Econ Ch. 6

In the short run, a firm's capital is fixed, while in the long run, a firm can change its quantities of both labor and capital inputs.

What are the differences between a firm's production in the short run and the long run?

A production function shows the relationship between a firm's inputs (capital and labor) and its output quantity.

What does a production function tell us?

In reaction to an increase in the price of one input (say, labor), the firm will substitute away from units of that input to another (in this case, capital) in the long run.

What does the curvature of an isoquant imply about the two inputs, capital and labor?

The marginal rate of technical substitution is the rate at which the firm can trade one input (X) for another (Y) holding output constant, and is equal to the marginal product of input X over the marginal product of input Y. For the standard case, the MRTS implies a curved isoquant. As you move down and to the right along the isoquant, the marginal product of labor becomes low relative to the marginal rate of capital.

What does the diminishing marginal product of labor tell us about the relationship between labor inputs and marginal product?

The curvature of the isoquant demonstrates the degree of substitutability between capital and labor. A nearly straight isoquant implies that the MRTS is nearly constant along the isoquant, implying that the two inputs are close substitutes for each other in the production process. A more curved isoquant indicates that capital and labor are poor substitutes for each other in the production process.

How does the amount of output change as the isoquants are farther from the graph's origin? Why can't two isoquants cross?

Technological change, A, enters the production function as a scale factor: Q = Af(K,L). This type of technological change implies that after an improvement in technology, the firm produces extra output using the same level of productive inputs as prior to the change.

How will a firm react to an increase in the price of one input relative to another?

Returns to scale refers to the change in the amount of output in response to a proportional change in all the inputs. Constant returns to scale indicate that a proportional change in all inputs changes the quantity of output by that same proportion. Increasing returns to scale means that a proportional change in all inputs changes the quantity of output more than proportionately. Finally, decreasing returns to scale imply that a proportional change in all inputs changes the quantity of output less than proportionally.

What is an isocost line? What does its slope tell us about the relative cost of labor and capital?

Fixed costs don't depend on how much output a firm produces—they are the same whether the firm produces one unit of output or one million units of output or even zero units of output. Variable costs depend on how much the firm produces: As output increases, variable costs increase.

What is the difference between fixed costs and variable costs?

In the long run, the firm can adjust the level of each of its inputs. In the short run, at least one input is fixed and cannot be adjusted by the firm.

What is the difference between the short run and the long run?

An isocost line is the curve that shows all the input combinations that yield the same cost. Since the slope of the isocost line is the negative ratio of wages to the capital rental rate, -W/R, we can use the slope to determine the cost tradeoff of substituting labor for capital (or vice versa).

What is the marginal rate of technical substitution? What does it imply about an isoquant's shape?

The expansion path plots the optimal input combinations for each output quantity. The total cost curve plots the output quantities from the expansion path against the total cost of the productive inputs.

When is a production function said to have constant returns to scale, increasing returns to scale, or decreasing returns to scale?

A producer's isoquants share many of the same characteristics as a consumer's indifference curves. Isoquants farther from the origin are associated with higher output levels. Isoquants cannot cross because if two isoquants did, it would imply that the same quantities of inputs yield two different quantities of output.

Why is a firm's marginal product of labor more relevant than the marginal product of capital in the short run?