Transcript Managerial Economics & Business Strategy

Managerial Economics &
Business Strategy
Chapter 5
The Production Process and Costs
Guiding the Production Process
• Two Roles of the Manager
• Produce as much as possible
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How do you induce maximum worker effort from you
employees?
• Allow to earn tips
• Profit sharing
• Employ the right level of inputs
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How many workers/inputs do you hire?
Hire labor until the value of marginal product of labor equals the
wage
• VMPL = w, where VMPL = P x MPL.
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Hire capital until the value of marginal product of capital equals
the rental rate
• VMPK = r, where VMPK = P x MPK .
Can we do it?? (number 11)
• You are a manager for Herman Miller – a major
manufacturer of office furniture. You recently hired an
economist to work with engineering and operations experts
to estimate the production function for a particular line of
office chairs. The report from these experts indicates that
the relevant production function is Q=2(K1/2)(L1/2) where K
represents capital equipment and L is labor. Your company
has already spent a total of $10,000 on the 4 units of capital
equipment it owns. Due to current economic conditions, the
company does not have the flexibility needed to acquire
additional equipment. If workers at the firm are paid a
competitive wage of $100 and chairs can be sold for $200
each, what is your profit-maximizing level of output and
labor usage? What is your maximum profit?
Typical Production Functions
• Linear
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Q = F(K,L) = aK + bL
Inputs are perfect substitutes
• Leontief
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Q = F(K,L) = min{bK,cL}
Also called fixed proportions production function
Need one left and one right shoe
• Cobb-Douglas
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Q=F(K,L) = K1/2L1/2
Shows that goods are substitutes, but not perfect substitutes
Leontief???
• Q = F(K,L) = min{6K, 5L}
• How much output is produced when 4 units of labor
and 8 units of capital are employed?
• Q = F(8,4) = min{6*8, 5*4} = min{48, 20}
• Q = 20 units of output
How do you find the MPL and
MPK of the production function?
Q  f ( K , L)
Q
Q
MPL 
and MPK 
L
K
Can we do it?
• How many units of labor should we employ if the
wage rate is $2.00, the price of the output is
$10.00, capital is fixed at 1, and the production
function is given by Q = f(K,L) = K0.5L0.5
• MPL = 0.5K0.5L-0.5
• VMPL = 10(0.5(1)L-0.5) = 5L-0.5
• Hire until VMP = w
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5(1/L0.5) = 2
5/2 = L0.5
25/4 = L
6.25 units of labor should be hired