Question

If given a specific production function is as follows:

Q=L²K² where, Q = output, L= number of workers employed in the production, K= number of capital equipment (machines) employed in the production process. Can you examine what kind of returns to scale is associated with this production function. Please pick one of the following three returns to scales as your answer and explain why you thing your answer is correct. [Constant Returns to Scale, Increasing Returns to Scale, Decreasing Returns to Scale). Prove your answer using hypothetical numbers.

"Lean's deluxe garment bag sales increased from 4,800 units to 6,000 units in response to price drop from $30/unit to $20/unit.” Calculate arc price elasticity of this product using mid-point formula.

Answer 1

1. Increasing Returns to Scale
Explanation: Q=L²K²
Let L = tL and K = tK where t > 1
Q' = (tL)²(tK)²
So, Q' = t²⁺²L²K²
So, Q' = t⁴Q
Thus, there are increasing returns to scale as power of t > 1.

Let, L = K = 10
So, Q = L²K² = (10)²(10)² = (100)*(100) = 10,000

Let, t = 2; L = tL = (2*10) = 20; K = tK = (2*10) = 20
So, Q' =(tL)²(tK)² = (20)²(20)² = 400*400 = 160,000 = 2⁴(10,000) = 2⁴Q
Thus, when we increase both inputs by a proportion 2, output increases by a greater proportion = 2⁴.

2. P1 = $30; Q1 = 4800
P2 = $20; Q2 = 6000

Using midpoint method, arc price elasticity =

The arc price elasticity = -0.56