Question

3. For each of the following productions determine whether there are IRS, CRS or DRS. a) y- ziz212

Answer 1

Answer 3

A function exhibit increasing returns to scale if we increase all inputs by t times output gets increased by more than t times, A function exhibit decreasing returns to scale if we increase all inputs by t times output gets increased by less than t times and A function exhibit constant returns to scale if we increase all inputs by t times output gets increased by exact t times. Note that t must be greater than 1.

Mathematically a function exhibit increasing returns to scale(IRS) if F(tx , ty) > tF(x,y).

A function exhibit Decreasing returns to scale(DRS) if F(tx , ty) < tF(x,y)

a function exhibit Constant returns to scale(CRS) if F(tx , ty) = tF(x,y)

a)

y = f(z₁ , z₂) = z₁z₂^1/2

f(tz₁ , tz₂) = t^3/2z₁z₂^1/2 > tz₁z₂^1/2 = tf(z₁ , z₂) for all t > 1

Hence this function exhibit increasing returns to scale(IRS)

b)

y = f(z₁ , z₂) = z₁² + z₂

f(tz₁ , tz₂) = t²z₁² + tz₂ = t(tz₁² + z₂) > t(z₁² + z₂) = tf(z₁ , z₂) for all t > 1

Hence this function exhibit increasing returns to scale(IRS)

(c)

y = f(z₁ , z₂) = 3z₁ + 2z₂^1/2  

f(tz₁ , tz₂) = 3tz₁ + 2t^1/2z₂^1/2 = t(3z₁ + 2(z₂/t)^1/2) < t(3z₁ + 2z₂^1/2) = tf(z₁ , z₂) for all t > 1

Hence this function exhibit decreasing returns to scale(DRS)