S1 - production process Flashcards
what is the production function
defines maximum amount of output that can be produced with a given set of inputs
Q = f(K,L)
Level of output, quantity of capital input, quantity of labour input
what are long and short run decisions
short run - period of time where some factors of production are fixed and constrain choices
Suppose level of capital is fixed - manager can only decide how much labour to utilise
Q = f(L) = f(K*,L) —> K is fixed
Long run - period of time over which all factors of production are variable and can be adjusted by a manager
what are measures of productivity
total product - maximum level of output that can be produced with a given amount of inputs
Average product - measure of the output produced per unit of input
Average product of labour: Q/L
Marginal product - change in total product attributable to the last unit of an input
Marginal product of labour: Change in Q / change in L
Marginal returns can still be positive but at a decreasing rate - producing one more unit is becoming less beneficial - diminishing rate
what is profit maximising input usage
manager should continue to employ labour up to the point when VMPL = w in the range of diminishing marginal product
To maximise in short run, manager will hire labour until the value of the marginal product of labour equals the wage rate
what are the forms of production functions
linear
Leontief
Cobb Douglas
what is linear production function
linear = assumes a perfect linear relationship between all inputs and total output
Q = f(K,L) = aK + bL
Marginal products = the constants a or b
Average products = whole equation / K or L
what is Leontief production function
Leontief = assumes inputs are used in fixed proportions
Q = f(K,L) = min{aK,bL} —> choose lowest of the two numbers
L shape isoquant
what is Cobb Douglas production function
Cobb-douglas = assumes some degree of substitutability among inputs
Q = f(K,L) = K^a L^b
Marginal = aK^(a-1)L^b or bK^aL^(b-1)
Average = whole equation / K or L
Smooth conex isoquant
what are isoquants
graphically represent the various combinations of inputs K an dL which yield a given level of output
Marginal rate of technical substitution = rate at which a producer can substitute between two inputs and maintain the same level of output
Absolute value of the slope of the isoquant
MRTS = MPL/MPK
Diminishing MRTS = as less of one input is used, increasing amounts of another input must be employed to produce the same level of output
what is isocost
combination of inputs that yield the same cost
wL + rK = C
The further form the origin, the higher the costs
Changes in input prices change the slopes of isocost lines
what is the cost minimising input rule
Total cost line is tangent to production function
a firm should employ inputs such that the marginal rate of technical substitution equals the ratio of inout prices
MPL/MPK = w/r
Produce at a given level of output where the marginal product per dollar spent is equal for all inputs
MPL/w = MPK/r
