Production

Learning Objectives: • What is a Production Function?• Where do firms get technology?• What is the difference between the short run and long run?• How do firms make input hiring decisions? • How do firms substitute one input for another?

Production Function• A production function summarizes the relationship between

output and the set of inputs utilized in the production of that output.

• Short run vs. Long run• Short run production function: • Long run production function:

Where does technology come from?• In-house R&D• Licensing• Publications• Reverse engineering • Employee poaching • Patent filings • Location spillover effects

Marginal Product & Average Product• Marginal Product of an input is the extra output accruing

from the addition of one extra unit of the input, holding all other inputs constant.

• Average Product of an input is the amount of output being produced per unit of the input.

Specialization and Efficiency• Efficiency comes from specialization of inputs. • As more of an input is added to the production process, the

marginal product rises initially, then decreases, and may as well become negative.

• Example: Hanshin Electric Railway, 2007

Production TableK L Q L Q P =P* Wage

5 0 0 - - - - 5 - 505 1 5 1 5 5 5 5 25 505 2 15 1 10 10 7.5 5 50 505 3 30 1 15 15 10 5 75 505 4 50 1 20 20 12.25 5 100 505 5 75 1 25 25 15 5 125 505 6 105 1 30 30 17.5 5 150 505 7 125 1 20 20 17.85 5 100 505 8 140 1 15 15 17.5 5 75 505 9 130 1 -10 -10 14.44 5 -50 50

Profit maximizing input level• Firms will continue hiring an input up to:

• Example: An Urban Farm Designed To Make One Thing: A Grilled Ham And Cheese Sandwich

Production Functions• Linear:

• Leontief:

• Cobb-Douglas:

Isoquant • An isoquant gives different combinations of inputs

producing the same level of output. • Slope of an isoquant:

• Law of Diminishing MRTS • Example: Why gasoline is suddenly $3 a gallon | and could

go lower

Isocost• Isocost line gives the combinations of inputs requiring the

same monetary contribution.

Cost Minimizing Condition

𝑀𝑅𝑇𝑆𝐾𝐿=𝑀𝑃𝐿

𝑀𝑃𝐾=𝑤𝑟

Optimal Input Substitution • If the price of an input rises, firms will substitute the

costlier input with cheaper substitutes.