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The firm uses the following function to calculate the production output (PO) : PO = 5.3 C^2 L^15 , where C=capital invested and L=labour employed. If the capital in invested (C) increases by 20% , the change in PO will be? a. 20% b. 32% c. 44% d. 56% Ans. c. 44%?
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The firm uses the following function to calculate the production outpu...
Calculation of Change in Production Output (PO) due to Increase in Capital Investment (C)
Given function to calculate the production output (PO):
PO = 5.3 C^2 L^15
Where:
C = Capital invested
L = Labour employed
Step 1: Calculate the initial production output (PO1)
Let's assume the initial capital investment (C1) and labour employed (L) to be constant values.
PO1 = 5.3 C1^2 L^15
Step 2: Calculate the new capital investment (C2) after a 20% increase
Since the capital investment (C) increases by 20%, the new capital investment (C2) can be calculated as follows:
C2 = C1 + 0.2C1
C2 = C1(1 + 0.2)
C2 = 1.2C1
Step 3: Calculate the new production output (PO2) with the increased capital investment
Using the given function, substitute the new capital investment (C2) and the constant value of labour employed (L) into the equation:
PO2 = 5.3 C2^2 L^15
PO2 = 5.3 (1.2C1)^2 L^15
PO2 = 5.3 * 1.44C1^2 L^15
PO2 = 7.632C1^2 L^15
Step 4: Calculate the change in production output (ΔPO)
The change in production output (ΔPO) can be calculated by subtracting the initial production output (PO1) from the new production output (PO2):
ΔPO = PO2 - PO1
ΔPO = 7.632C1^2 L^15 - 5.3 C1^2 L^15
ΔPO = (7.632 - 5.3) C1^2 L^15
ΔPO = 2.332C1^2 L^15
Step 5: Calculate the percentage change in production output
The percentage change in production output can be calculated using the formula:
Percentage change = (ΔPO / PO1) * 100
Substituting the value of ΔPO and PO1:
Percentage change = (2.332C1^2 L^15 / 5.3 C1^2 L^15) * 100
Percentage change = (2.332 / 5.3) * 100
Percentage change = 43.92%
Therefore, the change in production output (PO) due to a 20% increase in capital investment (C) is approximately 43.92%.
Hence, the correct answer is option c. 44%.
Given function to calculate the production output (PO):
PO = 5.3 C^2 L^15
Where:
C = Capital invested
L = Labour employed
Step 1: Calculate the initial production output (PO1)
Let's assume the initial capital investment (C1) and labour employed (L) to be constant values.
PO1 = 5.3 C1^2 L^15
Step 2: Calculate the new capital investment (C2) after a 20% increase
Since the capital investment (C) increases by 20%, the new capital investment (C2) can be calculated as follows:
C2 = C1 + 0.2C1
C2 = C1(1 + 0.2)
C2 = 1.2C1
Step 3: Calculate the new production output (PO2) with the increased capital investment
Using the given function, substitute the new capital investment (C2) and the constant value of labour employed (L) into the equation:
PO2 = 5.3 C2^2 L^15
PO2 = 5.3 (1.2C1)^2 L^15
PO2 = 5.3 * 1.44C1^2 L^15
PO2 = 7.632C1^2 L^15
Step 4: Calculate the change in production output (ΔPO)
The change in production output (ΔPO) can be calculated by subtracting the initial production output (PO1) from the new production output (PO2):
ΔPO = PO2 - PO1
ΔPO = 7.632C1^2 L^15 - 5.3 C1^2 L^15
ΔPO = (7.632 - 5.3) C1^2 L^15
ΔPO = 2.332C1^2 L^15
Step 5: Calculate the percentage change in production output
The percentage change in production output can be calculated using the formula:
Percentage change = (ΔPO / PO1) * 100
Substituting the value of ΔPO and PO1:
Percentage change = (2.332C1^2 L^15 / 5.3 C1^2 L^15) * 100
Percentage change = (2.332 / 5.3) * 100
Percentage change = 43.92%
Therefore, the change in production output (PO) due to a 20% increase in capital investment (C) is approximately 43.92%.
Hence, the correct answer is option c. 44%.
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The firm uses the following function to calculate the production output (PO) : PO = 5.3 C^2 L^15 , where C=capital invested and L=labour employed. If the capital in invested (C) increases by 20% , the change in PO will be? a. 20% b. 32% c. 44% d. 56% Ans. c. 44%?
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The firm uses the following function to calculate the production output (PO) : PO = 5.3 C^2 L^15 , where C=capital invested and L=labour employed. If the capital in invested (C) increases by 20% , the change in PO will be? a. 20% b. 32% c. 44% d. 56% Ans. c. 44%? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The firm uses the following function to calculate the production output (PO) : PO = 5.3 C^2 L^15 , where C=capital invested and L=labour employed. If the capital in invested (C) increases by 20% , the change in PO will be? a. 20% b. 32% c. 44% d. 56% Ans. c. 44%? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The firm uses the following function to calculate the production output (PO) : PO = 5.3 C^2 L^15 , where C=capital invested and L=labour employed. If the capital in invested (C) increases by 20% , the change in PO will be? a. 20% b. 32% c. 44% d. 56% Ans. c. 44%?.
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