A management consulting firm produces reports for clients using highly skilled c

Question

A management consulting firm produces reports for clients using highly skilled consultants (H) and moderately skilled analysts (M). Its production function is f(H,M)=H0.5M 0.5. The wage rate for consultants is $360/hour and the wage rate for analysts is $90/hour.

a) What returns to scale property does this production function exhibit? Show this mathematically.

b) Show that the isoquant associated with producing 6 reports is given by H=36/M (or H=36M-1) . Using simple calculus, provide an expression for the marginal rate of technical substitution (the slope of the isoquant).

c) What is the marginal rate of technical substitution when 3 analysts are employed (and 6 reports are produced)? What does this imply about how many consultants could be substituted for 1 analyst and still produce the same number of reports?

d) State the cost minimization problem of the firm mathematically. How many consultants and analysts will the firm employ to produce q reports if its objective is to minimize costs? In other words, solve for H*(q) and M*(q).

e) Derive an expression for the firm’s long-run cost function.

f) The management consulting industry in New York City is very competitive as it easy for experienced executives to start their own boutique consultancies. Given that firms will enter the industry until economic profits are driven to zero, what will the price of a report be in the longrun?

I really need to understand this so if you could be as clear as possible that would be great. Thanks!!

Explanation / Answer

a) Production function : f(H,M)=H0.5M0.5

Let H = aH and M = aM and put them in the above

New production function = (aH0.5 )(aM0.5 ) = aH0.5M0.5

or New production function = a * old production function

hence this function exhibit constant return to scale.

b) Marginal Rate of technical Substitution = MP of H/MP of M = df/dH / df/dM = 0.5M0.5H-0.5 / 0.5M-0.5H0.5

= M/H

c) When MRTs is M/H it implies that to 1 consultants could be substituted for 1 analyst and still produce the same number of reports.

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