Firms: Competitive Supply in Perfectly Competitive Markets

Part II: Microeconomics

Perfectly Competitive Markets

• 6 Units

Unit 5A: The Consumer's Choices

Unit 5B: Applying Choice Theory

Unit 6A: Firms: Production and Costs

Unit 6B: Firms: Competitive Supply

Unit 7: The Efficiency of Markets

Unit 8: Government Policies

Firms: Competitive Supply

(Mankiw & Taylor, Ch 6)

Preview of Unit 6B

1. We have developed our basic theory about production and costs.
2. Now we turn to the firm's supply decision and discuss the supply curve. We try and answer questions such as: how do the firm's technology and costs affect its selling strategy in perfectly competitive markets? When would a competitive firm leave the market?
3. To do so, we need to frame the firm's profit maximizing problem, and distinguish between the short run and the long run perspectives.

Perfect Competition

Recall the basic framework of the model of a perfectly competitive market:

• Buyers and sellers act as price takers (there are very many of them) PRVE TAKERS
• The traded goods are homogeneous (the identity of the seller is indifferent to the buyer). HOMOGENEUS
• Firms can freely enter or exit the market.

As a result, a perfectly competitive market is such that the choice of any single buyer or seller in the market has a negligible impact on the market IRRILEVANTE price.

Defining Revenue

Total revenue for a firm is the selling price times the quantity sold. TOTAL SELLING Q. SOLD REVENUE = PRICE

from which we can derive the usual notions: RA= = P/R. x Unit Solo!) Average Revenue: RA = R - = p (R per unit sold) q AR Marginal Revenue: RM = Δα (increase in R from one additional unit sold) Increase in R from 1 additional × R = p . q

Defining Revenue: Market Environment

All these are just definitions, independent of the type of market one is dealing with.

In order to have a revenue function (telling us how a firm's revenue reacts to a firm's choice) one has to bring in explicitly the market environment the firm is facing. MARKET ENVIROMENT

Whether a firm is acting in a perfectly competitive market or under imperfect competition, shows up in the revenue function.

Defining Profit

Profit is defined as the difference between revenue and costs: II = R - C REVENUE T = R-C 6 COSTS PROFITS

And again this is just a definition. In order to have a profit function (telling us how a firm's profit reacts to a firm's choice) one has to bring in explicitly information about R and C:

• About Revenue: the market environment the firm's facing, yielding a Revenue function. MARKET ENVIROMENT SR -LR
• About Costs: whether the choice perspective is short-run or long-run and hence whether the SR or the LR cost function applies

Defining Profit: Economic vs. Accounting

When defining profits, total costs are subtracted from total revenue, and these costs include both explicit and implicit costs.

Thus there is a difference between economic profit and accounting profit: the latter only includes the firm's explicit costs.

Hence: Economic profit is smaller than accounting profit.

When total revenue exceeds both explicit and implicit costs, the firm earns economic profit.

Defining Profit: Firm Views

How an Economist Views a Firm How an Accountant Views a Firm Economic profit Accounting profit Implicit costs Revenue Revenue Total opportunity costs Explicit costs Explicit costs FROM MANKIW AND TAYLOR, ECONOMICS 4TH EDITION 9781473725331 @ CENGAGE EMEA 2017

Defining Profit: Opportunity Costs

Economics-wise, total costs include all of the opportunity costs of the firm. ZERO ECONOMIC PROFIT

Hence, when a firm is earning zero economic profit, this means that the firm's revenues are compensating the firm's owners for the time and money that they have expended to keep their businesses going, which means positive accounting profits ZERO ECONOMIC = PROFIT REVENUES COMPENSATING · TIME MONEY EXPENDED POSITIVE ACCOUNTING PROFITS

Defining Profit: Maximization

Firms are assumed to act so as to maximize profit It is generally the case (i.e., whether markets are perf comp or not) that: ADJUSTING Maximizing profit means trying and adjusting revenue and costs in such a way that their difference is as large as possible.

• " If the firm's choices are such that AR > AC, profit is increasing: keep acting in this way!
• " If the firm's choices are such that AR < AC, profit is decreasing: stop it!

Hence the firm will be at rest and profit at a maximum when AR = AC AR

Perfectly Competitive Firms and Profit Maximization: Supply in the Short Run

We now want to apply our generic definition of profit II = R - C to the specific case at hand.

Revenue: price taking behaviour means R = R(q) = pq where p is given: the revenue function is a straight line from the origin, whose slope is the given p: this implies that RM = == p Δα ΔR STRAIGHT LINE FROM THE ORIGIN SLOPE "GNEN P

Costs: The short run perspective means that the short run total cost function is relevant here: C = CSR (q)

Perfectly Competitive Firms and Profit Maximization: Short Run Profit Function

The firm maximizes its short run profit function: ITSR (q) = R(q) - CSR (q) =|pq - CSR (q)

And by doing so it identifies its optimal level of q for given p - which is indeed what supply is. Optimal level of 9, given P

Perfectly Competitive Firms and Profit Maximization: Three Approaches

One can see the solution to this problem in three equivalent ways First approach: ITSR (q) = R(q) - CFR (q) = pq - CFR (q)

Just graph the two curves R(q) and CER (q), and look for their maximum distance: geometrically, this is where the two curves are parallel to each other.

