These are obviously ymmv estimates. The calculations assume 1000 tokens of prompt and an average of 500 tokens of chat history in the request (eg. the chat history grows on average from 0 to 1000 over the course of the chat) for about 1500 tokens per chat response.
When asked for 30-50 word answers gpt-3.5-turbo takes about 4 seconds to complete its response (shorter responses mean more chat iterations per hour, longer responses mean fewer chat iterations per hour, my read is the final cost per hour isn't super sensitive to the average response length, but ymmv).
Lets assume the human takes about 6 seconds to respond back to a chat response. That means the conversational back-and-forth cycle time is 4 + 6 = 10 seconds, or one GPT-3.5 completion required every 10 seconds.
Putting this all together means gpt-3.5-turbo conversations burn about 1500 tokens every 10 seconds, or about 500K tokens/hour. GPT-3.5-turbo tokens cost $0.002/1K tokens, or $1 per hour of chat.
gpt-4 is slower (fewer tokens per hour in a conversational chat scenario) and more expensive per token. gpt-4 takes about 9 seconds to produce 40 word responses, or 9 + 6 = 15 seconds per conversational cycle, or one GPT-4 completion required every 15 seconds.
This means gpt-4 conversations burn about 1500 tokens every 15 seconds, or about 360K tokens/hour.
GPT-4 pricing is more complicated than GPT-3.5 pricing. I'm going to assume the costs are dominated by the prompts rather than the responses, because that looks to be true in most of the calculations I tried. Using the smaller/cheaper gpt-4-0314 variant we get 360K tokens/hour * $0.02/1K = $7/hour of chat and using the larger gpt4-32k-0314 model we get 360K tokens/hour * $0.12/1K = $43/hour. That said, there's no point in using the 32k model with 1500 token completion requests. You should only use the 32k model if you are sending more than 8k requests, so we assume the request context in the 32k case is 15,000 not 1,500 and get a cost of $430/hour(!).
Call center employee in the Philippines makes about $6/hour ($1K/month). An average utilization factor of 3 simultaneous text conversations per employee results in $2 per chat hour. Call center employees in the US make about $18/hour or $6 per chat hour at a utilization of 3 simultaneous text conversations.