Numerical Problems: 2.1 Profit Maximization: Equations. Rochester Instruments, Inc., operates in the highly competitive electronics industry. Prices for its RII-X control switches are stable at $50 each. This means that P = MR = $50 in this market. Engineering estimates indicate that relevant total and marginal cost relations for the RII-X model are: TC = $78,000 + $18Q + $0.002 MC =TC/Q= $18 + $0.004Q A. Calculate the output level (Q) that will maximize RII-X profit. B. Calculate this maximum profit. 2.2 Profit Maximization: Equations. 21 st Century Insurance offers mail-order automobile insurance to preferred-risk drivers in the Los Angeles area. The Company is the low-cost provider of insurance in this market but doesn't believe its $750 annual premium can be raised for competitive reasons. Its rates are expected to remain stable during coming periods; hence, P = MR = $750. Total and marginal cost relations for the company are as follows: TC = $2,500,000 + $500Q + $0.005 MC = TC/Q = $500 + $0.01Q

A. Calculate the output level (Q) that will maximize 21 st century insurance profit. B. Calculate this maximum profit.

2.3 Revenue Maximization. Desktop Publishing Software, Inc. develops and markets software packages for business computers. Although sales have grown rapidly during recent years, the company's management fears that a recent onslaught of new competitors may severely retard future growth opportunities. Therefore, it believes that the time has come to "get big or get out." The marketing and accounting departments have provided management with the following monthly demand and cost information:

P = $1,000 - $1Q TC = $50,000 + $100Q MR = TR/Q = $1,000 - $2Q MC = TC/Q = $100 A. Calculate monthly quantity, price, and profit at the Revenue maximizing output level. B. Calculate these same values for the profit-maximizing level of output. C. Calculate the same values for the Average Cost minimization method.

2.4 Average Cost Minimization. Giant Screen TV, Inc., is a San Diego-based importer and distributor of 60-inch screen, high-resolution televisions for individual and commercial customers. Revenue and cost relations are as follows:

TR = $1,800Q - $0.006 MR = TR/Q = $1,800 - $0.012Q TC = $12,100,000 + $800Q + $0.004 MC = TC/Q = $800 + $0.008Q

A. Calculate output (Q), marginal cost (MC), average cost (AC), price (P), and profit () at the average cost-minimizing activity level. B. Calculate these values at the profit-maximizing activity level.