Microeconomics: Production Function and Short Run vs Long Run

Production Function and Short Run vs Long Run

• A production function is a statement of the functional relationship between inputs and outputs.
• It shows the maximum output that can be produced from given inputs.
• A production function can be written as Q = ƒ (x1, x2……xr), where Q is the maximum quantity of output and x1, x2……xr are the quantities of the various inputs.
• In the short run, at least one factor input is fixed, and the firm can only adjust the quantity of variable factors to change output.
• In the long run, the firm can adjust the quantities of all factor inputs, and all costs are variable.

Law of Non-Proportional or Variable Returns

• The law states that as more units of a single variable factor input are added, output will initially increase more-than-proportionately, then proportionately, and eventually less-than-proportionately.
• This is because of the law of diminishing marginal returns, which states that if an increasing number of units of one factor input are combined with a fixed supply of other factors, there will, beyond a certain point, be a less-than-proportional increase in total output.
• Marginal product of labour is the change in total product due to a one-unit increase in labour.
• Average product of labour is output per unit of labour input.

Stages of Production

• Stage I: Positive increasing marginal returns
• Stage II: Positive diminishing marginal returns
• Stage III: Zero marginal returns
• Stage IV: Negative marginal returns

Profit Maximization and Input Choice

• A firm will maximize profit by hiring units of labour as long as the marginal revenue product of labour (MRPL) is greater than or equal to the marginal factor cost of labour (MFCL).
• MRPL = MP x Price of a unit of output
• MFCL = Price of a unit of labour
• As more workers are employed, MP diminishes, and revenue will start falling. The firm will stop adding more workers when MRPL equals MFCL.

Economic Cost versus Accounting Cost

• Economists are concerned with economic costs, which include opportunity costs, whereas accountants are concerned with accounting costs, which do not include opportunity costs.
• Opportunity cost is the cost associated with forgone opportunities, or the value of a resource in its next best use.

Cost Concepts

• Sunk cost: a cost that has been made and cannot be recovered, but should be ignored when making future economic decisions.
• Private cost: the cost incurred by the producer, often excluding social costs.
• Social cost: the total cost incurred by society, including private costs and external costs such as pollution.

Fixed Costs

• Fixed costs (FC) are the total obligations per period of time incurred by the firm for fixed inputs.
• FC are not related to the volume of output.
• Examples of FC include depreciation of building and equipment, rent on property, and labour under long-time contracts.

Variable Costs

• Variable costs (VC) vary directly with output.
• VC are incurred by the firm for employing the variable inputs associated with any level of output.
• Examples of VC include raw materials, power, components, and wages paid to workers employed on a flexi-time method.

Total Cost (TC)

• TC is the sum of TVC and TFC.
• The TC curve has the same shape as the TVC curve but lies above it by a vertical distance OA.

Marginal Cost (MC)

• MC is the change in TC resulting from a one-unit change in output.
• MC is equal to ΔTC ÷ ΔQ or ΔTVC ÷ ΔQ.
• The sum of the marginal costs of producing each unit equals the TVC of production.

Average Total Cost (ATC)

• ATC is the cost of producing one unit of output.
• ATC is equal to TC ÷ Q or (TFC + TVC) ÷ Q.

Average Fixed Cost (AFC)

• AFC is the cost of producing each unit in terms of fixed cost.
• AFC is equal to TFC ÷ Q.
• As output increases, AFC falls continuously.Here are the study notes in bullet points:

Cost Curves

• Total Cost (TC) curve is a graph that shows the total cost of producing different levels of output
• Average Fixed Cost (AFC) curve declines as output increases
• Average Variable Cost (AVC) curve is U-shaped, reflecting law of diminishing returns
• Marginal Cost (MC) curve is also U-shaped
• AVC and MC curves intersect at the minimum point of AVC
• MC curve cuts AVC curve from below at the minimum point of AVC

Relationship between Productivity and Costs

• As Average Product (AP) increases, AVC decreases
• As Marginal Product (MP) increases, MC decreases
• AP and MP are at their maximum when AVC and MC are at their minimum
• MC intersects AVC at its minimum point from below

Derivation of Short Run Average Total Cost (SRATC) Curve

• SRATC curve is the summation of AFC and AVC
• As output increases, AFC falls and AVC rises, causing SRATC to have a U-shape
• MC intersects SRATC at its minimum point

Cost Curves in the Long Run

• Long Run Average Cost (LRAC) curve is the envelope curve of all SRAC curves
• LRAC curve is downward sloping due to economies of scale
• LRAC curve shifts downward due to external economies of scale
• LRAC curve shifts upward due to external diseconomies of scale

Economies of Scale

• Economies of scale occur when firms reduce their unit costs by increasing their scale of production
• Internal economies of scale include:
  • Technical economies
  • Managerial economies
  • Financial economies
  • Buying and trading economies
  • Risk bearing economies
  • Research and development economies
• External economies of scale include:
  • Infrastructure
  • Ancillary firms
  • Concentration
  • Reputation
  • Research and development
  • Education
  • Skilled labor

Diseconomies of Scale

• Diseconomies of scale occur when firms experience increasing unit costs due to their large size
• Internal diseconomies of scale include:
  • Managerial difficulties
  • Internal communications
  • Industrial relations
• External diseconomies of scale include:
  • Local road congestion
  • Land and factory scarcity
  • Labor shortages

Survival of Small Firms

• Small firms survive due to:
  • Demand for variety
  • Inability to obtain economies of scale
  • Personal services
  • Size of the market
  • Low fixed costs
  • Limited demand (or luxury items)
  • Ambition
  • Lack of finance

Production Function and Short Run vs Long Run

• A production function is a statement of the functional relationship between inputs and outputs.
• It shows the maximum output that can be produced from given inputs.
• A production function can be written as Q = ƒ (x1, x2……xr), where Q is the maximum quantity of output and x1, x2……xr are the quantities of the various inputs.
• In the short run, at least one factor input is fixed, and the firm can only adjust the quantity of variable factors to change output.
• In the long run, the firm can adjust the quantities of all factor inputs, and all costs are variable.

