Production and Cost Theory

Theory of Production and Cost

• This chapter covers basic production concepts, cost analysis, short-run production, and cost functions
• The topics include: production function, input types, economic and accounting cost, cost functions, and their relationships

Chapter Objectives

• Define production and production function
• Differentiate between fixed and variable inputs
• Describe short-run total, average, and marginal product
• Compare the three stages of production in the short run
• Explain the differences between accounting cost and economic cost
• Describe total cost, average cost, and marginal cost functions
• Explain the relationship between short run production functions and short run cost functions

Theory Of Production In The Short Run

• Raw materials must be transformed into outputs to provide better utility
• The process of converting inputs (land, labor, capital, entrepreneurial ability) into outputs

Definition of Production

• Turns inputs into outputs
• Production creates worth or benefit
• Tangible (goods) or intangible (services) result

Production Function

• The maximum output that can be produced with a given amount of inputs and technology
• Can be an algebraic equation, table, or graph

Inputs

• Q = f(X1, X2, X3,..., Xn), where Q is output and X1, X2, X3, ..., Xn are different types of inputs
• Classification of inputs: fixed and variable

Fixed Inputs

• The quantity cannot be easily changed when market conditions necessitate immediate output adjustment
• While not absolutely fixed, they remain constant during an immediate requirement
• Examples include buildings, land, and machinery because their quantity can't be easily changed in the short term

Variable Inputs

• Quantities can be changed rapidly to match desired output changes
• The quantity can be easily reduced if market demand decreases and vice versa
• Unskilled labor is a classic example

Short Run

• Economic context: a period when at least one input remains fixed
• It is a period insufficient to alter all inputs simultaneously
• Short run durations vary across firms
• The analysis focuses on production with one variable and one fixed input

Production Function (Capital and Labor)

• Q = f(L), where Q is output and L is the quantity of labor
• Output increases by increasing the amount of labor used
• Illustrates the possible outputs from using different amounts of labor with fixed capital
• Output changes are only achievable when the amount of labor changes because capital is fixed

Total, Average, and Marginal Product

• Variables that describe the impact of a variable input on production

Total Product (TP)

• The maximum amount of output from specific combinations of variable and fixed inputs
• Increasing variable input increases total product up to a point
• Combining more variable input with fixed input raises total product
• Employing too much variable input with fixed input leads to output decline
• TP function trend in the short-run:
  • Increases at an increasing rate
  • Increases at a decreasing rate
  • Reaches a maximum point
  • Falls as the quantity of the variable input rises

Marginal Product (MP)

• It is the change in output from one more unit of variable input while other inputs are constant
• Marginal Product of Labour (MPL) applies to the addition of one worker
• MP₁ measures the slope of the total product curve at a given point
• MP = dTP/dL = ΔQ/ΔL
• Marginal product of the variable input trend in the short run:
  • First increases
  • Reaches its maximum
  • Decreases to a negative value as more variable input combines with fixed input

Average Product (AP)

• The level of output each unit of input produces on average
• It is the mean contribution of each variable input to total output
• Mathematically, the ratio of total output to variable input number
• The average product of labor (APL) is given by APL = TP/L
• Average product of labor increases, reaches maximum, and then declines

Graphs

• The AP curve can be measured by the inclination of rays extending from the origin to a point on the TP curve
• APL at L2 is the ratio of TP2 to L2 and is the inclination of ray a
• When APL is increasing, MPL > APL
• When APL is at its maximum, MPL = APL
• When APL is decreasing, MPL < APL

Example Cut-Flower Firm

• Given: Q= 4KL- 0.6K2 - 0.1L2, where Q is cut-flower quantity, L is labor, K is fixed capital (K=5)
• Need to determine:
  • Average product of labor (APL) function
  • Level of labor which maximizes cut-flower output
  • Maximum achievable amount of cut-flower production

Law of Variable Proportions

• Adding successive units of a variable input to a fixed input will, beyond some point, decrease the marginal product attributed to each additional unit of the variable resource
• Hiring more workers with constant capital eventually leads to smaller output increases

Assumptions of the Law of Variable Proportions

• Assumes fixed technology
• Assumes that the techniques of production do not change
• All labor units are of equal quality (innate ability, education, training, experience) Marginal product diminishes because more workers are used relative to available plant and equipment
• The law starts to operate when the number of workers exceeds L1 in Figure 4.1, after the marginal product curve reaches its maximum and is also called the law of diminishing returns

Stages Of Production

• Determining the variable input (labor) for a firm depends on factors beyond labor productivity
• Economists define three short-run production stages

Stage I

• The average product (APL) increases to a maximum
• Extends from the origin to the point where MPL = APL, up to L2 in figure 4.1
• The region is not efficient due to the variable input being too small and the fixed input being underutilized

Stage II

• Ranges from APL at its maximum (MPL=APL) to MPL at zero (L2 to L3 in figure 4.1)
• Output still increases with more labor but at a decreasing rate
• Also known as diminishing marginal returns
• Scarcity of the fixed factor is the reason for decreasing average and marginal products
• The efficient region of production is where the marginal product of the variable input is positive

