An assumption of Ricardian model is constant returns to scale production function with single production factor (labor). Therefore, the marginal product of labor (or, in the usual manner of presentation, its inverse, the units of labor required to produce one unit of good) completely describes the production function. This was so intuitively clear that I never bothered to check.
A production function F(x): Rn → R has constant returns to scale if F(ax) = aF(x) for all a > 0, where x is a n-vector and a is a scalar. In other words, it's economists' way of saying degree 1 homogeneous.
The claim is that if n = 1, then F(x) = cx for some real number c. The proof is simple. Suppose F has constant returns to scale, and denote F(1) = c. Then ac = aF(1) = F(a) for all a > 0. F(0) = 0 follows from the observation that F(0) = aF(0) for all a > 0. Finally, since F(1) = -F(-1), it follows -ac = aF(-1) = F(-a) for all a > 0.
Of course, I could have used Euler's theorem which states that F(x) is homogeneous of degree k iff nF(x) = ΣixiFi where Fi is partial derivative of F regard to xi. Thus, single factor CRS function satisfies F(x) = xF'(x). Solving differential equation yields F(x) = cx.
