Question
Maria is launching a start-up to make paper cups for the coffee shops in the Boston area. To make cups, she uses both labor (
Maria is launching a start-up to make paper cups for
the coffee shops in the Boston area. To make cups,
she uses both labor (
L
) and equipment (capital, or
K
). Her production function is
4
.
.
, where
Q
is the number of cups produced, measured in thousa
nds. Labor and capital are Maria's only costs. The
daily wage (
w
) is $400 per person-day and the rental price of capital (
r
) is $100 per machine-day.
1. To get her start-up going, Maria initially hires 4 workers and rents 4 machines per day to produce 16
thousand cups per day.
a. Show that Maria is not minimizing her cost at this level of output.
b. What mix of inputs
L
and
K
could Maria use to make the same qu
antity of cups at a minimal cost?
c. How much would Maria save with th
e cost-minimizing choices of inputs?
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