Lecture 8 22 March: International trade Week 4B
2. Ownership assignment: Patent
Suppose the government assigns ownership of the knowledge to whoever produces it • If Abbey produces the knowledge, she then receives a patent/copyright for the vaccine and can legally exclude other members from using the vaccine • Knowing the private valuations of the other members, Abbey’s optimal decision is to produce the knowledge
✅ Lecture 11 - April 10: Markets: A review What does a firm do?
• Production of goods/services the “supply side”
• Use input in a production to deliver outputs
• Firms offer a means of coordinating work:
o Eliminates need to negotiate over every task a worker does o Internalizes externalities in different layers of production
• Many types of firms e.g. sole proprietor, partnership, limited liability company etc.
• Most basic primitive of a firm is technology
• A technology is a way of describing how inputs are turned into an output
• Types of Inputs o Labour (L) o Capital (K) o Raw Materials Bob’s Book Binding Assembly Line
• Bob owns a company that binds hardback books
• Books are bound with Book Binder 2000 technology
• Each machine has maximum output of 36 books per minute with a crew of 6.
(1xLoader, 3x Gluer, 2x Packer)
• Lower output is possible with less people by having people double up jobs
Production function
• Describe what is technically feasible when a firm uses inputs efficiently
• A production function describes the highest output Q that a firm can produce for every specified combination of inputs
• While firms use a variety of inputs, we will keep things simple by thinking about only 2 input: labour (L) and capital (K) machine=1
• We write production function as Q = F (K, L)
Productivity Total product (TP)
• Total quantity of outputs given the level of inputs
• F(K, L) gives us the total productivity of K units of capital and L units of labour Marginal product (MP)
• Increase in output from an additional unit of inpu
• Hold capital fixed @ K
• Consider what happens when we increase L by smallest amount possible
• Partial derivative
Law of diminishing returns
• As use of input increases in equal increments (with other inputs fixed),
a point will eventually be reached where the resulting additions to output decrease
• Flatter slops of production function when labour increase Profit maximization
• Firm’s profit = Total revenue minus total cost
• Firm’s objective is to maximise profits Profits in terms of inputs
• Suppose that firm gets p for each unit of output, it must pay w for each unit of labour and r for each unit of capital
• To maximize profit: pF(K, L) revenue − wL – rK cost
• Profit maximization problem with multiple inputs is hard to solve
Profits in terms of outputs
• Differentiate π(Q) = TR(Q) − TC(Q) to maximise profit
• Optimal level of production Q ∗ satisfy MR(Q ∗ ) = MC(Q ∗ )
Total cost function
• Cost function = finds cheapest way of producing a certain amount of output given input prices Suppose
• Cost of labour = $40,000 for 1 unit
• Rental cost of machine = $50,000 How should we produce 72 units?
• Cost of 12 workers and 2 machines: $580,000
• Cost of 9 workers and 3 machines: $510,000
• Cost of 8 workers and 4 machines: $520,000
• TC (72) = $510,000 cheapest option = minimising cost Importance of minimizing costs
• Firms perform better when they can operate with lower costs, without compromising other aspects of output e.g. quality
• Even public sector & non-profit organisations are increasingly judged on their ability to deliver services at minimum possible cost
Reminder on cost
• Economic profits consider opportunity costs (explicit &
implicit costs) of all resources used in production
Time & cost Time horizon
• At any given point in time,
inputs are either variable (can adjust) or fixed (cannot adjust)
• Time horizon = whether firm can adjust level of inputs Short run Period during which at least 1 fixed input
Long run Period needed for all variable inputs Fixed costs Costs do not vary with level of output Variable costs Costs that vary with level of output
Short run costs
• SRTC(Q) = FC + VC(Q)
• FC = need to pay fixed cost regardless of Q (cannot adjust level of fixed input)
• VC = need more of variable input to produce higher Q, hence higher (variable) cost Bob’s Short Run Costs
• Suppose Bob has 2 machines (must rent on yearly contracts)
• Contract can be reversed by shutting down, but no. of machines cannot be adjusted
• Capital is fixed short run k = 2
• Regardless of the amount produced, 2 machines cost $100,000 does not change with Q
• Bob can adjust his labour as he sees fit.
Shape of production function & cost function
• K=2 fixed F(2, L) tells us how much labour we need to produce a given amount of Q
• We can use this to calculate VC(Q)
• Both curves shapes are connected
Short run costs vs. long run costs
• Short run = fixed capital
• Short run and long run costs will coincide only when it is efficient to use exactly 2 units of capital in the production function
Agenda
• Firms operate in environments that can change rapidly with production decisions of their competitors and the whims of their consumers.
• To stay competitive, firms must constantly assess whether their production processes are optimal
On the production side, decisions often revolve around 3 issues:
• What technology should a firm use?
• How much should a firm produce? MR = MC
• When should a firm exit market?
