Course: Microeconomic - Production Function

A student of the Faculty of Economics and Business has T hours to prepare the exams of Introduction to Microeconomics and Mathematical Methods. He estimates that by studying t₁ hours for the first course he will obtain a grade equal to N₁ = F(t₁). On the other hand, the second subject, which is more difficult and tiring, will obtain a grade equal to N₂ = F(t₂). Furthermore, consider that T = t₁ + t₂. These 2 functions can be viewed as functions of grade production.

1. A colleague tells you that to maximize the average grade between the two exams you should consider the average product of both production functions. Given your knowledge of economics, is the recommendation correct? Explain

2. Consider now that T = 60, i.e., the student has 60 hours to allocate to both tests.

On the other hand,N1=3+0,05t1 and N2=1.5+(0.15t20.001t22),

where PMg₁ = dN₁ / dt₁ = 0.05 and PMg₂ = dN₂ / dt₂ = 0.15 - 0.002t₂.

Calculate the optimal number of hours allocated for the study of both tests.

3. You are asked to help the struggling student by calculating the average of the grades he should achieve by studying the number of hours calculated above. In addition, the student wants to know the Average Product (AP) of the study hours for both tests.