The external demand and marginal cost functions of the marketing divisions of the firm are, respectively:
Qm = 160-10Pm or Pm=16-0.1Qm and MR=16-0.2Qm
The marginal cost functions of the production and marketing divisions of the firm are, respectively:
MCp'=2-0.1Qp and MCm=1+0.1Q
A perfectly competitive market exists for the intermediate product at P=$6.
Determine algebraically the profit-maximizing outputs for the production and marketing divisions of the firm and the optimal transfer price for the intermediate product and the price of the final product.