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Suppose that a firm's production function is q = 10 L 0.5 K 0.5 . This means that the marginal rate of technical substitution is

Suppose that a firm's production function is q = 10 L^0.5K^0.5. This means that the marginal rate of technical substitution is K/L.The cost of a unit of labour is 20 and the cost of a unit of capital is 80. The firm wants to produce 100 units of output. If both capitaland labour are variable, how many units of capital (K) should be hired in the long run?

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