Find the returns to scale for the following Cobb--Douglas production function. Q=L^(1/3)K^(3/4) Option 1: Increasing returns to scale Option 2: Decreasing returns to scale Option 3: Constant returns to scale Option 4: No returns to scale

Answer: Increasing returns to scale. Solution: For a Cobb-Douglas function Q = L^a K^b, returns to scale depend on a + b. Here a + b = 1/3 + 3/4 = (4+9)/12 = 13/12 > 1. Since the sum of exponents exceeds 1, the function shows increasing returns to scale.

Micro

Production & Costs

Easy

Find the returns to scale for the following Cobb--Douglas production function.

$Q=L^{1/3}K^{3/4}$

Increasing returns to scale

Decreasing returns to scale

Constant returns to scale

No returns to scale

✅ Correct Option: 1

For a Cobb-Douglas function $Q = L^a K^b$ , returns to scale depend on $a + b$ . Here $a + b = \frac{1}{3} + \frac{3}{4} = \frac{4+9}{12} = \frac{13}{12} > 1$ . Since the sum of exponents exceeds 1, the function shows increasing returns to scale.

2025: 28 May Shift 1

Keeping the capital as a fixed input, as 3, when the quantity of labor changes from 3 to 4, the total product with labor also rises from 40 to 50 units. What is the average product after the change?

50
13.33
12.5
40

2025: 22 May Shift 2

Given the production function $f(tx_1, tx_2) > tf (x_1, x_2)$ , what it exhibit:

2025: 27 May Shift 2

At the minimum point of the long run average cost curve .......... is observed.

2025: 29 May Shift 1

What is the main purpose of Cost Reduction Technologies in business?

2025: 30 May Shift 1

If the production is increased to 300 vases, what will happen to Fixed cost per unit?

2026: 11 May Shift 1

What happens to the total cost (TC) of production if the quantity of output in the production is reduced to 0 (zero)?

Where, TC=Total cost, FC=Fixed Cost, VC=Variable Cost.

Find the returns to scale for the following Cobb--Douglas production function. Q=L1/3K3/4Q=L^{1/3}K^{3/4}Q=L1/3K3/4

Solution

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Find the returns to scale for the following Cobb--Douglas production function.

$Q=L^{1/3}K^{3/4}$