ECO104: Production and Cost Overview

• ECO104: Managerial Economics is the course name.
• The course facilitator is Tristan Jake G. Faderogao.

Production and Cost Overview

• Part III focuses on Production and Cost.
• Economic analysis and decisions involve demand analysis, production and cost analysis, product pricing and output decisions, as well as capital expenditure analysis.
• The economic, political, and social environment involves business conditions, factor market conditions, competitors' reactions, and organizational architecture.
• Cash flows and risk affect firm value (shareholders' wealth).

Production Economics

• Includes the production function, production functions with one variable input, and determining the optimal use of the variable input.
• Also includes production with multiple variable inputs, measuring the efficiency of a production process, and returns to scale.

The Production Function

• A mathematical model, spreadsheet, or graph relating the maximum feasible output quantity from given input amounts. Formula: Q = αLB1 KB2
• Inputs: Resources or factors of production like raw materials, labor, or equipment.
• The Cobb-Douglas production function is a mathematical model used to represent the relationship between inputs and output.

Total Output Table – Deep Creek Mining Company

• Table 7.1 shows output based of capital input in brake horsepower (250 to 2,000) and labor input (# of workers) (1 to 10).

Production Function: Fixed and Variable Inputs

• A fixed input is required in the production process but its quantity remains constant over a given time, regardless of output.
• A variable input is defined as one whose quantity changes depending on the desired output quantity.
• Short Run: A time period where one or more resources is fixed or cannot be varied. Long Run: A time period where all resources employed in a production process can be varied.

Production Functions with One Variable Input

• Marginal product is the incremental change in total output from using one more unit of an input, while holding other inputs constant.
  • Formula: MPL = ΔQ/ΔL or ∂Q/∂L
• Average product refers to the ratio of total output to the amount of variable input used.
  • Formula: APL = Q/L

Production Functions with One Variable Input: Law of Diminishing Marginal Returns

• Initially, adding workers increases labor specialization, raising marginal output and total output.
• Adding more workers (2nd, 3rd, or 4th) leads to greater production, but eventually, marginal output declines due to limited specialization opportunities and crowding effects.
• Adding more workers (5th, 6th, and 7th) results in smaller production increases and the marginal product of labor becomes zero or negative.

Production Functions with One Variable Input: Increasing Returns with Network Effects

• Network effects is when a network product's installed base improves productivity for new customer acquisition.
• Microsoft Office and Apple’s iPhone are examples of these network-based relationships.
• Beyond 30% adoption, each additional share point increases adoption probability, reducing marketing expenses.

Production Functions with One Variable Input: Information Services under Increasing Returns

• Insights comparing things and information production include the seller of information being able to sell it again.
• The production and marketing of things are have diminishing returns while information has increasing returns.
• Things have high distribution costs with a supply side focus, but information has low distribution costs with focus on demand side thinking.

Production Functions with One Variable Input: The Relationship Between Total, Marginal, and Average Product

• Figure 7.4 shows a production function with total product (TP) and a single variable input highlighting TP, AP, and MP concepts.
• The TP function increases at an increasing rate.
• The TP function increases at a decreasing rate.
• The MP curve is decreasing up to L3.
• In negative returns, the TP function decreases, and the MP curve continues decreasing, becoming negative beyond L3.
• Inflection point at L₁.
• The MP curve intersects the AP curve at its maximum.

Determining the Optimal Use of the Variable Input

• Marginal Revenue Product (MRPL) is how much an additional unit of input increases total revenue, also called marginal value added.
• Formula: MRPL = ΔTR / ΔL
• Marginal value added: The increase in revenue from a production stage or service Marginal Factor Cost (MFCL): The cost added to total cost by an additional unit of variable input.
  • Formula: MFCL = ΔTC / ΔL

Determining Optimal Use of Variable Input: Input Level

• Given marginal revenue product and marginal factor cost, the optimal variable input amount is determined.
• An economic activity should be expanded as long as the marginal benefits exceed the marginal costs.
• For short-run, the optimal variable input level occurs where MRPL = MFCL.

