Question

Norway oil production is given by the following function: N(L)=18L ² +66L+22, where L represents the labor in 10,000 workers (1 unit of labor represents 10,000 workers). Similarly, US oil producers have the aggregate production function N(L)=−7L² +216L+18. What would be the number of workers employed by each country, Norway and the US, allowing that to have the same increase (rate of change) in oil production?

a. 50,000 workers
b. 60,000 workers
c. 20,000 workers
d. 40,000 workers

Answer 1

The student is asked to find the number of workers at which the Norway and US oil production have the same rate of change. By equating the derivatives of their production functions, we find that L equals 3. Since 1 unit of labor represents 10,000 workers, the correct number of workers is 30,000, which is not listed in the given options.

Step-by-step explanation:

The question wants us to find the amount of labor (L) at which the rates of change of the Norway oil production function and the US oil production function are equal. To do this, we need to equate the derivatives of the two production functions because the derivative represents the rate of change of a function. So, we will find the derivatives and solve for L.

For Norway:
N'(L) = 36L + 66

For the US:
N'(L) = -14L + 216

We set these equal to each other to solve for L:

36L + 66 = -14L + 216
50L = 150
L = 3

Since 1 unit of labor represents 10,000 workers, L = 3 corresponds to 30,000 workers. However, this is not one of the provided options. If the question contains a typo and intended to include 30,000 as an option instead of those listed, the correct answer would be 30,000 workers. Otherwise, based on the choices provided, the correct answer cannot be determined from the calculations.