Ralph manages a two-product firm. The technology requires a mixture of capital and labor to produce each product. Capital is shared, while labor is specific to each of the two products. For each of the products, units of capital (K) and labor (Li) must satisfy qi (KLi )1/2, for i = 1, 2, where qi refers to units of output of product i.

Total capital is limited to a maximum of 200 units, K 200. Capital costs PK = $300 per unit, labor for product 1 costs PL1 = $250 per unit, and labor for product 2 costs PL2 = $400 per unit. In addition, when a product is sold and removed from inventory, packaging and shipping costs (B) are $50 for each unit sold. All factor costs (capital and labor) are treated as product costs. Ralph will produce and sell q1 = 100 units and q2 = 50 units.

Required:

(1) Find the optimal combination of inputs, total cost, and marginal cost of each product.

(2) Determine accounting unit cost of each product where labor costs are direct costs of each product and shared cost is allocated based on relative direct cost.

(3) Does unit cost equal marginal cost? Briefly explain.