Stage III

• Increasing variable input decreases total product
• Total product curve slopes downwards
• Also known as negative marginal returns because the variable input's marginal product becomes negative
• Excessive variable input relative to fixed input is the cause and fixed input is over-utilized
• The increase in variable inputs is contributing negatively to total product
• Stage III exists when labor beyond L3 because additional labor is counterproductive

Theory Of Costs In The Short Run

• Definition and types of costs

Definition of Cost

• Cost is the monetary value of inputs to produce a product
• Acquiring inputs requires purchase from resource suppliers

Economic vs Accounting Profit

• Accountants: Profit = Total Revenue - Explicit Costs
• Economists: Economic Profit = Total Revenue - Economic Costs (Explicit Costs + Implicit Costs)

Accounting Cost

• Ignores the value of non-purchased (self-owned) inputs
• Does not include direct expenses, wages/salaries, cost of raw materials, interest on borrowed funds, depreciation allowances and utility expenses

Explicit Costs

• Out-of-pocket expenses for purchased inputs
• Profit calculated with only explicit costs is accounting profit

Economic Cost

• Includes the monetary value of all inputs (purchased and non-purchased)
• Calculating economic costs involves estimating the opportunity costs of non-purchased inputs
• The estimated monetary cost for non-purchased inputs is known as implicit cost

Implicit Cost

• Ex: Mr. X quits a job paying Birr 10,000/month to run a firm
• Salary forgone is the opportunity cost of his labor at Birr 10,000/month
• Economic cost = implicit cost + explicit cost

Economic Profit

• Economic profit will give the real profit
• Accounting profit is greater than economic profit by the implicit cost amount

Short Run Cost

• A cost function represents the total cost (C) required for producing a certain quantity (Q) of output by the equation C = f(Q)

Total Cost (TC)

• Short run can be divided into:
  • Total Fixed Cost (TFC)
  • Total Variable Cost (TVC)

Fixed Costs

• Do not change with the level of output
• Unavoidable unless the firm shuts down
• Include: administrative staff salaries, building depreciation, land maintenance, and rent

Variable Costs

• Change directly with the level of output
• Zero if output is zero
• Include: raw materials, direct labor, and expenses for fuel, water, and electricity

Calculating Total Cost

• In short run, TC = TFC + TVC

Total Fixed Cost(Shape)

• TFC is a straight, horizontal line parallel to the output (x) axis
• Because it does not vary with output level

Total Variable Cost

• TVC has an inverse S-shape, illustrating the law of variable proportions
• TVC increases at a decreasing rate because productivity increases with more variable factor employed
• After optimal combination, variable factor productivity declines, and TVC increases at an increasing rate

Total Cost (Shape)

• TC curve is derived by vertically summing TFC and TVC at each output level
• Has an inverse S-shape like TVC
• When output is zero, TVC is also zero; thus, TC = TFC

Per Unit Costs

• Can be derived from total cost functions and are important for short-run firm analysis

Average Fixed Cost (AFC)

• Total fixed cost per unit of production
• AFC = TFC/Q
• The AFC curve declines continuously and approaches both axes asymptotically

Average Variable Cost (AVC)

• Total variable cost per unit of output
• Calculated by dividing TVC by the level of output: AVC = TVC/Q
• The short-run AVC initially decreases, reaches a minimum, and then increases, making its curve U-shaped due to the law of variable proportions

Average Total Cost (ATC)

• It is also known as Average Cost(AC) is the total cost per unit of output
• Calculated by dividing total cost by the level of output: AC = TC/Q
• Expressed as AC = (TVC + TFC)/Q = AVC + AFC
• Thus, AC can also be obtained by adding AVC and AFC vertically

Marginal Cost (MC)

• It is the extra cost a firm pays to produce a one more unit of output
• MC is the change in total cost from a small change in output level, or MC = dTC/dQ
• MC is also the change in TVC with respect to a unit change in the level of output
• MC = (dTFC + dTVC)/dQ = dTVC/dQ, since dTFC/dQ = 0 Given the inverse S-shaped TC and TVC, MC decreases initially, reaches its minimum, and then increases

MC Curves

• AVC, AC, and MC curves are all U-shaped due to the law of variable proportions
• In the provided figure, the AVC curve is at its minimum at Q1, while the AC curve reaches its minimum at Q2
• AFC (the vertical difference between AC and AVC) continuously decreases as output increases
• Notably, the MC curve intersects both the AVC and AC curves at their minimum points

The relationship between short run production and cost curves

These conditions suggest that the connection among MC and MPL as well as the relationship between AVC and AMPL can be derived if the business uses labour as a variable input in the short term and takes capital as a set input when the cost of labour is w, which is constant

Marginal Cost And Marginal Product of Labour

• MC  TVC / Q, where TVC  w.. The expression shows that mc and MPL are negatively associated
• Mc decreases when MPL increases and vice versa

Average Variable Cost and Average Product of Labour

• AVC  TVC / Q,, where, TVC  w.L

Basic production concepts, cost analysis, and cost functions are covered. Topics include production function, types of inputs, economic and accounting cost, as well as their relationships. It also describes total cost, average cost, and marginal cost functions.