A comprehensive account of the theory of the singly quasidegenerate Josephson junction parametric amplifier is given. In this mode the signal and idler frequencies are both approximately equal to half the pump frequency, and hence the signal and idler channels have a common termination. It is shown that the performance of the amplifier characterized by properties such as gain-bandwidth product, noise temperature, and saturation depends strongly on the embedding microwave circuit. In particular any uncompensated series reactance may deteriorate the overall performance. Internal shot and Johnson noise as well as incident thermal radiation is included in the discussion. It is shown that the noise temperature is virtually independent of noise injected from external sources and that minimum noise temperature is automatically achieved if the amplifier is tuned to maximize the gain-bandwidth product. The analytical results are illustrated by self-consistent numerical solutions of the circuit equations. Journal of Applied Physics is copyrighted by The American Institute of Physics.