As the slope of R(q) is p and that of CSR (q) is MCSR (q), maximum profit is given by the value of q such that price equal marginal cost: p = MCSR (q) MAXIMUM DISTANCE PARALLEL TO EACH OTHER

Perfectly Competitive Firms and Profit Maximization: Total Cost and Revenue

Total Cost SR Total Cost function €18.00 Revenue function 16.00 14.00 Max Profit 12.00 10.00 8.00 6.00 4.00 2.00 0 2 4 6 8 10 12 14 Quantity of Output ADAPTED FROM MANKIW AND TAYLOR, ECONOMICS 4TH EDITION 9781473725331 @ CENGAGE EMEA 2017

Perfectly Competitive Firms and Profit Maximization: Change in Profit

Second approach: ITSR (q) = pq - CER (q)

Consider a change in profit: AITSR = pAq - MCSRAq AnSR DITSR Aq = p - MCSR DQ P-MC

The profit function has a maximum where its slope is zero: AITSR /Aq = 0, and hence price equal marginal cost: SLOPE = 0 CONSEGUENZA p = MCSR (q) DATO CHE DEVE FAR ZERO

Perfectly Competitive Firms and Profit Maximization: Marginal Revenue and Cost

Third approach: Comparing the Marginal Revenue curve (which is a constant equal to price) with the Marginal Cost curve

• When Marginal Revenue exceed Marginal Cost, the firm should increase its quantity to increase profit È INFERIORE
• When Marginal Revenue falls short of Marginal Cost, the firm should decrease its quantity to increase profit RM= CM - PROFIT MAXIMIZED
• When Marginal Revenue equals Marginal Cost, profit is maximized.

Perfectly Competitive Firms and Profit Maximization: Costs and Revenue Graph

Costs and Revenue The firms maximizes its profit where marginal cost equal marginal revenue MC MC2 ATC P = MR1= MR2 P = AR = MR AVC MC1 0 Q1 QMAX Q2 Quantity FROM MANKIW AND TAYLOR, ECONOMICS 4TH EDITION 9781473725331 @ CENGAGE EMEA 2017

Perfectly Competitive Firms and Profit Maximization: Example

An example: K = 50, r = 0.10 -> CF = rK = 5; w = 2 q = f (L, K) = KVL = 50VL -> L(q, K) = q2/2500 ↓ CSR (q) = 5 + -> MCSR (q) = q2 1250 1250 2q q 625 q MCSR (q) = p-> 625 = p -> q(p) =625p

Perfectly Competitive Firms and Profit Maximization: Numerical Example

A numerical example Quantity (Q) Litres (TR) Total revenue (€) Total cost (€) Profit (€) (TC) Marginal Marginal cost (€) revenue (€) (TR -TC) (MR = ATR/AQ) (MC = ATC/AQ) Change in profit (€) (MR - MC) 0 0 200 -200 0.4 0.1 0.3 1,000 400 300 100 0.4 0.2 0.2 2,000 800 500 300 0.4 0.3 0.1 3,000 1,200 800 400 0.4 0.4 0 4,000 1,600 1,200 400 0.4 0.5 -0.1 5,000 2,000 1,700 300 0.4 0.6 -0.2 6,000 2,400 2,300 100 0.4 0.7 -0.3 7,000 2,800 3,000 -200 0.4 0.8 -0.4 8,000 3,200 3,800 -600 FROM MANKIW AND TAYLOR, ECONOMICS 4TH EDITION 9781473725331 @ CENGAGE EMEA 2017

Perfectly Competitive Firms and Profit Maximization: Supply Curve

The profit maximizing condition MCSR (q) = p solves mathematically for q as a function of p: q = q(p) associates to each price the profit maximizing quantity, yielding the firm's supply curve.

Geometrically, as price varies the supply curve traces out the marginal cost curve itself, which accordingly coincides with the supply curve.

However, surely if the market price is very low, one expects the firm to stop production, and its optimal quantity to be zero: when does this occur?

Perfectly Competitive Firms and Profit Maximization: Profit Condition

It is tempting to answer: when profit turns negative, i.e. when ITSR (g) = pq - CER (q) < 0 ->p -- CSR (q) q SR = p - ACER < 0 i.e., price falls below average total cost.

.but this answer is wrong, as it overlooks the short-run perspective.

Perfectly Competitive Firms and Profit Maximization: Fixed Costs

In the SR the firm is facing fixed cost, which have to be borne independently of the quantity produced (i.e., even if that quantity is zero).

Hence, so long as price exceeds average variable cost, production is worth carrying out as it fetches a revenue high enough to cover (at least part of) the fixed cost: the firm runs a loss, which is however smaller than that associated to stopping production altogether.

There follows that the SR supply curve includes that part of the marginal cost curve lying above the crossing point between the marginal cost curve and the average variable cost curve (which coincides with the minimum of the latter).

Perfectly Competitive Firms and Profit Maximization: Supply Curve Graph

Price This section of the firm's MC curve is also the firm's supply curve. MC P2 ATC P1 AVC 0 Q1 Q2 Quantity FROM MANKIW AND TAYLOR, ECONOMICS 4TH EDITION 9781473725331 @ CENGAGE EMEA 2017

Perfectly Competitive Firms and Profit Maximization: Shutdown Price

Only if price falls below the average variable cost will the firm stop production.

Hence, the overall SR supply curve is zero (overlapping the vertical axis) for p < ACER , and overlaps the marginal cost curve for p ≥ ACyk The shutdown price p is the lowest price level at which the firm is indifferent between carrying out production or stopping it.

The value of q such that p = ACER (q), lies at the minimum of the ACUR curve. SR V