Chapter Notes

Here are your study notes for the chapter on Production and Costs.

Production and Costs

In economics, we study the behavior of both consumers and producers. This chapter focuses on the producer, or firm. A firm's main activity is production, which is the process of transforming inputs into an output.

Inputs are the resources a firm uses, such as labor, machines, land, and raw materials. The output is the final product or service. This output can be sold to consumers or to other firms for further production. The money a firm spends on inputs is its cost of production. The money it earns from selling the output is its revenue. The goal of a firm is to maximize its profit, which is the difference between revenue and cost.

• A tailor uses inputs like a sewing machine, cloth, thread, and their own labor to produce an output: shirts.
• A farmer uses inputs like land, labor, a tractor, seeds, and water to produce an output: wheat.
• A car manufacturer uses inputs like a factory, machinery, labor, steel, and rubber to produce an output: cars.

This chapter explores the relationship between a firm's inputs and its output, and then examines the costs involved in this process.

Production Function

The production function of a firm describes the relationship between the inputs it uses and the maximum amount of output it can produce. It essentially tells us the most a firm can create with any given combination of inputs, assuming it is using them efficiently.

Efficiency means it's impossible to get more output from the same level of inputs. The production function is defined for a specific level of technology. If technology improves, a firm can produce more output with the same inputs, creating a new production function.

The inputs used in production are called factors of production. For simplicity, we often focus on just two factors:

• Labour (L): The human effort involved.
• Capital (K): The machines, tools, and buildings used.

The production function can be written as an equation: q = f(L, K) This means the quantity of output (q) is a function of (or depends on) the amount of labour (L) and capital (K) used.

Isoquant

An isoquant is a curve that shows all the possible combinations of two inputs (like labour and capital) that produce the same level of output. The concept is similar to an indifference curve for consumers. Each isoquant represents a specific quantity of output.

For example, a firm might be able to produce 50 units of output using:

• 6 units of labour and 3 units of capital.
• 4 units of labour and 4 units of capital.
• 3 units of labour and 6 units of capital.

All three of these combinations would lie on the same isoquant for q = 50.

Isoquants are negatively sloped. This is because if you want to maintain the same level of output while using less of one input (like capital), you must use more of the other input (labour). A higher isoquant represents a higher level of output.

The Short Run and the Long Run

To understand production, we must distinguish between two time periods: the short run and the long run. These are not defined by a specific duration like days or months, but by the firm's ability to change its inputs.

• The Short Run: A period in which at least one factor of production is fixed. A firm cannot change the quantity of this fixed factor. To change its output level, the firm can only adjust its variable factors. For example, a farmer might have a fixed amount of land (capital) but can hire more or fewer workers (labour).
• The Long Run: A period in which all factors of production can be varied. In the long run, a firm can change the amount of both labour and capital. There are no fixed factors in the long run.

Total Product, Average Product and Marginal Product

When we analyze production in the short run, we look at how output changes when we vary one input while keeping others fixed. This leads to three important concepts.

Total Product

Total Product (TP) is the total quantity of output produced by a firm using a certain amount of a variable input, while all other inputs are held constant. It shows the overall relationship between the variable input and the total output.

Average Product

Average Product (AP) is the output per unit of the variable input. It tells us, on average, how much each unit of the variable input is producing.

It is calculated as: AP = Total Product / Units of Variable Input For labour, the formula is: AP_L = TP_L / L

Marginal Product

Marginal Product (MP) is the change in total output that results from using one additional unit of the variable input, holding all other inputs constant. It measures the contribution of the very last unit of input used.

It is calculated as: MP = Change in Total Product / Change in Variable Input For labour, the formula is: MP_L = ΔTP_L / ΔL

Alternatively, the marginal product of the nth unit is: MP_L = (TP at L units) - (TP at L-1 units)

The Law of Diminishing Marginal Product and the Law of Variable Proportions

As a firm in the short run adds more and more of a variable input (like labour) to a fixed input (like land), the marginal product of the variable input doesn't stay constant.

The Law of Variable Proportions (also known as the Law of Diminishing Marginal Product) states that the marginal product of an input first increases, but after reaching a certain point, it starts to fall.

Why does this happen? It's about factor proportions—the ratio of the variable input to the fixed input.

1. Increasing Marginal Product: Initially, when there are few workers on a large piece of land, each new worker can specialize and make the production process more efficient. The factor proportions become more suitable for production, so each additional worker adds more to the total output than the previous one. MP rises.
2. Diminishing Marginal Product: After a certain point, the fixed factor (land) becomes "crowded." There are too many workers for the available space and equipment. Each additional worker has less of the fixed factor to work with, so their individual contribution to output starts to decrease. MP falls.

Shapes of Total Product, Marginal Product and Average Product Curves

When graphed, these concepts have distinct shapes that illustrate their relationships.

