Modelling the producer: Costs and supply decisions

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 N˚ of employees 0 1 2 3 4 5 6 7 8 Output 0 3 10 24 36 40 42 42 40 Tons of wheat per year Number of employees

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

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

The production function of a farm Y Maximum Output b 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 TP Tons of wheat per year DY = 14 DL = 1 Number of employees mP = DY / DL = 14 mP, AP Number of employees

The production function of a farm TP Tons of wheat per year DY = 14 DL = 1 Number of employees mP, AP mP Number of employees

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

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

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

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 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 Z Units of capital (K) Y Y= 150 X B Y= 100 A Y= 50 Units of labour (L)

Isoquants and Isocosts The technical rate of substitution 7 6 Units of capital (K) 5 X TRS = - (Slope of the Isoquant) 4  K 3 2 1 0 2 3 4 5 6 7 8 9 10 Units of labour (L)  L

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 Imagine 5 combinations A, B, C, D, E Cost = (L x pL)+ (K x pK) Units of capital (K) Units of labour (L) If pL = 1€ & pK = 1€ If pL = 5€ & pK = 1€ Combination 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 capital (K) Units of labour (L)

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

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 ...

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 Output (Y) 0 1 2 3 4 5 6 7 TFC (€) 12 12 12 12 12 12 12 12 The total cost of a firm is obtained by adding the total fixed cost … TFC

Costs and supply Output (Y) 0 1 2 3 4 5 6 7 TVC (€) 0 10 16 21 28 40 60 91 TVC … and total variable cost

Costs and supply TC Output (Y) 0 1 2 3 4 5 6 7 TFC (€) 12 12 12 12 12 12 12 12 TVC (€) 0 10 16 21 28 40 60 91 TVC TFC

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 TC Working out the marginal cost mC DTC=5 DY=1

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

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

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)

AC Supply curve z s Costs and supply mC Price AVC pz ps Output (Y ) qs qz

Modelling the producer: Costs and supply decisions