Consider a hospital that produces output (Q) and has two production inputs, nurse-hours (N) and beds
(B). the hospital faces input costs of WN = 15 and WB = 25. Assume the hospital's production function is: Q =NαB1-α, where α1/2.
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 BR = 250. Assuming the hospital would like to keep its output level at 120, how many nurse-hours (NR) will it require?
d) Suppose instead the CON rule limits the number of beds to BR ′ = 100. Again, assuming the hospital keeps its output level constant, how many nurse-hours (NR′) will it now require?
e) What is the hospital's total cost of producing this level of output using BR′ and NR′?
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?