Law of Non-Proportional or Variable Returns

• The law states that as more units of a single variable factor input are added, output will initially increase more-than-proportionately, then proportionately, and eventually less-than-proportionately.
• This is because of the law of diminishing marginal returns, which states that if an increasing number of units of one factor input are combined with a fixed supply of other factors, there will, beyond a certain point, be a less-than-proportional increase in total output.
• Marginal product of labour is the change in total product due to a one-unit increase in labour.
• Average product of labour is output per unit of labour input.

Stages of Production

• Stage I: Positive increasing marginal returns
• Stage II: Positive diminishing marginal returns
• Stage III: Zero marginal returns
• Stage IV: Negative marginal returns

Profit Maximization and Input Choice

• A firm will maximize profit by hiring units of labour as long as the marginal revenue product of labour (MRPL) is greater than or equal to the marginal factor cost of labour (MFCL).
• MRPL = MP x Price of a unit of output
• MFCL = Price of a unit of labour
• As more workers are employed, MP diminishes, and revenue will start falling. The firm will stop adding more workers when MRPL equals MFCL.

Economic Cost versus Accounting Cost

• Economists are concerned with economic costs, which include opportunity costs, whereas accountants are concerned with accounting costs, which do not include opportunity costs.
• Opportunity cost is the cost associated with forgone opportunities, or the value of a resource in its next best use.

Cost Concepts

• Sunk cost: a cost that has been made and cannot be recovered, but should be ignored when making future economic decisions.
• Private cost: the cost incurred by the producer, often excluding social costs.
• Social cost: the total cost incurred by society, including private costs and external costs such as pollution.

Fixed Costs

• Fixed costs (FC) are the total obligations per period of time incurred by the firm for fixed inputs.
• FC are not related to the volume of output.
• Examples of FC include depreciation of building and equipment, rent on property, and labour under long-time contracts.

Variable Costs

• Variable costs (VC) vary directly with output.
• VC are incurred by the firm for employing the variable inputs associated with any level of output.
• Examples of VC include raw materials, power, components, and wages paid to workers employed on a flexi-time method.

Total Cost (TC)

• TC is the sum of TVC and TFC.
• The TC curve has the same shape as the TVC curve but lies above it by a vertical distance OA.

Marginal Cost (MC)

• MC is the change in TC resulting from a one-unit change in output.
• MC is equal to ΔTC ÷ ΔQ or ΔTVC ÷ ΔQ.
• The sum of the marginal costs of producing each unit equals the TVC of production.

Average Total Cost (ATC)

• ATC is the cost of producing one unit of output.
• ATC is equal to TC ÷ Q or (TFC + TVC) ÷ Q.

Average Fixed Cost (AFC)

• AFC is the cost of producing each unit in terms of fixed cost.
• AFC is equal to TFC ÷ Q.
• As output increases, AFC falls continuously.Here are the study notes in bullet points:

Cost Curves

• Total Cost (TC) curve is a graph that shows the total cost of producing different levels of output
• Average Fixed Cost (AFC) curve declines as output increases
• Average Variable Cost (AVC) curve is U-shaped, reflecting law of diminishing returns
• Marginal Cost (MC) curve is also U-shaped
• AVC and MC curves intersect at the minimum point of AVC
• MC curve cuts AVC curve from below at the minimum point of AVC

Relationship between Productivity and Costs

• As Average Product (AP) increases, AVC decreases
• As Marginal Product (MP) increases, MC decreases
• AP and MP are at their maximum when AVC and MC are at their minimum
• MC intersects AVC at its minimum point from below

Derivation of Short Run Average Total Cost (SRATC) Curve

• SRATC curve is the summation of AFC and AVC
• As output increases, AFC falls and AVC rises, causing SRATC to have a U-shape
• MC intersects SRATC at its minimum point

Cost Curves in the Long Run

• Long Run Average Cost (LRAC) curve is the envelope curve of all SRAC curves
• LRAC curve is downward sloping due to economies of scale
• LRAC curve shifts downward due to external economies of scale
• LRAC curve shifts upward due to external diseconomies of scale

Economies of Scale

• Economies of scale occur when firms reduce their unit costs by increasing their scale of production
• Internal economies of scale include:
  • Technical economies
  • Managerial economies
  • Financial economies
  • Buying and trading economies
  • Risk bearing economies
  • Research and development economies
• External economies of scale include:
  • Infrastructure
  • Ancillary firms
  • Concentration
  • Reputation
  • Research and development
  • Education
  • Skilled labor

Diseconomies of Scale

• Diseconomies of scale occur when firms experience increasing unit costs due to their large size
• Internal diseconomies of scale include:
  • Managerial difficulties
  • Internal communications
  • Industrial relations
• External diseconomies of scale include:
  • Local road congestion
  • Land and factory scarcity
  • Labor shortages

Survival of Small Firms

• Small firms survive due to:
  • Demand for variety
  • Inability to obtain economies of scale
  • Personal services
  • Size of the market
  • Low fixed costs
  • Limited demand (or luxury items)
  • Ambition
  • Lack of finance