Sellers & Incentives

Sellers and Incentives

• sellers try to maximise profit
• ref. Perfectly competitive markets

Seller’s Problem

Seller's Problem

Seller’s Problem

1. How to make the product?
2. What is the cost of making the product?
3. How much can the seller get for the product in the market?

Important

We assume that sellers aim to maximise profit.

• the most that can be produced from any given combination of inputs and technology
• knowing the prices of inputs and how production affects cost
• knowing the market price of product and how revenue changes with output level

Making the product

• capital: physical, e.g. factories, structures, equipment (NOT money invested)
• productoin: how to combine inputs to make output
• short run time horizon: at least one input is fixed; firm can only adjust some input levels to adjust output
• long run time horizon: seller can change all inputs
  • given long enough, all factors or inputs of production become variable
  • time is relative, and short/long run varies across industries
• marginal product: increase in product per worker… and then it decreases
  • workers are more efficient when they specialise in production and coordinate with one another → easy when there are relatively few workers
  • once there are TOO MANY workers → workers get in one another’s way → every additional worker contributes less output than the worker before (law of diminishing marginal returns)

Marginal cost

Learning Objectives

• to differentiate fixed cost from variable cost
• understand what sunk costs are
• you should also be able to explain what marginal cost is
• demonstrate the relationship between marginal product and marginal cost

Notes

• fixed cost: costs paid regardless of output decision
• total cost: sum of variable cost + fixed cost at that level of output; cheapest way to produce corresponding output
  • variable cost e.g. is labor
• sunk cost: even if firm produces nothing, incurs fixed cost
• marginal cost: $\frac{\text{change in total cost}}{\text{change in output}}$
• marginal cost and marginal product are inversely related
  • marginal product ↑ = marginal cost ↓

Optimal quantity for price taker

Formula

P* = MC(q*)

• profit: $\text{revenue}-\text{cost}$
• revenue: $\text{market price}\times \text{quantity sold}$
  • every time seller sells one more unit, total revenue increases by $P\ast$
• in Perfectly competitive markets, firms have no control over price → price-takers → only decide quantity produced
• marginal revenue: increase in revenue from selling 1 more unit
  • for a price-taker, marginal revenue = market price
• ↑ revenue > ↑ cost = ↑ marginal revenue > ↑ cost
  • if marginal cost > market price, seller should not produce more
• marginal revenue: $\frac{\text{change in total revenue}}{\text{change in output}}$
  • seller produces more if marginal revenue > marginal cost
• $\pi$: symbol for Profit
  • $\pi =R(q)-C(q)$

Producer surplus

• willingness to accept: lowest price a seller is willing to get paid to sell an extra unit of the good
• producer surplus: excess of market price over marginal cost
  • area between the price line and supply curve of the firm → find by calculating the area of the triangle
• a measure of seller welfare – how producers gain/lose from policies, price intervention, or market changes
• producer surplus is NOT profit
• total variable cost: area under marginal cost/supply curve
• assume that firms have identical cost curves → Market PS = $n\times \text{PS of firm}$, where $n$ is number of firms
• ↑ market price = ↑ producer surplus
  • producers prefer higher market price; would be less happy if market price ↓

Ecosnomic vs Accounting profit

• short-run decisions: to participate in the market or shut down

• long-run decisions: to stay or leave

• TODO

Link to original

Price-Taker

• $MR=P\ast$ at any $q$
• price taker’s MR curve = demand curve for its product; MC curve = supply curve
• buyers expect $P\ast$ and will buy as long as it’s at this price
• forgone profit
  • your profit margin might be higher at a lower quantity, but you’re leaving money on the table by not producing more
  • maximising profit at quantity where $P=MC$
• if ATC > MC = you’re LOSING MONEY

Unavoidable fixed costs

• if there are sunk fixed costs, the firm still incurs losses even if it shuts down

copy from slides later

$$\begin{gathered} \text{Profit}(Q\ast )\ge \text{Profit}(Q=0) \\ TR(Q\ast )-VC(Q\ast )-\text{Fixed Cost}\ge -\text{Fixed Cost} \end{gathered}$$

Break ties (break-even)

• if P* = AVC, stay and just continue from an economic POV (though business POV may differ)
  • this accounts for implicit costs → no missing opportunity cost

Shut down

• shutdown: decision to produce $Q=0$ in the short run
• when price-taker is indifferent between producing Q* and shutting down, these conditions are true:
  1. $P\ast =MC$
  2. $P\ast =AVC$
  • at Q*, MC = AVC
  • minimum AVC is shutdown price