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The objective function for firm <math>k\,</math> is:
:<math>\pi_k - = (t_{k+1}-t_k)\cdot p_k = (\frac{\Delta p_{k+1}}{\Delta q_{k+1}} - \frac{\Delta p_{k}}{\Delta q_{k}})\cdot p_k\,</math>
Likewise for firm <math>n\,</math>:
:<math>\pi_k - pi_n = (t''-t_n)\cdot p_n = (\frac{t'' - \Delta p_{n}}{\Delta q_{n}})\cdot p_n\,</math>
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