Marginal Revenue Product and Marginal Factor Cost for Deep Creek Mining Company

• Table 7.3 highlights revenues and costs with variable labor input.

Production with Multiple Variable Inputs: Isoquants

• Production isoquant refers to an algebraic function or geometric curve showing combinations of two inputs for a specific output level.
  • The isoquants for Deep Creek Mining are displayed in Figure 7.6.
• While each shows the possibility of input substitution, choices are limited in reality.
• Some input combinations may require too much of one input.
• Substitution options are limited by the production technology.

Production with Multiple Variable Inputs: Technical Substitution

• Marginal rate of technical substitution (MRTS) tells the rate one input may be substituted for another to produce a given quantity.
  • MRTS is also the slope of the tangent line to the isocost for any point on the curve
  • Formula: MRTS = -(K₁-K₂)/(L₁-L₂) = -ΔK / ΔL

Determining Optimal Combination of Inputs: Isocost Lines

• The total cost of each possible input combination depends on the market prices of those inputs. -Assuming input can shift between perfectly elastic markets, it is assumed the per-unit price if each input remains constance, regardless of amount purchased. -Formula: C = C₁L + CK
• Production decisions can be formulated in two ways.
  • First is minimizing total cost given output constraints
  • Second, is maximizing output given cost constraints

Determining Optimal Combination of Inputs: Minimizing Cost Subject to an Output Constraint

• At the optimal input mix, the slopes of the isocost & isoquant lines are equal. Formula: dK/dL = MRTS = MP1/MPk
• Taking the derivative of the isocost line: dK/dL = -CL/CK
• Condition for equilibrium (equimarginal criterion): MP1/MPk = CL/CK or MP1/CL = MPk/CK

Optimal Production Process: Fixed Proportions

• The previous section discussed the least-cost mix of divisible inputs, while some production needs involve specific equipment with set worker numbers.
• Linear programming methods help determine the least-cost process for fixed proportion production instead of calculus.

Optimal Production Process: Production Processes and Process Rays

• A production process has a fixed-proportions setup. A production process is seen graphically as a ray from the origin, its slope shows the proportional quantity of specific resources to produce one output unit.
• Along Process Ray M₁, two workers operate a 1,250-bhp drilling machine with a ray’s slope of 625 bhp/mine worker. Not all fixed proportion production processes are the same in efficiency.

Measuring the Efficiency of a Production Process

• Allocative Efficiency: Measures how closely production is to using the least-cost input mix or process while achieving a desire output. Technical Efficiency: Measures how closely production is to achieving maximum potential output given an input mix. Overall Production Efficiency: A measure of both technical and allocative efficiency.

Returns to Scale

• Returns to scale is the proportionate output increase due to a given proportionate increase in all inputs.
• Production scale increases are shown graphically with a two-dimensional isoquant map.
• The relationships between inputs and outputs include:
  • Increasing returns, where output increases are more than \lambdaλ; that is, Q(2) > λQ(1)
  • Decreasing returns, where they are less than λ; that is, Q(2) < λQ(1) Constant returns, where they are exactly λ; that is, Q(2) = λQ(1)

Returns to Scale: Increasing and Decreasing

• Company production often increases and then has decreasing returns to scale.
• Early increasing returns are often due to capital and labor specialization opportunities when more efficient equipment replaces all-purpose tools.
• Later decreasing returns typically result from complex coordination and controls faced by management as scale increases.

Returns to Scale: The Cobb-Douglas Production Function

• A simpler case is when returns to scale are determined by Cobb Douglas's parameter sum (β₁ + β2): Q = αLB₁ KB₂
• If β₁ + β2 is less than, equal to, or greater than 1, Cobb-Douglas will exhibit decreasing, constant, or increasing returns.
• The estimates allow one to test for increasing, constant, or decreasing returns to scale.

Returns to Scale: Cobb-Douglas Research

• Moroney estimates a three-variable model: Q = αLIBLAKB [7.20]
• Q is firms value added by the production plants
• Production and non-production work hour elasticity indicates a specific industrial output.