# T 1000 k25 175 the marginal product of labor mp 75 25

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Givens: 60 * L + 20 * K min L>0, K > 0 s.t. 1000 < K.25 * 1.75 The marginal product of labor: MP, = .75 * :25 The marginal product of capital: MPK = .25 * 576 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the first term is units of capital raised to the 25 power;
and, the second term is units of labor raised to the 75 power. The marginal product of labor equals the product of three terms: the first term is.75; the second term is units of capital raised to the 25 power; the third term is units of labor raised to the -25 power. The marginal product of capital equals the product of three terms: the first term is 25; the second term is units of labor raised to the 75 power; the third term is units of capital raised to the - 75 power. The wage rate is \$60 per unit of labor. The rental rate is \$20 per unit of capital. The output quota is 1000 units. Question: What is minimum total cost? \$94,000 \$26,000 \$32,000 \$72,000 \$48,000 \$80,000 \$8,000 \$100,000

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• Fall '19
• Economics, \$10, \$20, \$8,000, \$40, marginal product of labor

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