Chapter 1. Technology Some Definitions: 1. Net output (netput) – difference between good 𝑦𝑦𝑗𝑗𝑜𝑜 produced as an output versus 𝑦𝑦𝑗𝑗𝑖𝑖 of the good j as an input, 𝑦𝑦𝑗𝑗 = 𝑦𝑦𝑗𝑗𝑜𝑜 − 𝑦𝑦𝑗𝑗𝑖𝑖 . If 𝑦𝑦𝑗𝑗 > 0 produce more than is used. If 𝑦𝑦𝑗𝑗 < 0 produce less than is used. 2. Production plan – list of netputs of various goods such as 𝑦𝑦⃗ which includes netputs for j variable goods. 3. Production possibilities set – set of all feasible production plans, Y. Describes all patterns of inputs and outputs that are technologically feasible. 4. Restrictions on production – in production, adjustment periods may be needed. For example, in the short run, cannot change all inputs because some are fixed. For example, 𝑧𝑧⃗ list of maximum inputs in a time period, so 𝑌𝑌(𝑧𝑧⃗) is a restricted or short run production possibilities set. For example, if capital (k) is fixed and labor is variable (ℓ) we would have 𝑌𝑌�𝑘𝑘�� = �(𝑦𝑦, −ℓ, −𝑘𝑘) in 𝑌𝑌: 𝑘𝑘 = 𝑘𝑘��. 5. Input requirement set – set of all input bundles that produce at least 𝑦𝑦 units of an output. This is written as 𝑉𝑉(𝑦𝑦) = {𝑥𝑥⃗ in ℝ𝑛𝑛+ : (𝑦𝑦, − 𝑥𝑥⃗ )is in Y}. 6. Isoquant – gives all in put bundles that produce exactly y units of an output. This is written as 𝑄𝑄(𝑦𝑦) = {𝑥𝑥⃗ in ℝ𝑛𝑛+ : 𝑥𝑥⃗ is in 𝑉𝑉(𝑦𝑦) and 𝑥𝑥⃗ is not in 𝑉𝑉(𝑦𝑦 ′ ) ∀ 𝑦𝑦 ′ > 𝑦𝑦}. 7. Production function – one output produced from inputs. For example 𝑓𝑓(𝑥𝑥⃗) = {𝑦𝑦 in ℝ: 𝑦𝑦 is maximum output associated with − 𝑥𝑥⃗ in 𝑌𝑌}. 8. Transformation function – set of technologically efficient production plans. May include multi-output settings for example 𝑇𝑇(𝑦𝑦⃗) = 0.

Chapter 1. Technology

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