# 10025

Multi product firm

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 = vKL1.

Likewise, producing q2 units of the second product requires capital

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(K) and labor (now L2 = 0) such that: q2 = vKL2. 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

q1

q2

MC1(q;

MC2(q;

50

50

50

100

50

150

100

50

100

100

100

150

150

50

150

100

150

150

(f) Write a short paragraph interpreting your findings.