We reconsider the calculation of the relative abundance of muons in photon- and proton-induced air cascades. The calculation is relevant to the performance of a new generation of cosmic-ray telescopes presently in the planning or construction stage. We first solve the one-dimensional cascade equations analytically for a power photon spectrum as well as for individual showers. The formalism allows the consideration of physics issues without reliance on electromagnetic cascade Monte Carlo simulation and brings to the forefront several ambiguities in the high-energy calculation. The relative abundance of high-energy particles in a flatter (e.g., E-2) source spectrum can result in similar muon content of photon and hadron showers even with N()X photoproduction cross sections of order 1 mb. A high-energy photoproduction cross section of this magnitude does not necessarily require new physics and can conceivably result from the QCD gluon structure of a high-energy photon. 1989 The American Physical Society.