What is the price of capital?

A new footwear company started its operation in St. Vincent and the production function Q = 85KL2. Since the labor cost is EC $ 20 and the MRTS is the K = 1.5) What is the price of capital? b) If the desired output is 2,500 units, How many units of capital and labor will be used?

a) Q = 85 • K • L w ² = 20 MRTS [L, K] = – MPL / MPK =- w / r MPL = ∂ Q / ∂ L = 170 K • L • MPK = ∂ Q / ∂ L = 85 • L ² MRTS [L, K] = – (170 • K • L) / (85) • L ² =- 2K / L-2K / L = -20 / rK / L = -10 / rr = 10 liters / KK = 1.5L [this condition it is appropriate in the form, instead of MRTS r] 10L/1.5 L = 10/1.5 = 20 / 3 ≈ $ 6.67 b) MPL / w = MPK / r 2K / L = 20 / r K / L = 10 / r K / L = 10 / (20 / 3) K / L = 1.5 K = 1.5 l L = QK/1.5 = 85 • K • L ² = 85 • 1.5 • L • L ² = 127.5 • L ³ Q = 127.5 • L ³ L ³ = 2500/127.5 ≈ Q/127.5 = 19.608 L ³ 1000/51 = L = ³ √ (1000-51) = 10 / ³ √ 2697 ≈ 51 K = 1.5 l = 15 / √ 51 ≈ 4.0448 ³ Answers: a) r ≈ $ 6.67 b) ≈ 2.697 L, K ≈ 4.0448 but I'm not sure if this condition MRTS for your task is displayed correctly.

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