Question

In the model of bureaucracy, let b(y)=y¹/² and c(y)=y²

a.) Calculatestudent y* belowmeaning the value of y that maximizes B(y)-C(y). For what values of y does B(y) = C(y)? se tUhis to find yᵇ and show that yᵇ>y*

Answer 1

To solve for y* and yb in the context of bureaucratic models, we differentiate B(y) - C(y), and equate B(y) and C(y), solving the respective equations to find the values of y for each scenario.

Step-by-step explanation:

This problem involves finding the value of y that maximizes the difference B(y) - C(y), given B(y) = y1/2 and C(y) = y2. To find the maximizing value of y, denoted as y*, we should set the first derivative of B(y) - C(y) to zero and solve for y. On the other hand, to find when B(y) = C(y), we simply set these two functions equal to each other and solve for y.

To maximize B(y) - C(y), we need to determine when the first derivative is zero. This requires finding the derivatives B'(y) = 1/(2sqrt(y)) and C'(y) = 2y, and then solving the equation 1/(2sqrt(y)) - 2y = 0. After finding y*, we compare it to yb, which is the value of y when B(y) = C(y). By solving this set of equations, we can show that yb > y* which has implications in the context of bureaucratic efficiency.