Appendix 7,8,9

Isoquant depends on two factors

1. Technology—which determines how much output a firm receives from employing a given quantity of inputs. 2. Input prices—which determine the total cost of each combination of inputs.

An Isoquant Graph

A curve that shows all the combinations of two inputs, such as capital and labor, that will produce the same level of output.

Isocost lines 1

A firm wants to produce a given quantity of output at the lowest possible cost. We can show the relationship between the quantity of inputs used and the firm's total cost by using an isocost line.

Isocost lines 2

All the combinations of two inputs, such as capital and labor, that have the same total cost.

Another Look at Cost Minimization 1

At the point of cost minimization, the isoquant and isocost lines are tangent, so they have the same slope.

Isoquants

Firms search for the cost-minimizing combination of inputs that will allow them to produce a given level of output.

Another Look at Cost Minimization 4

In this chapter, we defined the marginal product of labor (MPL) as the additional output produced by a firm as a result of hiring one more worker. Similarly, we can define the marginal product of capital (MPK) as the additional output produced by a firm as a result of using one more machine.

Point of Cost Minimization

MPL/w= MPK/r This expression tells us that to minimize cost for a given level of output, a firm should hire inputs up to the point where the last dollar spent on each input results in the same increase in output. If this equality did not hold, a firm could lower its costs by using more of one input and less of the other.

Marginal rate of technical substitution (MRTS) 2

The MRTS is equal to the change in capital divided by the change in labor, so it will become smaller (in absolute value) as we move down an isoquant

Marginal rate of technical substitution (MRTS) 1

The rate at which a firm is able to substitute one input for another while keeping the level of output constant.

Another Look at Cost Minimization 5

The slope of the isocost line equals the wage rate (w) divided by the rental price of capital (r).

The Slope and Position of the Isocost Line

The slope of the isocost line is equal to the ratio of the price of the input on the horizontal axis divided by the price of the input on the vertical axis multiplied by -1.

Another Look at Cost Minimization 3

The slope of the isocost line tells us the rate at which a firm is able to substitute labor for capital, given current input prices. Only at the point of cost minimization are these two rates the same.

Another Look at Cost Minimization 2

Therefore, at the point of cost minimization, the marginal rate of technical substitution (MRTS) is equal to the wage rate divided by the rental price of capital. The slope of the isoquant tells us the rate at which a firm is able to substitute labor for capital, given existing technology.