To answer these questions, it will be useful to think about not just SRTC and LRTC, but also a variety of alternative cost measures that allow the firm to evaluate the firm’s position
Short run marginal cost
Increase in short run total costs to produce 1 additional unit of output Short run average total cost
𝑆𝑅𝑨𝑻𝑪(𝑄) = 𝑆𝑅𝑻𝑪(𝑄)
𝑄 =𝑭𝑪 + 𝑽𝑪(𝑄)
𝑄 = 𝑨𝑭𝑪(𝑄) + 𝑨𝑽𝑪(𝑄) 𝑨𝑭𝑪(𝑄)
• Since FC is constant, AFC(Q) must decline throughout AFC(Q) Falling over large spread of quantity
𝑨𝑽𝑪(𝑄)
• AVC(Q) depends on AVC(Q) ≶ SRMC(Q)
• SRATC(Q) shape depend on share of FC & shape of SRMC(Q) Trade-offs in technology
Car wash business Consider 2 technologies for washing cars Short run costs Method 1 bucket & hose
No large physical capital required but capacity constraint affects marginal product
• Low FC must decline throughout
• Diminishing MP of labour
• Given diminishing MP of labour,
SRMC(Q) and AVC(Q) are rising over output
• SRATC = U-shaped over output because
o At low output, larger share of FC AFC(Q) falling o At high output, larger share of VC(Q) AVC(Q) rising
• SRMC(Q) must intersect min AVC(Q) & min SRATC(Q)
Short run costs Method 2 automation
Large investment machinery FC constant marginal product electricity VC
• High FC because of production method
• Constant MP electricity
• Given constant MP electricity,
SRMC(Q) and AVC(Q) are constant over output
• SRATC is declining over output because o AFC(Q) is declining throughout o AVC(Q) is constant throughout Long run costs
• Recall long run = all inputs become variable (fixed costs become variable inputs)
• Firms can therefore select any short run production method
• Since costs differ across short run production methods, for a given level of output, firms should choose cheapest production method
• Hence, for a given production level Q,
LRATC(Q) should reflect ATC of the production method with minimum SRATC(Q) Technology & scale
• For example, in car wash business,
firms would choose between method 1 and method 2, depending on which is cheaper at given production level
• At lower production level, cheaper method method 1
• At higher production level, cheaper method method 2
• Graphically, LRATC(Q) should envelope all SRATC(Q)
• Thus, LRATC(Q) ≤ SRATC(Q)
Shape of LRATC(Q) shows important info about technology of production Economies of scale LRATC falling over output range
Diseconomies of scale LRATC rising over output range
Efficient scale Lowest level of production that minimise LRATC D. Firm and managerial economics
✅ Lecture 12 - April 12: Key decisions and concepts
• We saw firms choose technologies to minimize costs in long run
• Today we will think how firms behave in short run & long run when prices change
• How much should a firm produce? Q*
• When should a firm enter/exit the market?
• We will concentrate on cases where firm is too small to influence prices Profit maximisation
• Recall firm’s objective is to maximise economic profit differentiate, think at margin π(Q) = TR(Q) − TC(Q)
• A profit maximizing firm would
o Produce Q ∗ that maximises π(Q)
o Only want to operate when π(Q ∗ ) is positive
Profit maximisation: perfectly competitive markets Perfectly competitive markets
• Firms are price-takers = perfectly elastic demand curve = market price P ∗ 𝑀𝑅(𝑄) = 𝜕𝑻𝑹(𝑄)
𝜕𝑄
𝑀𝑅(𝑄) = 𝜕𝐏 ∗ × 𝐐(𝑄) 𝜕𝑄 𝑀𝑅(𝑄) = 𝐏 ∗ × 𝐐(𝑄) 𝑀𝑅(𝑄) = 𝐏 ∗ 𝜕𝑄
• Firm’s demand curve = average revenue AR(Q) & marginal revenue MR(Q)
𝐴𝑅(𝑄) = 𝐓𝐑(𝑄) 𝐴𝑅(𝑄) = 𝐏 ∗ 𝜕𝑄
• Profit-maximising firm chooses to produce Q ∗ MR(Q ∗ ) = P ∗ = MC(Q ∗)
Firm’s profits
Entry and exit: perfectly competitive markets When should a firm operate?
• To be willing to operate in market,
firm need to have total revenue that at least covers total costs (must make positive profits from producing Q ∗)
TR (Q ∗) ≥ TC (Q ∗ )
• Total costs = opportunity costs not sunk costs Matt’s computer store
• Profit maximising to sell 5 computers a day
• Supplying that quantity generates revenue of $2,500
• Requires variable costs (labour) of $600 a day
• Rent has been paid for the next month and amounts to $2,000 a day Should the store operate (i) tomorrow, and (ii) in a month?
Tomorrow
• TC = $600 (The rent is sunk)
• TR = $2500 > TC = $600
• Thus, the store should operate today In a month
• TC = $600 + $2000 (The rent is now part of opp. costs)
• TR = $2500 < TC = $2600
• Thus, the store should shut down in a month Supply perfectly competitive markets
• Given market price P ∗
firm will choose Q ∗ such that MR(Q ∗ ) = P ∗ = MC(Q ∗ )
• At any given price, profit-maximising Q ∗ is depicted by MC(Q ∗ )
• Recall firm’s total revenue must at least cover total opportunity costs not including sunk cost & MC cuts ATC at minimum
AR (Q ∗) = P ∗ ≥ ATC (Q ∗)
• Firm’s supply curve = MC curve above minimum ATC
Short run perfectly competitive markets 1. Entry/exit (short run)
• No. of firms is fixed in short run
• No exit/entry
• Even firms that prefer to shutdown in long run may “stay” in short run as many of their costs are sunk
• For n firms indexed by i,
short-run industry supply = sum of firm short-run supply QS = ∑n i Q ∗ i
• Firms upward-sloping short-run supply = industry supply also upward-sloping
2. Firm profits (short run)• Each firm i chooses its profit-maximising level of production Q ∗ i
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• Whether firm makes profits or not will depend on P ∗ ≶ SRATC(Q ∗ i )
• Firms that decide to shut down (i.e. zero production) will incur losses equal to its sunk costs