The following data relates to the operation of a company over a period of two years; year 1: 12,000 units in output level, Ghc21,000 in cost with an inflation index of 1.05; year 2: 16,000 units in output level, Ghc26,7500 in cost with an inflation index of 1.03. The cost function at an inflation index of 1.08 will be A. C = 1.56x + Ghc2,300 B. C = 1.45x + Ghc2,320 C. C = 1.62x + Ghc2,160 D. C = 1.50x + Ghc2,125
Question
The following data relates to the operation of a company over a period of two years; year 1: 12,000 units in output level, Ghc21,000 in cost with an inflation index of 1.05; year 2: 16,000 units in output level, Ghc26,7500 in cost with an inflation index of 1.03. The cost function at an inflation index of 1.08 will be A. C = 1.56x + Ghc2,300 B. C = 1.45x + Ghc2,320 C. C = 1.62x + Ghc2,160 D. C = 1.50x + Ghc2,125
Solution
Based on the given data, we can determine the cost function at an inflation index of 1.08.
In year 1, the output level was 12,000 units and the cost was Ghc21,000. The inflation index for that year was 1.05.
To find the cost function, we can use the formula C = mx + b, where C represents the cost, x represents the output level, m represents the slope, and b represents the y-intercept.
Using the given data, we can calculate the slope (m) as follows: m = (cost in year 2 - cost in year 1) / (output level in year 2 - output level in year 1) = (Ghc26,750 - Ghc21,000) / (16,000 - 12,000) = Ghc5,750 / 4,000 = Ghc1.4375
Now, let's calculate the y-intercept (b) using the formula: b = cost in year 1 - (m * output level in year 1) = Ghc21,000 - (1.4375 * 12,000) = Ghc21,000 - Ghc17,250 = Ghc3,750
So, the cost function at an inflation index of 1.08 is C = 1.4375x + Ghc3,750.
Comparing this with the given options, we can see that none of the options match exactly. Therefore, none of the options A, B, C, or D are correct.
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