**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^{σ}C^{β}

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=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: **

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(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.

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(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 = a_{0}+a_{1}xa_{1}+a_{2}x_{2}+ ____________a_{n}x_{n }

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(Where Y = Production, a_{0} = Constant, a_{1} a_{2} …..a_{n} = Coefficient factors, X_{1},X_{2}..X_{n}= Factors of Production)

(b) Quadrate P.F→Y= a+bx+cx_{2}

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

(c) Square root P.F. Y= a+b√x_{1}+cX_{2 }

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(d) Cubic P.F. Y = a_{0}+a_{1}x+b_{2}x_{2}+a_{3}x_{3 }

(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

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(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.

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(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

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

(g) Relatively elastic = Flatter demand curve.