Modelling the producer: Costs and supply decisions Production function Production technology The supply curve

Modelling the producer Up until now, we have focused on how consumers choose bundles of good But we have not examined how these goods are produced We have implicitly assumed that they just “exist” But, clearly, a theory of decision should also explain the decision to produce goods. We shall see that the framework of consumer choice can also be used to understand producer choices

Modelling the producer The production function Isoquants and Isocosts Costs and supply

The production function The production function is the relation between inputs to production and the amount of output produced for a given technology For the moment, let us assume that there is a single input to production (simplification) A farm using labour to produce wheat

The production function of a farm Number of employees Tons of wheat per year N˚ of employees Output

The production function of a farm Y Feasible Impossible Production frontier Number of employees Tons of wheat per year

The production function of a farm Y b Decreasing returns starting from b Tons of wheat per year Number of employees

The production function of a farm Y b Maximum Output Tons of wheat per year Number of employees

The production function Total output (TP): The average output (AP): The marginal product (mP):

The production function of a farm Tons of wheat per year mP, AP  Y = 14  L = 1 mP =  Y /  L = 14 TP Number of employees

The production function of a farm  Y = 14  L = 1 mP TP Tons of wheat per year mP, AP Number of employees

The production function of a farm TP mP AP = TP / L Tons of wheat per year mP, AP Number of employees

The production function of a farm Decreasing returns (inflexion point) TP mP AP = TP / L Tons of wheat per year mP, AP Number of employees

The production function of a farm Maximum output TP mP AP = TP / L Tons of wheat per year mP, AP Number of employees

The production function Relation between the average and marginal products The average product is maximal when it is equal to the marginal product If mP>AP, then the average product must be increasing If mP<AP, then the average product must be decreasing

Modelling the producer The production function Isoquants and Isocosts Costs and supply

Isoquants and Isocosts Lets go back to the case with several inputs to production. Imagine a case with 2 inputs …which are labour (L) and capital (K)… We define an isoquant as the set of combinations of inputs that are just sufficient to produce the same level of output. This is where the analogy with consumer choice will become obvious

Isoquants and Isocosts Units of labour (L) Units of capital (K) Y= 150 Y= 100 Y= 50 X Y Z A B Isoquants are a 2-D mapping of the 3-D production function Just like: Indifference curves are a 2-D mapping of the 3-D utility function

Isoquants and Isocosts Units of labour (L) X  K  L TRS = - (Slope of the Isoquant) The technical rate of substitution Units of capital (K)

Isoquants and Isocosts Reminder : The marginal product of a factor is the increase in total output (TP) following a marginal increase in that factor ( ∂ L or ∂ K) On any given Isoquant : Note the similarity with the marginal rate of substitution

Isoquants and Isocosts The overall aim of the firm is to maximise profits, i.e. the difference between revenue and production costs However, for a given price of output, the combination of inputs that maximises profits is also the one that minimises costs Therefore, when choosing the best combination of inputs, the aim of the firm is to minimise the cost of production for any level of output

Isoquants and Isocosts A210 B36 C44 D63 E 2 Combination Units of capital (K) Units of labour (L) 12 €52 € 9 €33 € 8 €24 € 9 €21 € 12 €20 € Cost = (L x p L )+ (K x p K ) If p L = 1€ & p K = 1€ If p L = 5€ & p K = 1€ Imagine 5 combinations A, B, C, D, E The best combination depends on the price of the inputs

Isoquants and Isocosts Isocost: Set of combination of inputs available for a given cost of production All the spending on a single input Units of labour (L) Units of capital (K)

Isoquants and Isocosts Units of capital (K) Units of labour (L) The optimal combination of inputs minimises the production cost for a given level of output  C Optimal combination The isocost curve is tangent to the isoquant Definition of the technical rate of substitution at C !!!

Isoquants and Isocosts The optimal combination is at the tangency of the isoquant and the isocost Therefore : The ratio between the marginal output of an input and its price (marginal cost of the input) is the same for all inputs...

Modelling the producer The production function Isoquants and Isocosts Costs and supply

There are different types of costs to consider Depending on the type of input  Fixed / Variable costs Depending on the time horizon  Short / Long term

Costs and supply Important note: Economic costs take into account the existence of an opportunity cost The opportunity cost is the cost of giving up the next-best alternative. What is the cost of a year at university ? Objective costs: fees, books, laptop, food, rent, etc. Opportunity cost: The year’s worth of (minimum) wages you are forgoing whilst you are at university. In France, that’s 12,000 € !!

Costs and supply Fixed and variable costs Fixed costs are the incompressible costs that the firm incurs regardless of the level of production.  Example: lighting of a factory floor, setup cost of a new production line, etc. Any other production cost is part of the variable cost, because their size increases with the level of production.

Costs and supply The time horizon is important in determining the fixed/variable nature of production costs. In the short run, the firm cannot change the production technology (the method of production) or the combination of inputs (the size of the production plant is fixed) In the long run, all the inputs are theoretically adjustable. Most of the inputs that are fixed in the short run become variable in the long run.

Costs and supply The total cost curve gives the total expenditure on inputs required for any given level of output. It is the minimal cost of production for that level It is obtained through the cost-minimisation process described in the previous section For each level of output (isoquant), the firm chooses the combination on the lowest (tangent) isocost curve.

Costs and supply TFC Output (Y) TFC (€) 12 The total cost of a firm is obtained by adding the total fixed cost …

Costs and supply TVC … and total variable cost Output (Y) TVC (€)

Costs and supply TVC Output (Y) TVC (€) TFC (€) 12 TC

Costs and supply The average cost curve gives the unit cost of production for each level of output. It obtained by dividing total cost (TC) by the level of output (Y) The average fixed cost falls with the level of output An increasing production means that the total fixed cost can be spread over more units

Costs and supply The marginal cost curve gives the increase in total cost for a one-unit increase in output. The marginal cost curve at a given level of output gives the slope of the total cost curve for that level of output

Costs and supply mC TC  Y=1  TC=5 Working out the marginal cost

Costs and supply Output (Y ) Costs( € ) mC General form of the marginal cost

Costs and supply Costs( € ) AFC AVC mC x AC z y Output (Y ) Average and marginal costs

Costs and supply The marginal cost curve cuts the average cost curve at its minimum point If the marginal cost is lower than the average cost, the average cost is decreasing If the marginal cost is higher than the average cost, the average cost is increasing If the marginal cost is equal to the average cost, the average cost does not change

Costs and supply This is important as it tells us about the level of returns to scale If the average cost is decreasing, then total costs are increasing more slowly than output ⇒increasing returns to scale If the average cost is increasing, then total costs are increasing faster than output ⇒ decreasing returns to scale

Costs and supply The profit maximising condition A firm’s profit is given by total revenue minus total cost : The firm chooses its output such that profit is maximised (marginal profit is zero)

Costs and supply On a perfectly competitive market, the price p is given by the market. We will see next week that in order to maximise its profits, the firm will choose its output q such that the marginal cost of production equals the price ⇒ p = mC This condition gives the supply curve of the firm Note: if the market price is less than the average variable cost, the firm will prefer to produce nothing (shutdown condition)

Costs and supply Price AVC mC AC z Output (Y ) s pzpz psps qzqz qsqs Supply curve