I was recently contacted by a researcher, who works for a game show about food and culture, to ask my permission to use a photo from my food blog on their tv show. The researcher sent me a link to watch episodes from the show to see how the photo would be used, and from what I can tell, a still of the picture would appear for about four seconds while a question is being asked relating to it. The price offered so far by her is twenty dollars, but she has also asked what I would want to be paid for the photo and said she would check with her boss about meeting the price I would quote if it was higher. Any advice?
You have to estimate how much they are really prepared to pay, there are 3 sides to this: what is their budget, what is the "real" market value of you picture and how badly they want your specific picture (or, what's their next best option).
To know how much to charge them you need to find out all 3, in this order:
For the budget part - Who makes the show? On what channel(s) and at what time will it air? Who is the host? What are the ratings?
A prime-time show on a major network will have a real budget and will be used to paying market-value for everything, on the other hand an amature production for youtube is unlikely to be able to afford real market value.
For the market value start by looking at what the big agencies are charging for this - pick up the phone and call Getty or another big agency TV stations are likely to work with and ask what they charge for a 4 seconds appearance in a game show (do this second so you can answer question the agency uses to determine pricing).
This is the price you start the negotiation with (do it, this one phone call can easily raise the initial price from $20 to something in the $500 range or more)
What's their next best option - how unique is your image? did they contact you because they can't get the image elsewhere or because they think you'll be cheap? are there other bloggers with similar images they can contact? based in what you've seen how important to them this particular image is?
In any case $20 is pretty low, on shutterstock.com (a cheap microstock site, not an actual image agency TV stations are likely to work with) images for broadcast with an audience of more than 250,000 viewers start at $199