The theory of the firm and industry equilibrium

Martin J. Osborne
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1.1 Exercises on the production function

  1. What production function models each of the following technologies?
    1. One computer can be made from two 32 megabyte memory chips or a single 64 megabyte chip.
    2. Every course requires 1 instructor, 2 teaching assistants, and 1 lecture room.

    Solution

    1. F(z1, z2) = z1/2 + z2 where input 1 is 32-megabyte chips and input 2 is 64-megabyte chips.
    2. F(z1, z2) = min{z1, z2/2, z3} where input 1 is instructors, input 2 is TAs, and input 3 is lecture rooms.

  2. A firm's production function is given by
    F(z1, z2) = 2z1/4
    1    z2.
    How much output does it produce if it has 16 units of input 1 and 2 units of input 2?

    Solution

    It produces the output F(16, 2) = 2(16)1/4(2) = 2(2)(2) = 8.