Washington Instrument Produces Various Electronic Products Including Electronic Calculators

Washington Instrument produces various electronic products including electronic calculators. The marketing division (m) of the company purchases the integrated circuits used in the calculators, manufactures the various other components (e.g., case, batteries, buttons, etc.), and then assembles and distributes the final calculators under its own brand name (MBA-Whiz). The integrated circuits are produced by a separate production (p) division of the firm. The production division can sell the integrated circuits in the competitive open market at a standard price of $1.50/unit. Likewise, the marketing division can purchase integrated circuits in this market at $1.50/unit. The demand function for this particular calculator is:Q_m = 1350 -50P_mwhere Q_m is quantity sold per month and P_m is the price per unit. The marginal cost function of the calculators (excluding the cost of the integrated circuit) is:MC_m = .0025Q_mThe marginal cost function of the production division for these integrated circuits is:MC_P = .00375Q_pwhere Q_p is the quantity of integrated circuits produced per month.
(a)Determine the profit-maximizing price and outlet level of calculators for the marketing division.
(b)Determine the profit-maximizing price and output level of integrated circuits for the production division.
(c)Determine the optimal intracompany transfer price for integrated circuits.
(d)Determine the number of integrated circuits the production division should sell
(i)internally to the marketing division and (ii) externally on the open market.
(e)Determine the number of integrated circuits the marketing division should buy
(i)internally from the production division and (ii) externally on the open market.