Unit 03 – Producer’s Theory
It was possible to understand from the previous class that consumer’s gain utility from buying goods. In this unity, we will learn how companies make important operation decisions.
Demand curves come from Utility Maximization, but Supply curves are determined by the producer and how he decides to make up the prices, because it is known that producers want always to maximize their profits. The supply curves show how efficient the production is.
Firm production functions
A key concept is technology, because it is from technology that the producer turn the inputs into outputs. The inputs are Labor (hours of work) and Capital (everything else that goes in a production). The outputs are the function between labor and capital: q = f(L,K).
Short-run vs Long-run
Short run is a period over which some inputs are fixes. The Long-run is a period over which all inputs are variable.
It’s the break between when some inputs are fixed and all inputs are variable.
How firms make short-run decisions?
L (variable); K(fixed)
The questions which the producer must ask to himself in order to maximize his own profits are: How many workers should I hire? To answer this question, the producer uses the concept of Marginal Product of Labor, which is like the Marginal Utility concept: (Δq/ΔL)
. Diminishing Marginal Product: the next worker you hire works less and less
. Intuitively: the reason why an additional worker works less is due to the fact that he has the same amount of work as his predecessors. Example: digging a hole. In the short-run there will be only one shovel, but on the long-run there can be a distribution and an addition of work.
How firms make long-run decisions?
They choose Labor and Capital and trade them off.
The difference with production is the budget constraint is going to be itself determined by the same system. You’re not going to develop your production function, but you’re going to develop your budget constraint and you’re going to decide both. Mathematically it’s represented by q = L.K
. If you’re trading off K and L and deciding to produce, then you get what’s called Isoquants: q = sqrt (K.L).
They are the parallel to indifference curves. Just as there were sets of goods across which you were indifferent, isoquants are sets of inputs along which production is the same. So along a given isoquant, q is fixed. Each of those isoquants is a different level of q, but they show how you can vary K and L to get the same amount of q. I can choose a lot of combinations of K and L along that isoquant to produce a given amount of output. They have, therefore, the same characteristics of an indifference curve. The further out the better because you’re producing more. They can’t cross. They slope is downwards because there is a trade-off between K and L.
What determines the slope of an isoquant?
The substitutability between the labor and the capital will determine the slope of these isoquants.
Perfectly substitutable inputs
It’s a linear isoquant because you don’t care if you have three capital and one labor, you don’t care as long you you get a total of four (the maximum): q = K + L.
Perfectly non-substitutable inputs
Given the amunt of one input, it doesn’t matter how much you have of the other. This also known as the Leontieff production functions: q = Min (K, L).
Marginal Rate of Technical Substitution = Slope of isoquant
The rate which you can substitute one input for another in a production function.
ΔK / ΔL à constant q
It will change along the isoquant. The principle of diminishing marginal product implies that the MRTS is going to be falling as you go down the isoquant, due to the diminishing of productivity.
Returns to scale
What happens if we increase all inputs proportionally? A change in scale is an equal increase or decrease in all inputs? It depends on the production process.
. Constant returns to scale: f(2L,2K) = 2f(K,L) = 2q
. Increase returns to scale: f(2L, 2K) > 2f(K,L) > 2q
. Decrease returns to scale: f(2L, 2K) < 2f(K,L) < 2q
Productivity and costs
Productivity improvement, as it adds aggregate productivity (A) | q = A.f(K,L)
Given how much we work, what determines how much stuff we can have, with how much capital we have, and how productively we make use of it?
Productivity: which is how much we produce for a given amount of inputs, has followed an interesting trend in the US = less capital of a decrease in savings (the amount we save is the amount available to use as capital) and the IT revolution.
Costs: maximization of profits |π=R-C
. Fixed costs: they cannot vary in the short-run (K)
. Variable costs: they can vary in the short-run (L)
. Total costs: (Fc + Vc)
. Marginal costs: the change in cost with a change in output | MC = ΔC/Δq. It is defined by the wage rate multiplied by the number of hours needed to produce one additional unit.
. Average costs: AC = c / q
q = f (L, K)
c (q) = f (WL + rK)
Fc = r.K(constant)
Vc = W.L(q) – more productivity, more labor
SRTC = r.K(constant) + W.L(q)
MC = ΔC/ΔK = W.ΔL/Δq | MC = W / MPl
The more productive is a worker, the less expensive is producing the next unit. The less productive is the next worker, the more expensive is producing the next unit.
Input mix is chosen to maximize production efficiency which equates to minimizing costs. Relative price of capital and labor to determine how we choose between capital and labor.
Isocots lines, which are just like budget constraints, represent the cost of different combinations of inputs, just like our old budget constraint represented the cost of different consumption goods.
Each of the isocosts give you the combination of inputs that cost a certain amount.
What’s the slope of isocost line? It’s the negative of the wage rental ratio. It’s –W/r; It’s the trade-off between labor and capital’s going to determine by the relative prices of those inputs.
Economically efficient input combination for a given level of output (q) is going to be determines by the tangency of the isoquant with the isocost | q = K.L
Isoquant = MRTS = MPl/MPk = W / r
MPl / W = MPk / r
As firms produce more, they may hold Constant or may change the ratio of their inputs, but they’ll clear use more inputs. But they mix of the inputs they’ll use will change with their production levels | q comes from market competition.
Fixed vs Sunk Costs
. Fixed costs are on the long-run; they foregone once you produce.
. Sunk costs are the ones you’ve already paid, for example, the tuition fee of your college before you becoming a doctor.