The blastoderm of the fruit fly Drosophila melanogaster is unusually well suited for analysis of fundamental questions in animal development. One such question is how genes specify the positional information which determines the developmental pathways (fate) of cells at appropriate spatial locations. In this paper we propose a dynamical model of gene regulation which explicitly describes how positional information is used in the blastoderm. The model is applied to analyze important experimental findings on the dependence of cell fate on the concentration of the Bicoid morphogen. The model shows that positional information in the presumptive middle body is cooperatively determined by maternal products of the bicoid and hunchback genes.