UNIT 12: INPUT-OUTPUT RELATIONSHIP (PRODUCTION FUNCTION)

The law of diminishing return

"As more of a variable input X is added to a fixed factor, total output increases at an increasing rate and later decreases at a decreasing rate until a point is reached where additional quantities of input X will yield diminishing marginal returns, assuming all other factors remain constant."

Ways of expressing production function

- Q = f (L,K,N,M,T) - Y = a +bx - Output depends on inputs i.e. when inputs increase, output will increase and vice versa

Assumptions of the law of returns to scale

-All factors are variable -A constant technology -The product can be measured in physical quantities -Perfect competition -Long-run period of production

Types of return to scale

-Constant returns to scale: if inputs double and outputs double too -Increasing returns to scale: if inputs double and outputs increase more than double -Decreasing returns to scale: if inputs double and outputs increase less than double

Assumptions of the law of diminishing return

-Existence of a variable factor of production and other factors are constant -All units of the variable factor are homogenous -The price of the product is given and constant -It assumes a short-run period -It assumes that technology is constant -It is possible to change the prepositions in which various inputs are combined

Stages of the law of variable portions

-Stage 1: Inefficient stage, because at that stage all factors of production are not fully used as AP is still increasing -Stage 2: Efficient stage because at stage 2 all resources are fully utilized as shown by TP reaching its maximum -Stage 3: Inefficient stage because there is over-exploitation of fixed factors by variable inputs as shown by TP decreasing and MP is negative

Equilibrium in a firm

-The firm is at equilibrium when its highest isoquant is tangent to its isocost -The point of tangency represents the least cost combination of two inputs

Properties of Isoquants

-They are negatively inclined -It lies above and to the right of another represents a higher output level -No two isoquants can intersect with each other -Each isoquant is convex to the origin -In between two isoquants, there can be a number of isoquants showing various levels of output -No isoquant can touch either axis

Relationship between TP, AP, and MP

-When AP is rising it is always less than MP and when it's falling, it is always greater than MP -MP = AP, when AP is at its maximum -MP = 0, when TP is at its maximum

Production function (definition)

An expression that shows the relationship between inputs and outputs

Cost minimization and expansion path of a firm

If all points of tangency like L, M, and N are joined by a line is known as the expansion path of a firm. It shows how proportions of two factors used might be changed as the firm expands,

Marginal product

The additional output produced by an extra unit of a variable factor MP = ∆TP / ∆L(variable input)

Average product (definition) (formula)

The level of output per unit of variable inputs AP = TP / variable output (labor)

Marginal Rate of Technical Substitution (MRTS) (definition) (formula)

The slope of the isoquant that shows the rate at which one input is substituted by another while maintaining the same level of output MRTS = ∆ horizontal axis / ∆ vertical axis

Total product (definition)

Total output from the use of all factors of production

Isocost curve (definition)

a curve that represents the locus of all combinations of the two factor inputs which result from the same total cost.

Isoquant (definition)

aka a production indifference curve is a curve joining different inputs combinations that give the same level of output

Isocost (definition)

aka cost constraint is a line which joins different combinations of two inputs which exhaust producer's income

The law of returns to scale

an expression of the relationship between output and the scale of inputs in the long run when all inputs are increased in the same proportion