The short-run production function refers to the production function where at least one input is fixed and cannot be changed.

• For example, in a bakery, the oven may be a fixed input in the short run because it cannot be easily expanded or reduced. The variable inputs, such as labor and ingredients, can be increased or decreased in the short run to increase or decrease output.
• The short-run production function can be represented by a curve showing the relationship between the quantity of variable inputs and the quantity of output produced.

• Fixed factors of production are those inputs that cannot be easily changed in the short run, such as capital or equipment.
  • These inputs have a fixed quantity or capacity and cannot be easily expanded or reduced.
  • For example, a factory may have a fixed number of machines or a fixed amount of space, which cannot be easily changed in the short run.
  • In the long run, however, these fixed factors of production can be changed by adding or reducing the amount of capital or equipment.
• Variable factors of production are those inputs that can be easily changed in the short run, such as labor or raw materials.
  • These inputs can be increased or decreased to adjust the level of output produced.
  • For example, a factory can hire more workers or purchase more raw materials to increase output, or reduce labor or materials to decrease output.
• The distinction between fixed and variable factors of production is important because it helps firms understand how to allocate their resources in order to maximize profits. By understanding which factors are fixed and which are variable, firms can determine the optimal combination of inputs that will produce the desired level of output at the lowest cost.

Total product, average product, and marginal product are three important concepts in production theory that help firms understand the relationship between input and output.

• Total product refers to the total amount of output produced by a firm using a given set of inputs or factors of production.
  • For example, if a firm produces 100 units of output using 10 units of labor and 5 units of capital, the total product is 100 units.
• Average product refers to the average amount of output produced per unit of input.
  • It is calculated by dividing the total product by the quantity of input used.
  • For example, if a firm produces 100 units of output using 10 units of labor, the average product of labor is 10 units of output per unit of labor.
• Marginal product refers to the additional amount of output produced by using one more unit of input, holding all other inputs constant.
  • It is calculated as the change in total product divided by the change in input.
  • For example, if a firm produces 100 units of output using 10 units of labor, and then produces 120 units of output using 11 units of labor, the marginal product of labor is 20 units of output for the additional unit of labor.
• Example

• • The total product of labor is the total quantity of pizzas produced using a given amount of labor. For example, when one unit of labor is used, 10 pizzas are produced. As more labor is added, the total product increases. When seven units of labor are used, the total product is 77 pizzas.
  • The average product of labor is calculated by dividing the total product by the quantity of labor used. For example, when two units of labor are used, the total product is 25 pizzas, and the average product is 12.5 pizzas per unit of labor.
  • The marginal product of labor is calculated by measuring the change in total product resulting from adding one more unit of labor. For example, when three units of labor are used, the total product is 45 pizzas. When four units of labor are used, the total product is 60 pizzas. The marginal product of labor is therefore 15 pizzas (the difference between 60 and 45).

• The law of diminishing returns, also known as the law of variable proportions, is a fundamental concept in economics that states that as a firm adds more units of a variable factor of production, while keeping other factors constant, the marginal product of that factor will eventually decrease.
  • This means that the increase in output resulting from adding each additional unit of the variable factor will become smaller and smaller.

• In the example of the pizza restaurant, suppose that the restaurant has a fixed number of ovens but can hire additional workers to make pizzas.
  • Labor is a variable factor of production, while ovens are a fixed factor of production. As more workers are hired, the marginal product of labor will eventually decrease due to the limited availability of oven space.
  • Initially, as the restaurant hires more workers, the marginal product of labor may increase, meaning that each additional worker adds more output than the previous worker. This is because there may be idle oven space that can be used more efficiently with additional labor.
  • However, as the restaurant hires even more workers, the marginal product of labor will begin to decline.
    • This is because the oven space becomes increasingly crowded and each additional worker has less and less space to work. As a result, the marginal product of labor decreases, and the firm may experience diminishing returns to labor.
    • At some point, adding more labor will result in less and less output per worker, and may even lead to negative returns if the workers are so crowded that they begin to interfere with each other's work.

Short-run cost function is a concept in economics that refers to the costs of producing goods or services in the short run, when some factors of production are fixed and others are variable.

• In the short run, a firm can adjust its output by changing the amount of variable factors, such as labor and raw materials, but it cannot change the fixed factors, such as capital equipment and buildings.

The short-run cost function consists of two types of costs: fixed costs and variable costs.

• Fixed costs are those costs that do not vary with changes in the level of output, such as rent, insurance, and salaries of management staff.
• Variable costs are costs that vary with changes in the level of output, such as raw materials, labor, and electricity.

• Total Cost (TC) is the sum of all costs incurred by a firm in producing a certain level of output.
  • It includes both fixed costs (FC) and variable costs (VC). Mathematically, TC = FC + VC.
• Average Cost (AC) is the total cost per unit of output.
  • It is calculated by dividing total cost by the quantity of output produced. Mathematically, AC=TC/Q, where Q is the quantity of output produced.
• Marginal Cost (MC) is the additional cost of producing one more unit of output.
  • It is calculated as the change in total cost when one more unit of output is produced. Mathematically, MC=ΔTC/ΔQ.
• Average Total Cost (ATC) is the total cost per unit of output, including both fixed and variable costs.
  • It is calculated as ATC=TC/Q, where Q is the quantity of output produced.
  • Alternatively, it can be calculated as ATC=AFC+AVC, where AFC is average fixed cost and AVC is average variable cost.
• Total Fixed Cost (TFC) is the cost of the fixed inputs used in production, such as rent, salaries of management staff, and insurance.
  • These costs do not vary with changes in the level of output.
• Average Fixed Cost (AFC) is the fixed cost per unit of output.
  • It is calculated as AFC=TFC/Q, where Q is the quantity of output produced.
• Total Variable Cost (TVC) is the cost of the variable inputs used in production, such as raw materials, labor, and electricity.
  • These costs vary with changes in the level of output.
• Average Variable Cost (AVC) is the variable cost per unit of output.
  • It is calculated as AVC=TVC/Q, where Q is the quantity of output produced.

Understanding these cost concepts is important for firms to make informed decisions about production levels and pricing strategies. By analyzing their costs, firms can determine the most efficient level of output and adjust their production processes accordingly to maximize profits.

• A firm produces widgets and incurs the following costs:
  • Total Fixed Cost (TFC): $500
  • Total Variable Cost (TVC) at different levels of output:

• • We can calculate the Total Cost (TC) at each level of output by adding TFC to TVC

• • Using this table, we can calculate the Average Total Cost (ATC), Average Fixed Cost (AFC), Average Variable Cost (AVC), and Marginal Cost (MC) at each level of output:

• The shape of the short-run average cost (SAC) curve is U-shaped due to the presence of both fixed and variable costs.
  • At low levels of output, the SAC is high because the fixed costs are spread over a small number of units, resulting in a higher average cost.
  • As output increases, the fixed costs are spread over more units, resulting in a lower average cost.
  • However, as output continues to increase, the SAC begins to increase again due to the diminishing marginal returns of the variable factors of production.
• The shape of the marginal cost (MC) curve is due to the law of diminishing marginal returns.
  • Initially, as more units of the variable input are added to the production process, the marginal cost decreases because of the increasing returns.
  • However, at some point, diminishing returns set in, and the marginal cost begins to increase. This is because each additional unit of the variable input produces less output than the previous unit, causing the cost per unit to increase.
• The point where the MC curve intersects the SAC curve is the minimum point of the SAC curve, which represents the most efficient level of output for the firm.