This paper shows how an approximate competitive market equilibrium may be computed as the solution to a linear programming model, when production possibilities are described by activity analysis vectors and demand functions are locally linear. Numerical examples show that the degree of approximation may be expected to be very small in many cases. Prices and quantities of goods and resources and also incomes are explicit in the primal. (The defining characteristics of a market equilibrium are written as primal constraints.) Linearizations of inherently nonlinear expressions are attained by use of grid linearizations and the associated interpolation variables.