Short Run Profit Maximization In A Perfectly Competitive Output Market u Consider –Structure, then –Conduct, then –Performance. u Structure for Perfectly Competitive Markets –Many firms, and –Homogeneous output, and –Free entry and exit, and –Full and symmetric information. u THINK: Apples market, Cortland variety and Jonathan’s apple orchard
Short Run Profit Maximization In A Perfectly Competitive Output Market u Introduce some “new” notation. u Jonathan’s output: q u The aggregate output of the entire apple market: Q u The market price for apples: P –Jonathan is a “price taker”. –Jonathan’s perceived demand for HIS apples (δ) will be the prevailing market price P. –So… for Jonathan, or any other price taking firm… »Total revenue = tr = Pq »So marginal revenue = mr = P » δ = P = marginal revenue. Q $ D=Demand $ q mr = δ P S=Supply P
Jonathan’s Economic Profit and Loss when P=$528 u Just follow the rules for profit maximization: –1) Set mr=mc, 2) make sure at a max and not min, 3) check profit level –Note: since Jonathan is a price taker, if P=$528 mr=$528 u At mr=$528, the profit maximizing apple production is the highlighted line.
Economic Profits u Economic profits are the difference between total revenue and total costs. u Economic total costs include the opportunity costs of all inputs to the production process–in particular, the opportunity costs of the owner’s time and physical capital (equipment and space).
Accounting Profits u Accounting profits are defined as total sales revenue (the same as total revenue in the economic profits definition) minus operating costs (costs of goods sold + administrative and sales costs for those who know some accounting). u Accounting Profits = Sales Revenue - Accounting Costs
Did Jonathan Make Accounting Profits? u The blue line in the table illustrates that Jonathan makes an accounting profit of $40,800 when the apple price is $528/ton.
Reconciling Economic and Accounting Profits u The table to the right shows that Jonathan’s economic profits equal his accounting profits minus the opportunity cost of his time. u Thus, when the price of apples is $528/ton and 230 tons/year are sold, economic profits = $27,600
Question 1 u At a market price of $484/ton for apples, what is the optimal annual production of apples? u Marginal revenue = marginal cost at a production level of 220 tons/year. u This is the profit maximizing level of output when the market price is $484/ton.
Question 2 u At a market price of $440/ton for apples, what is the optimal annual production of apples? u Marginal revenue = marginal cost at a production level of 210 tons/year. u This is the profit maximizing level of output when the market price is $440/ton.
Question 3 u At a market price of $400/ton for apples, what is the optimal annual production of apples? u Marginal revenue = marginal cost at a production level of 200 tons/year. u This is the profit maximizing level of output when the market price is $400/ton.
Question 4 u Should Jonathan continue to operate the apple farm if the market price of apples is $400/ton?
Answer 4 u Jonathan’s economic profits are zero when the market price of apples is $400/ton ($0.20/pound, about the current wholesale price for first quality fresh apples). u Jonathan just recovers the opportunity cost of his time ($13,200), so he is indifferent between producing apples and taking a job at $12/hour.
Question 5 u Should Jonathan continue to operate the apple farm if the market price of apples is LESS THAN $400/ton?
Answer 5 u Depends on if we are talking long run or short run. u In the long run, Jonathan should not stay in the apple business if profits will continue to be negative. u In the short run, however, Jonathan must consider a little more. –Jonathan’s economic profits are negative if he operates and does the best that he can. –If Jonathan shuts down in the short run his economic loses will be ALL THOSE COSTS HE CAN NOT AVOID by shutting down, i.e., frequently called his sunk costs. –So, Jonathan must compare his (negative) profits from operating versus shutting down. –π(q*>0) = TR – avoidable costs – sunk costs. –π(q*=0) = -sunk costs –π(q*>0) > π(q*=0) when [TR - avoidable costs - sunk costs > - sunk costs] [TR - avoidable costs > 0] [TR > avoidable costs] [price > average avoidable costs]
Jonathan’s Cost Curves u Assume Land and Proprietor’s time are FIXED COSTS = $25,600 u Assume Hired Labor is the only VARIABLE COST
Jonathan’s Costs u So Land and Proprietor’s time are FIXED COSTS = $25,600 –If Q>0 no need for more discussion –If Q=0, then need to differentiate between »avoidable fixed costs »unavoidable fixed costs, a.k.a sunk costs u Assume Hired Labor is the only VARIABLE COST –Regardless of Q>0 or Q=0, all variable costs are avoidable, by definition u So when choosing to either operate or shut down with loses in the short run the rule is: –operate if revenues cover variable costs + avoidable fixed costs –otherwise shut down and see what happens u NOTE: most of the time books assume that ALL fixed costs are sunk.
Jonathan’s Short Run Supply Curve u So, in general, for a perfectly competitive firm, the srs firm = srmc firm for all points where srmc ≥ sravc (assuming all fixed costs are sunk). u For a perfectly competitive firm, choosing the output at which market price equals marginal cost maximizes profits. u Remember, it’s really mr=mc at q*, but since the firm is a price taker, P=mr all the time, so P=mc at q*. $P1 $P2 $P3 $P4 q4q3 q2 q1
Individual Producer’s Surplus u Recall: Producer’s surplus measures the gain to the firm from selling all units at the market price. u Marginal Producer’s Surplus on a given unit (the qth) is: Price – Marginal Cost for that unit. u Producer’s Surplus on all units supplied (q units) is: Total Revenue – Variable Costs. u Producer’s Surplus is: the area above the short run firm supply curve and below the market price u Producer’s Surplus is: Economic Profit + Fixed Costs.
Jonathan’s Producer Surplus u Jonathan’s individual producer’s surplus, when the market price is $528, is the sum of his economic profits ($27,600) and his fixed costs ($25,600) = $53,200.
The Short Run Market Supply Curve u The market supply curve is the sum of the quantities supplied by each seller at each market price. u Market supply, thus reflects the marginal costs of each of the producers in the market.
Short Run Market Supply Curve: Horizontal Summation Farm A’s Supply of Apples 0 200 400 600 800 1,000 1,200 1,400 1,600 0100200300400 Apples (tons/year) Price ($/ton) Farm B’s Supply of Apples 0 200 400 600 800 1,000 1,200 1,400 1,600 0100200300400 Apples (tons/year) Price ($/ton) u At a price of $1000/ton, add Farm A’s supply to Farm B’s supply to get market supply (about 560 tons/year). Add over all farms. u The market supply curve is the horizontal summation of the firms’ supply curves.
Producers’ Surplus u To get market producers’ surplus we simply sum the producer’s surplus over all the producers in the market. u So once we have the short run market supply curve, which reflects the marginal cost of each of the producers in the market, we have producers’ surplus as the area between the market price and above the short run market supply curve. u Producers’ surplus will still be total revenue – variable cost, aggregated over all producers.
u Recall the supply function for X = CD players: Q S = g(P X, P fop, P oc, S&T, N) Where: Q S = maximum quantity that producers are willing and able to sell P X = X’s price P fop = the price of factors of production P oc = the opportunity costs S&T = science and technology N = number of firms in the market Short Run Market Supply - Reprised u How does our scratch supply curve compare to the one we bought off the shelf?