Resolving the friction between Turnbull's (1983) and Klemperer-Meyer's (1989) Nash equilibria in affine supply functions

Turnbull (1983) describes unique symmetric Nash equilibria for supply function competition under demand uncertainty which consist of affine strategies that are nonlinear. For the same economy Klemperer and Meyer (1989) derive unique Nash equilibria that are linear. This note shows that the friction between both results comes from a mathematical error in Turnbull (1983). Correcting this error establishes the same linear Nash equilibria for both models.