The Firm and Profit Maximization Overheads

Neoclassical firm - A neoclassical firm is an organization that controls the transformation of inputs (resources it owns or purchases) into outputs (valued products that it sells), and earns the difference between what it receives in revenue, and what it spends on inputs

We define the production function as f represents the relationship between outputs and inputs x j is the quantity used of the jth input (x 1, x 2, x 3,... x n ) is the input bundle n is the number of inputs used by the firm y represents output

Returns (Profit) The profit from a production plan is the revenue obtained from the plan minus the cost of inputs used to implement it

Objectives of the firm We typically assume that a firm exists in order to make money A firm that wants to make money is called a for-profit firm, or a profit maximizing firm

The firm maximizes the returns from the technologies it controls taking into account: Given the profit max assumption The demand for final consumption goods Opportunities for buying and selling factors / products The actions of other firms in the market

The profit max problem

What is profit? Profit is revenue minus costs or

Explicit and implicit costs Explicit costs 1.purchase of expendable inputs including labor time 2.purchase of capital services (usually rent or lease) Implicit costs 1.value of produced expendables (feed for a cattle producer) 2.value of services provided by owned capital including financial capital and charges such as implicit rent, depreciation, compensation for operator labor, etc.

Accounting profit Accounting cost Accounting profit + depreciation on plant & equipmentexplicit costs total revenue - accounting cost

Economic profit Economic cost Economic profit + all implicit costsexplicit costs total revenue - economic cost

Why do we use economic profit? To reflect total costs and revenues for a decision To account for all resources used in production

Why do profits exist? All factors of production receive a payment Expendables receive their market price Labor receives wages Land receives rent Capital receives interest Firm owners receive profits

What are profits? Profits are the returns to Innovation Risk production delivery new products

The Profit Maximizing Output Level Profit = Revenue - Cost = R - C

Demand The individual demand curve facing a firm tells us, for different prices, the quantity of output that customers will choose to purchase from the firm The demand curve facing the firm show us the maximum price the firm can charge to sell any given amount of output

Example Inverse Demands p = y p = $1.85

Total Revenue Revenue is the total income that comes from the sale of the output (goods and services) of a given firm or production process

YPriceFCVCCTRProfit

YPriceFCVCCTRProfit

Total cost

Maximizing profit Choose the level of output where the difference between TR and TC is the greatest

YPriceFCVCCTRProfit

YPriceFCVCCTRProfit

Marginal cost (MC) Marginal cost is the increment, or addition, to cost that results from producing one more unit of output

yPriceFCVCCAFCAVCATCMCTRMRProfit

yPriceFCVCCAFCAVCATCMC

Marginal Revenue (MR) Marginal revenue is the increment, or addition, to revenue that results from producing one more unit of output Marginal revenue is the change in total revenue from producing one more unit of output

yPriceFCVCCAFCAVCATCMCTRMRProfit

yPriceTRMRProfit

yPriceTRMRProfit Another example Increase output from 4 to 5 units

A note on marginal revenue and price Marginal revenue is always less than price The firm must lower price in order to sell more units WHY?

p q q0q p0p0 5 Revenue Marginal Revenue Marginal Revenue = p 0

The lower price applies to all units and so the revenue per unit will be less than the price p0p0 q0q0 p1p1 q1q1 B A p q Demand MR = A - B

Profit Max Using MR and MC An increase in output will always increase profit if MR > MC An increase in output will always decrease profit if MR < MC

The rule is then Increase output whenever MR > MC Decrease output if MR < MC

yPrice CMCTRMRProfit Example Should we increase output from 3 to 4? Should we increase output from 4 to 5? Should we increase output from 5 to 6? Yes No !

Profit Maximization Using Graphs Profit is positive if TR > TC Output $ TR C

Profit Maximization Using MR and MC Profit on a given unit is positive if MR > MC Output $ MC Demand MR

Two intersections of MC and MR Output $ MC Demand MR

The optimal output level occurs where MC intersects MR from below Output $ MC Demand MR

Why average costs are irrelevant in the short-run The short-run decision is whether to produce one more unit or not Only marginal cost and marginal revenue are relevant for this decision

Marginal Decision Making and Short-run Decisions The marginal approach to profit states that a firm should take any action that adds more to its revenue than to its cost

Examples where marginal decision making is relevant advertising cost efficiency consultant adding a salesperson sprucing up sales area adding a two-year warranty to product

The shutdown rule Do we keep producing if we are losing money? It depends on what we mean by a loss It depends on whether we are in the short-run or in the long run It depends on which costs are fixed, which are variable, and which are sunk

Case 1 - TC > TR at all Q TR > TVC where MR = MC

TC > TR at all Q TR > TVC where MR = MC Output - y Cost VC CTR Marginal Cost & Revenue Curves Output - y Cost MC MR Total Cost & Revenue Curves

In the short-run fixed costs must be paid independent of the level of output At 6 units of output, total revenue more than covers total variable costs, leaving a residual to help cover fixed costs So the firm should produce 6 units in the short run

The shutdown rule In the short-run, the firm should continue to produce if total revenue exceeds total variable costs; otherwise, it should shut down

Case 2 - TC > TR at all Q TR < TVC where MR = MC

TR < TC at all Q TR < TVC where MR = MC Total Revenue and Cost Curves Output - y Cost TVC C TR Marginal Revenue and Cost Curves Output - y Cost MC MR

The shutdown rule In the short-run, the firm should continue to produce if total revenue exceeds total variable costs; otherwise, it should shut down

Shutdown in the long-run In the long-run the firm should exit the industry if it has any size loss

Shutdown and fixed costs that are not sunk In the short-run, if some of the fixed costs are not sunk, the firm may be better off to not operate when TR > TVC, if it can recover most of its sunk costs that are fixed costs, by shutting down

Suppose at 6 units of output, TFC =$50, TVC = $60 and TC = $110 But suppose that only $10 of the fixed costs are sunk, so that by shutting down the firm can recover $40.00 of fixed cost Suppose at 6 units of output, that total revenue is equal to $95. By operating the firm can make $35 over variable costs The firms net loss is then just $15.00 The firm's net loss by shutting down is only $10.00 The firm is better off by shutting down This will help cover the the fixed costs of $50 ( ) ( or )

Asset FixedVariableTotalSales DisposalTotalProfit/ Cost CostCost RevenueRevenueRevenueLoss Operate Shut-down

The End