Define and then derive the expression for the MRTS. How do you derive this? I thought derive meant to receive or take something.

Thanks.

MRTS is the marginal rate of technical substitution. In a two-input production function, it is simply the marginal product of X over the marginal product of Y. That is MRTS = -MPx/MPy and MPx is simply the first derivitive of the production function with respect to x

Thanks.

When the firm hires 6 workers the firm produces 90 units of output. Fixed costs of production are $6 and the variable cost per unit of labor is $10. The marginal product of the seventh unit of labor is 4. Given this information, what is the average total cost of production when the firm hires 7 workers?

The term "derive" has different meanings in different contexts. In this case, when we talk about "deriving the expression for MRTS," we mean to obtain or calculate it.

MRTS stands for the Marginal Rate of Technical Substitution. It measures the rate at which one input can be substituted for another while keeping the level of output constant. The MRTS helps in analyzing production efficiency and optimal input combinations.

To derive the expression for the MRTS, you need to have a production function that expresses the relationship between inputs and output. Let's assume a simple production function with two inputs, capital (K) and labor (L), represented by the function Q = f(K, L).

1. Take the partial derivative of the production function with respect to K, holding L constant:
∂Q/∂K = fK(K, L), where fK denotes the partial derivative of f with respect to K.

2. Similarly, take the partial derivative of the production function with respect to L, holding K constant:
∂Q/∂L = fL(K, L), where fL denotes the partial derivative of f with respect to L.

3. Determine the MRTS by taking the ratio of the two partial derivatives:
MRTS = (∂Q/∂K) / (∂Q/∂L) = fK(K, L) / fL(K, L).

By following these steps, you can derive the expression for the MRTS based on the given production function. The resulting MRTS equation will provide insights into the substitutability between capital and labor inputs in the production process.