# Return to problem 14 above. Now assume this is a multiperiod setting, as in Exhibit 3.2. Further…

Return to problem 14 above. Now assume this is a multiperiod setting, as in Exhibit 3.2. Further assume the interest rate is r = 10%. Spot factor prices are 100 per unit for capital, 150 per unit for labor for the first product and 192.5 per unit for labor for the second product. The first product now sells for 302.5 per unit, and the second sells for 363 per unit.

(a) Answer part (c) of the original exercise.

(b) Answer part (e) of the original exercise. Explain your findings. Also identify the point on the time line at which these costs are being calculated. Explain.

Problem 14: ((Ralph has grown up and now 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 the first product, capital (K ≥ 0) and labor (L1 ≥ 0) must satisfy the following, in order to produce q1 units: q1 ≤ √ KL1. Likewise, producing q2 units of the second product requires capital (K) and labor (now L2 ≥ 0) such that: q2 ≤ √ KL2. In addition, total capital is limited to a maximum of 200 units. (So K ≤ 200.) Naturally, K, L1 and L2 are all required to be non-negative. Capital costs 100 per unit, labor for the first product costs 150 per unit and labor for the second product costs 175 per unit. The first product sells for 275 per unit, and the second sells for 300 per unit.

(a) Initially suppose only the first product is present. Determine and interpret Ralph’s optimal production plan.

(b) Next suppose only the second product is present. Determine and interpret Ralph’s optimal production plan.

(c) Now assume both products are present. Determine and interpret Ralph’s optimal production plan.

(d) Repeat (a),(b) and (c) assuming the first product sells for 200 per unit. (e) Fill in the following table

(f) Write a short paragraph interpreting your findings.)

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