Suppose a market is supplied by symmetrically differentiated price-setting duopolists, where θ measures the degree of substitutability between firms' products. Firms have identical cost functions, in that their dependence upon capital and output are identically governed. However, firms may have different levels of capital, such that they have different effective marginal costs. Marginal cost is increasing, but at a rate that declines with capital, reflecting a relaxation of capacity constraints as a firm grows large. Demand and cost are given as follows: q1 = a - bp1 + 0bp2
q2 = a - bp2 +0bp1
C(q,k) = dp + (e/2k) q2
Compute equilibrium prices, quantities, and profits as functions of the firms' capital levels (k1,k2), the demand parameters (a,b,θ), and the cost parameters (d,e).