b2* + 132 + 15. The cost function of a firm is i. Derive an expression for the marginal cost ii. Find the value of x that minimizes the marginal cost function

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a. The cost function of a firm is C (x) = x – 6x2 + 13x + 15
i. Derive an expression for the marginal cost
ii. Find the value of x that minimizes the marginal cost function
b. The production function of a firm is Y = AK 3 L3.Y represents output, K is capital, and L is labor. A is a constant term.
This equation says that the firm uses labor and capital to produce its output.
i. Find the marginal products of labor
%3D
ii. Find the marginal product of capital.
C. A firm's revenue function is R (x) = 100x – 0.01a, and the cost function is C (x) = 50x + 10, 000, where x is output.
a. Compute the marginal revenue function and the marginal cost function.
b. Suppose the markets are competitive, which output level will maximize this firm's profit? Show all your
calculations.
Transcribed Image Text:a. The cost function of a firm is C (x) = x – 6x2 + 13x + 15 i. Derive an expression for the marginal cost ii. Find the value of x that minimizes the marginal cost function b. The production function of a firm is Y = AK 3 L3.Y represents output, K is capital, and L is labor. A is a constant term. This equation says that the firm uses labor and capital to produce its output. i. Find the marginal products of labor %3D ii. Find the marginal product of capital. C. A firm's revenue function is R (x) = 100x – 0.01a, and the cost function is C (x) = 50x + 10, 000, where x is output. a. Compute the marginal revenue function and the marginal cost function. b. Suppose the markets are competitive, which output level will maximize this firm's profit? Show all your calculations.
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