivalent to waiting an additional 500s for it.

1. In the Nash equilibrium, how many peak-time users and non-peak-time users are there? 

2. To achieve social efficiency ''to minimize total waiting time and inconvenience costs faced by all'', how many users should there be at each time? Suppose that the ISP charges an additional fee for using the internet during peak hours. Assume that each consumer values time at one cent per second . ''waiting an additional second is equivalent to paying an additional cent''. 

3. When the additional fee is 1 euro, how many users are there at each time? 

4, How much should the additional fee be in order to induce the socially efficient outcome?