Firms and Production Perloff Chapter 6

Firms An organisation that converts inputs into outputs which it sells. Ownership of the firm may be separated from its control creating a potential conflict of interest. Owners aim to maximise profits. Managers may maximise non profit objectives. We concentrate on models of the firm where there is no conflict of interest, we assume that decisions are taken in such a way as to maximise profit.

Production Function The relationship between the quantities of inputs and the maximum level of output produced. Short-run: the period of time in which at least one input is fixed. Central to the firms activities is the transformation of inputs into outputs. The technical process by which this is achieved is described by the production function Long-run: the period of time in which all inputs are variable.

Total product, marginal product and average product in the SR Source: Perloff

Production relationships in the SR Output, q , Units per day C 110 90 B 56 A 4 6 11 L , Workers per day AP , MP L L a 20 b 15 Average product, AP L 56/4=14 90/6=15 Marginal product, MP L c Source: Perloff 4 6 11 L , Workers per day

The long-run: 2 inputs variable Source: Perloff

Isoquant map K , Units of capital per day Combinations of inputs which can be used to produce the same level of output. 6 a b 3 e c f 2 q = 35 d 1 q = 24 q = 14 Source: Perloff 1 2 3 6 L , Workers per day

Properties of Isoquants Further from the origin:higher output Cannot cross Slope downward Convex to the origin K e b a d f c 6 3 2 1 L q = 14 = 24 = 35 Firms produce efficiently, they don’t waste inputs Higher indiff curves: higher output if b and e were the same level of output it would mean inputs are wasted. Cannot cross: Means two output levels can be produced with same input levels, why produce the lower level. Slope downwards: If upwards same output with high or low input levels, why? Source: Perloff

Substitutability of inputs 1 , Dutch potatoes per day q = 1 q = 2 q = 3 Source: Perloff x , British potatoes per day

Substitutability of inputs 2 Boxes per day q = 3 q = 2 q = 1 45 ° line Source: Perloff Cereal per day

Marginal rate of technical substitution K , Units of capital per year a 39 D K = – 18 b 21 D L = 1 – 7 The extra input quantity of input on the y-axis required when the quantity of the input on the horizontal axis is reduced by one. c 14 1 – 4 d 10 1 – 2 e 8 q = 10 1 Source: Perloff 2 3 4 5 6 L , Workers per day

MRTS and marginal product

Constant Returns to Scale Constant returns to scale: Doubling all inputs leads to a doubling of output. Potato Salad Production:

Returns to scale in the Cobb-Douglas Production Function Constant returns to scale Why might we have decreasing returns to scale? Double output by adding a identical factory. Organisational problems may arise. Increasing returns to scale Decreasing returns to scale

Example: Thread Mill a+b=0.82 K , Units of capital per year 600 q = 177 q = 200 500 q = 100 400 300 200 100 50 100 150 200 250 300 350 400 450 500 Source: Perloff L , Units of labor per year

Varying Scale Economies K , Units of capital per year d 8 q = 8 c  d : Decreasing returns to scale c 4 q = 6 b 2 b  c : Constant returns to scale a 1 q = 3 q = 1 a  b : Increasing returns to scale Source: Perloff 1 2 4 8 L , Work hours per year

Technical Progress An increase in the volume of output produced with the same volume of inputs.

Neutral technical progress K , Units of capital per year 39 21 14 10 q = 11 8 q = 10 Source: Perloff 2 3 4 5 6 L , Workers per day

Non-neutral technical progress K , Units of q = 10 q = 11 Results in the substitution of one input for another. 39 21 14 10 8 Source: Perloff 2 3 4 5 6 L , Workers per day