(iii) Bright Future, Ltd (BF) is a nonprofit foundation providing medical treatment
to emotionally distressed children. BF has hired you as a business consultant to
design an employment policy that would be consistent with its goal of
providing the maximum possible service given its limited financial resources.
You have determined that the service (Z) provided by BF is a function of its
medical staff input (M) and sound service input (S) which is given by:
Z = M + .5S + .5 MS - S2
BF’s staff budget for the coming year is $1,200,000. Annual employment costs
are $30,000 for each social service staff member (S) and $60,000 for each medical
staff member (M).2
(a) Using the Lagrangean multiplier approach calculate the optimal (i.e.,
service maximizing) combination of medical and social staff. Determine
the optimal amount of service provided by BF.
(b) Calculate BF’s marginal cost. Explain your answer.
(c) Using Excel-Solver verify your answer to (a).
(Show your work. Show the spreadsheets in detail. Provide print outs
with Solver window. To print the solver window, use print screen
command on your key board and then create a MS Word document
(iv) The own price elasticity of demand for a pack of cigarettes is estimated to be -.4.
Current price and consumption are $4.00 and 2 million units per year.
Assuming a linear demand relationship determine the demand equation for
cigarettes. Show all your calculations.