• Total Product (TP) Curve: This curve is positively sloped, meaning as you add more of the variable input, total output increases. It initially gets steeper (reflecting increasing MP) and then becomes flatter (reflecting diminishing MP).
• Marginal Product (MP) Curve: Reflecting the Law of Variable Proportions, the MP curve is shaped like an inverted 'U'. It rises first, reaches a maximum, and then declines.
• Average Product (AP) Curve: The AP curve is also an inverted 'U' shape.

Relationship between MP and AP Curves:

• When MP is greater than AP, the AP curve is rising. (The new worker is more productive than the average, so they pull the average up).
• When MP is less than AP, the AP curve is falling. (The new worker is less productive than the average, so they pull the average down).
• Because of this, the MP curve intersects the AP curve from above at the AP curve's maximum point.

Returns to Scale

This concept applies only to the long run, when a firm can change all of its inputs. Returns to scale describes what happens to output when all inputs are increased by the same proportion.

• Increasing Returns to Scale (IRS): When a proportional increase in all inputs results in a larger proportional increase in output. For example, doubling all inputs leads to more than double the output.
• Constant Returns to Scale (CRS): When a proportional increase in all inputs results in an increase in output by the same proportion. For example, doubling all inputs exactly doubles the output.
• Decreasing Returns to Scale (DRS): When a proportional increase in all inputs results in a smaller proportional increase in output. For example, doubling all inputs leads to less than double the output.

Costs

To produce output, a firm must pay for its inputs. The cost function describes the least possible cost of producing each level of output, given the prices of the factors of production and the available technology.

Short Run Costs

In the short run, some costs are fixed and some are variable.

• Total Fixed Cost (TFC): The cost a firm incurs on its fixed inputs. This cost does not change, no matter how much output is produced. Even if output is zero, TFC must be paid.
• Total Variable Cost (TVC): The cost a firm incurs on its variable inputs. This cost increases as the firm produces more output. TVC is zero when output is zero.
• Total Cost (TC): The sum of fixed and variable costs. TC = TFC + TVC.

From these, we can derive the average and marginal costs:

• Average Fixed Cost (AFC): AFC = TFC / q. Since TFC is constant, AFC continuously decreases as output (q) increases.
• Average Variable Cost (AVC): AVC = TVC / q.
• Short Run Average Cost (SAC): SAC = TC / q. It is also the sum of the other two averages: SAC = AFC + AVC.
• Short Run Marginal Cost (SMC): The change in total cost from producing one extra unit of output. SMC = ΔTC / Δq.

Shapes of the Short Run Cost Curves

• TFC Curve: A horizontal straight line, as it remains constant at all output levels.
• TVC and TC Curves: Both curves slope upwards because more output requires more variable inputs, increasing costs. The TC curve is parallel to the TVC curve, but starts higher on the vertical axis by the amount of TFC.
• AFC Curve: A downward-sloping curve called a rectangular hyperbola. It gets closer and closer to the horizontal axis but never touches it.
• SMC, AVC, and SAC Curves: All three curves are 'U'-shaped. This shape is a direct result of the Law of Variable Proportions. Initially, as marginal product rises, less input is needed for each extra unit of output, so marginal cost falls. Later, as marginal product falls (diminishing returns), more input is needed, and marginal cost rises.

Key Relationships between the 'U'-shaped curves:

• The SMC curve cuts the AVC curve from below at the minimum point of the AVC curve. When SMC is below AVC, it pulls the average down. When SMC is above AVC, it pulls the average up.
• The SMC curve also cuts the SAC curve from below at the minimum point of the SAC curve for the same reason.
• The minimum point of the SAC curve lies to the right of the minimum point of the AVC curve. This is because SAC includes the ever-falling AFC, so it continues to fall for a while even after AVC has started to rise.

Long Run Costs

In the long run, all inputs are variable, so there are no fixed costs. Therefore, Total Cost (TC) is the same as Total Variable Cost (TVC).

• Long Run Average Cost (LRAC): The cost per unit of output in the long run. LRAC = TC / q.
• Long Run Marginal Cost (LRMC): The change in total cost from producing one more unit of output when all inputs can be varied.

Shapes of the Long Run Cost Curves

The shape of the long-run cost curves is determined by returns to scale.

• When a firm experiences Increasing Returns to Scale (IRS), its output increases more than its inputs. This means the cost per unit (LRAC) is falling.
• When a firm experiences Decreasing Returns to Scale (DRS), its output increases less than its inputs. This means the cost per unit (LRAC) is rising.
• When a firm experiences Constant Returns to Scale (CRS), its cost per unit (LRAC) is constant.

Typically, a firm first experiences IRS, then CRS, and finally DRS as it expands its scale of production. For this reason:

• The LRAC curve is 'U'-shaped. The downward-sloping part corresponds to IRS, the upward-sloping part corresponds to DRS, and the minimum point corresponds to CRS.
• The LRMC curve is also 'U'-shaped. Just like in the short run, the LRMC curve cuts the LRAC curve from below at the minimum point of the LRAC.