Production Function: Meaning, Curve, and Types (With Diagram)

Read this article to learn about Production Function. After reading this article you will learn about: 1. Meaning of Production Function 2. Production Function Curve 3. Types.

Meaning of Production Function:

(a) It is also known as Input Output relation.

(b) Cobb – Douglas Production function –

Q = K. L^σC^β

=K L^3/4 C^¼

(L = share of Labour, C= share of Capital)

Cobb – Douglas Production function is based on Constant elasticity of substitution. 

Production Function Curve:

Explanation of Production Function Curve:

(a) Total Physical Product of x (TPP_x) rises at increasing rate of return; MPPx rising and production function curve is concave upward.

(b) Beyond Inflexion point ‘A’, TPP_x rises but at diminishing rate & MPP_x starts to decline.

(c) TPP_x is highest at point ‘B’ or remains constant; and MPP_x = 0.

(d) TPP_x decreases then MPP_x become negative.

(e) At point ‘D’; MPP_x = APP_x and APP_x is maximum.

(f) When MPP_x > APP_x; then APP_x is increasing.

(g) When MPP_x < APP_x; then APPx; is decreasing but never becomes negative.

(i) When α+β = 1 →Law of constant return

(0 When α+β >1 →Law of increasing return

(J) When α+β ˃1→ Law of diminishing return

Types of Production Function:

(a) Linear P.F. When P.F. is homogeneous of the first degree

Y = a₀+a₁xa₁+a₂x₂+ ____________a_nx_n

(Where Y = Production, a₀ = Constant, a₁ a₂ …..a_n = Coefficient factors, X₁,X₂..X_n= Factors of Production)

(b) Quadrate P.F→Y= a+bx+cx₂

(Where a, b, c = constant, x = Production factor)

(c) Square root P.F. Y= a+b√x₁+cX₂

(d) Cubic P.F. Y = a₀+a₁x+b₂x₂+a₃x₃

(i) Maximum profit is obtained when. Marginal Return = Marginal Cost

(ii) Breakeven point → Total Return = Total Cost

(iii) Acc. To law of diminishing return, optimum profit will be at a point where, MC = MP

(iv) Optimum level of input use without resource limitation Law of diminishing return (F-P)

(v) Division under resource limitation Principal of equimarginal return (P- P)

(vi) Chose best crop enterprises Principal of opportunity cost (P-P)

(vii) Dept.-equity ratio = Differed liabilities /Net worth

(viii) A- Net capital ratio = Total Assets/Total liabilities.

(ix) When MPP is maximum, the MC will be lowest.

(x) MPP zero – When MC is minimum.

(xi) Rate of Turn Over = Gross Income / Total Assets x 100

(xii) Present value of future money is calculated by use of = P/ (1+i) ^t

(xiii) B. C ratio = Benefit/total cost (Mostly used to evaluate construction of Dam)

Relationship:

Elasticity of Production:

(a) When MP = 0, then E_p = 0 → Completely inelastic demand

(b) When MP = AP, then E_P = 1→ Unit inelastic demand (Ex. Demand of Agri. Products)

(c) When MP > AP, then E_P > 1 → Elastic demand (for monopoly)

(d) When MP = AP, then E_p < 1→ Relatively inelastic demand,

(e) When demand curve is flatter – Relatively elastic demand

(f) Perfect elasticity = Horizontal straight line. Perfect inelastic = Vertical demand curve for a commodity.

(g) Relatively elastic = Flatter demand curve.