Is it permissible for me to charge someone I know a price higher than the actual cost for a service I provided to them?

Your performance of this work is likely to be a form of ijarah (hiring/leasing), and you are entitled to request the wage you desire. There is no impediment to working for him if both parties agree on the amount of the wage. However, if the work is performed without specifying the wage, the ijarah is void (fasidah), and you are only entitled to a fair wage (ujrat al-mithl).

It is also possible that the person has appointed you as an agent (wakil) for a task. In this case, you may perform it either as a donation (tabarru'an) or for a wage. If it is for a wage, the wage must be specified, and any surplus money returned to its owner. If the wage is not specified at the time of the agency contract (aqd al-wakalah), the ijarah is void (fasidah), and you are entitled to a fair wage (ujrat al-mithl).