Lecture 9: PRODUCTION
Production Function for a Single Product
Production function: maximum output that can be produced using all possible
combinations of inputs on the basis of a given technology
Output = f (L, K, land, raw materials, efﬁciency parameter, returns to scale)
Capital = K, land, raw materials; land and raw materials “absorbed” into K for analysis simplicity
Technology = efﬁciency parameters, returns to scale; assume held constant
General form of production function: y = f (K, L)
Short-Run Production Function, Marginal Product, and Average Product
Short-run production function: labour variable, K and Tech ﬁxed
MP = slope of TP (Lotal product of labour), AP = y / L
Law of Diminishing Marginal Returns (Short-Run)
As L ↑ (K constant) → eventually MP ↓ aLd AP ↓ L
Technological Efﬁciency in the Short-Run
Realized when MP andLMP are bKth positive.
The Long Run Production Function
A process is technologically efﬁcient if it cannot be shown to be inefﬁcient.
Isoquant: locus of all technologically efﬁcient processes for producing a given quantity
- Vertical and horizontal segments simply represent constant output
General Properties of Isoquants
Property 1: an isoquant to right of another isoquant represents a higher level of output
Property 2: isoquants are downward sloping
Property 3: isoquants do no intersect each other
Property 4: isoquants are convex from the origin
Marginal Rate of Technical Substitution MRS LK = - ΔK / ΔL = MP / MP = MRTS = slope of the isoquant
The Concept of Returns to Scale (Long-run)
multiple in → multiple out; constant/increasing/decreasing returns to scale
Output expansion lines are lines representing the path of increasing output levels that
begin from the origin, with a shape that depends on the technology itself.
All isoquants have the same slope (MRTS) at the intersection of the OE line.
An OE line with constant MRTS is called an isocline.
Lecture 10: RETURNS TO SCALE
Non-homogenous production functions mean other factors besides K and L are in play.
IRS/DRS depends on direction the curve needs to move towards point.
Returns to scale are increasing at ﬁrst and then eventually decrease.
Technical indivisibility: mismatched input capacities wasting some productive capacity
Larger ﬁrms beneﬁt more from geometric relations (length/width vs area), labour time
(different chopping diameters), and spare equipment inventories (% of spare to used).
Cobb-Douglas Production Function: Y = K L
α + β = 1 → CRS, α + β < 1 → DRS, α + β > 1 → IRS
π = Total Revenue - Total Cost
π = P Y – (rK + wL) ; r*K = cost of capital, w*L = cost of labour
Isocost line (solve TC for K) → K = (TC - wL) / r
Lecture 11: PROFIT