This paper derives a Supply Function Equilibrium (SFE) of a pay-as-bid auction, also called discriminatory auction. Such an auction is used in the balancing market for electric power in Britain. For some probability distributions of demand a pure-strategy equilibrium does not exist. If demand follows an inverse polynomial probability distribution, SFE always exists. Assuming this probability distribution, the pay-as-bid procurement auction is compared to a SFE of a uniform-price procurement auction, the auction form of most electric power markets. The demand-weighted average price is found to be equal or lower in the pay-as-bid procurement auction.