Your wrote: $167 from $50?  

 Yes, that is the beauty of the scheme. The rest $117 will come from the producers, who will now get $73 instead of the entire $200 they were getting before. (Note, here producers mean the entire supply chain which includes foreign producers and domestic oil firms. Also I assume that currently gas in the US is not taxed, which is strictly not true, but a simplifying assumption.) 

 The steep fall in the price obtained by producers happens due to the supply curve being inelastic. That is something we can expect due to the nature of the oil production business. The average worldwide cost of production is $15 per barrel (exploration plus extraction), so producers are unlikely to put production due to a fall in prices. Supply should not start falling till the prices approach cost, and that means at current levels the supply is highly inelastic.