# Modeling Firms’ Behavior Most economists treat the firm as a single decision-making unit the decisions are made by a single dictatorial manager who rationally.

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Modeling Firms’ Behavior Most economists treat the firm as a single decision-making unit the decisions are made by a single dictatorial manager who rationally pursues some goal profit-maximization

Profit Maximization A profit-maximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits seeks to maximize the difference between total revenue and total economic costs

Output Choice Total revenue for a firm is given by TR(q) = P(q)  q In the production of q, certain economic costs are incurred [TC(q)] Economic profits (  ) are the difference between total revenue and total costs  = TR(q) – TC(q) = P(q)  q – TC(q)

Output Choice The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the  function with respect to q equal to zero

Output Choice To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost

Profit Maximization output revenues & costs TR TC q* Profits are maximized when the slope of the revenue function is equal to the slope of the cost function But the second-order condition prevents us from mistaking q 0 as a maximum q0q0

Marginal Revenue If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good’s price

Marginal Revenue If a firm faces a downward-sloping demand curve, marginal revenue will be a function of output If price falls as a firm increases output, marginal revenue will be less than price

Marginal Revenue Suppose that the demand curve for a sub sandwich is q = 100 – 10P Solving for price, we get P = -q/10 + 10 This means that total revenue is TR = Pq = -q 2 /10 + 10q Marginal revenue will be given by MR = dTR/dq = -q/5 + 10

Profit Maximization To determine the profit-maximizing output, we must know the firm’s costs If subs can be produced at a constant average and marginal cost of \$4, then MR = MC -q/5 + 10 = 4 q = 30

Average Revenue Curve If we assume that the firm must sell all its output at one price, we can think of the demand curve facing the firm as its average revenue curve shows the revenue per unit yielded by alternative output choices

Marginal Revenue Curve The marginal revenue curve shows the extra revenue provided by the last unit sold In the case of a downward-sloping demand curve, the marginal revenue curve will lie below the demand curve

Marginal Revenue Curve output price D (average revenue) MR q1q1 P1P1 As output increases from 0 to q 1, total revenue increases so MR > 0 As output increases beyond q 1, total revenue decreases so MR < 0

Marginal Revenue Curve When the demand curve shifts, its associated marginal revenue curve shifts as well a marginal revenue curve cannot be calculated without referring to a specific demand curve

Short-Run Supply by a Price- Taking Firm output price SMC SATC SAVC P* = MR q* Maximum profit occurs where P = SMC

Short-Run Supply by a Price- Taking Firm output price SMC SATC SAVC P* = MR q* Since P > SATC, profit > 0

Short-Run Supply by a Price- Taking Firm output price SMC SATC SAVC P* = MR q* If the price rises to P**, the firm will produce q** and  > 0 q** P**

Short-Run Supply by a Price- Taking Firm output price SMC SATC SAVC P* = MR q* If the price falls to P***, the firm will produce q*** q*** P*** profit maximization requires that P = SMC and that SMC is upward-sloping  < 0

Short-Run Supply by a Price- Taking Firm The positively-sloped portion of the short-run marginal cost curve is the short-run supply curve for a price- taking firm it shows how much the firm will produce at every possible market price firms will only operate in the short run as long as total revenue covers variable cost the firm will produce no output if P < SAVC

Short-Run Supply by a Price- Taking Firm Thus, the price-taking firm’s short-run supply curve is the positively-sloped portion of the firm’s short-run marginal cost curve above the point of minimum average variable cost for prices below this level, the firm’s profit- maximizing decision is to shut down and produce no output

Short-Run Supply by a Price- Taking Firm output price SMC SATC SAVC The firm’s short-run supply curve is that portion of the SMC curve that is above minimum SAVC

Supply Function The supply function for a profit- maximizing firm that takes both output price (P) and input prices (v,w) as fixed is written as quantity supplied = q*(P,r,w) this indicates the dependence of output choices on these prices

Supply Function The supply function provides a convenient reminder of two key points the firm’s output decision is fundamentally a decision about hiring inputs changes in input costs will alter the hiring of inputs and hence affect output choices as well

Producer Surplus in the Short Run A profit-maximizing firm that decides to produce a positive output in the short run must find that decision to be more favorable than a decision to produce nothing This improvement in welfare is termed (short-run) producer surplus what the firm gains by being able to participate in market transactions

Producer surplus is the shaded area below P* and above SMC Producer Surplus in the Short Run output price SMC P* q* If the market price is P*, the firm will produce q*

Producer Surplus in the Long Run By definition, long-run producer surplus is zero fixed costs do not exist in the long run equilibrium profits under perfect competition with free entry are zero

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