Could you make a bike frame out of 24kt gold? Obviously it's a silly idea. Apart from the cost, it's far too dense and not stiff enough to be a good frame material.

What I'm asking is would it be possible to make a ridable bike from gold? What calculations would be needed to work out what tube size/thickness would be needed?
According to Wikipedia, Gold has an "ultimate tensile strength" of 100 MPa, while steel runs from 400 to 5000. (Carbon fiber laminate is 1600.) 

Gold has a specific gravity of about 19, while steel has a specific gravity of about 7.8. So it would take about 4 times as much pure gold by volume, or about 9.7 times as much gold by weight. A 15 pound steel frame would weigh about 145 pounds in gold. 

Gold is currently trading about $1300 per (Troy) ounce, so that works out to 145 * 12 * $1300, or $2.26 million. I think even carbon would be cheaper (and lighter).

(And, of course, due to the weight of the frame, the frame strength would have to be beefed up, so you'd need more gold still.)