Consider a hospital that produces output (Q) and has two production inputs, nurse-hours (N) and beds
(B). the hospital faces input costs of W_{N} = 15 and W_{B} = 25. Assume the hospital's production function is: Q =N^{α}B^{1-α}, where α^{1/2}.
a) If the hospital's desired output level is Q = 120, find B∗ and N∗ that minimize cost.
b) What is the hospital's total cost, C, of producing this level of output using B∗ and N∗?
c) Suppose the state government imposes a certificate of need constraint on the number of beds. The new CON rule limits the number of beds to B_{R} = 250. Assuming the hospital would like to keep its output level at 120, how many nurse-hours (N_{R}) will it require?
d) Suppose instead the CON rule limits the number of beds to B_{R} ′ = 100. Again, assuming the hospital keeps its output level constant, how many nurse-hours (N_{R}′) will it now require?
e) What is the hospital's total cost of producing this level of output using B_{R}′ and N_{R}′?
f) Now suppose the hospital must keep its costs equal to its costs before the CON law. How many nurse-hours will it now require? What will its new output level be?