Question 29 of 31intermediate🔧 ApplyNumerical3 marks

Let the production function of a firm be

Q=5L12K12Q = 5L^{\frac{1}{2}}K^{\frac{1}{2}}

Find out the maximum possible output that the firm can produce with 100 units of LL and 100 units of KK.

Correct Answer

The maximum possible output that the firm can produce is 500 units.

Exercise: EXERCISES | Q: 28 | (Page 17)
For More Understanding

Explanation

The production function defines the maximum output for given inputs. By substituting the provided values of Labour (L) and Capital (K) into the given equation, we calculate the resulting output quantity.

Solution Steps

  1. Step 1: Identify the production function and given values. The function is Q=5L12K12Q = 5L^{\frac{1}{2}}K^{\frac{1}{2}}, where L=100L = 100 and K=100K = 100.

  2. Step 2: Substitute the values of LL and KK into the production function.

    Q=5(100)12(100)12Q = 5(100)^{\frac{1}{2}}(100)^{\frac{1}{2}}

  3. Step 3: Solve the exponents. The term (100)12(100)^{\frac{1}{2}} represents the square root of 100, which is 10.

    Q=5×10×10Q = 5 \times 10 \times 10

  4. Step 4: Calculate the final output.

    Q=500Q = 500
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