Overheads on Short-run Profit Maximination under Perfect Competition
ECON 201-4
November 1, 2001

Marginal Revenue
  • Total revenue is what the firms gets from selling its product. Total revenue is the firm's receipts or dollar sales. Total revenue is NOT the same as profit.
  • The marginal benefit to a firm from producing an additional unit is the extra revenue the firm gets from the sale of that unit.
  • Marginal revenue is the change in the firm's total revenue as a result of selling an additional unit. MR = change in (pQ) / change in Q where Q is output.
  • How marginal revenue changes as output changes depends on the type of market the firm sells in.

Perfect Competition
  • Characteristics of the industry
    • A very large number of firms selling and a very large number of buyers
    • Identical products -- buyers can't distinguish among the products of different firms.
    • Easy entry and exit -- no legal or significant economic barriers to new firms beginning production.
  • Example: corn, wheat

Revenues under Perfect Competition
  • Perfectly competitive firms are price takers.
    • Each firm is too small for its action to change the market price.
    • A firm can sell all it wants without changing the market price and none at any higher price.
  • The marginal revenue (marginal benefit) the firm gets from an additional unit equals the market price.

Economic Profit
  • Economic profit is the difference between total revenue and total economic costs.
  • Economic profit is the excess over the opportunity cost; it is how much extra the resources earn here compared to what they would earn in the next best alternative.
    • A positive economic profit tells you that you're doing better than in the alternatives.
    • Economic profit=0 says you're doing no better and no worse than in the alternatives-- you're doing equally as well.
    • Economic profit<0 says you're doing worse than in the alternatives. You'd earn more elsewhere.
  • Economic profit is smaller than accounting profit. Accounting profit is total revenue minus explicit costs whereas economic profit is total revenue minus both explicit and implicit costs.

Maximizing Profits
  • To maximize profits, follow the marginal principle:
    • Increase output if doing so adds more to benefits (revenues) than it adds to costs (if marginal benefit is greater than marginal cost).
    • Do not increase output if marginal benefits (revenues) are less than marginal costs.

Understanding marginal analysis
  • If MR > MC, increasing output ADDS to profits as the firm gets more from selling the extra unit than it costs the firm to produce it.
    • Adding to profit makes total profits larger -- closer to the firm's goal of the largest possible total profit.
    • Even if marginal revenue is only slightly greater than marginal cost, profits increase.
  • Do not increase output if MR < MC
    • The firm gets less from the sale of the unit than it costs the firm to produce this additional unit. Thus, producing it would LOWER the firm's profits. This contradicts the goal of maximum profits.

Shut Down
  • The firm should produce only if it at least covers its variable costs; that is, if total revenue is greater than or equal to total variable costs. Another way to judge if revenues cover varaible costs is to compare the revenue per unit (price) with variable costs per unit (SAVC).
  • If the firm does not cover variable costs, it should shut down. It pays its fixed costs (which it cannot avoid in the short-run). Profit =0-TFC = -TFC. The firm loses an amoun equal to its fixed costs.
  • Producing would, however, result in bigger losses. In addition to the amount of fixed costs, the firm would also lose the amount by which variable costs exceed the firm's revenues.
  • Why doesn't the firm just quit -- go out of business. It can't in the short-run. Some costs continue (interest on a bank loan, for example). In the long run, however, the firm will quit the business if the losses continue.

Mathematical Proof
To find the quantity which maximizes profits, find the value at which the first derivative with respect to quantity is zero:
d(Profit0/dQ = 0
d(TR-TC)/dQ = 0
d(TR)/dQ - d(TC)/dQ = 0 d(TR)/dQ = d(TC)/dQ
By definition, d(TR)/dQ = MR and d(TC)/dQ = MC
Therefore, the condition for maximum profits is MR=MC.
The second order condition (to ensure this is a maximum, not a minimum, is equivalent to saying that you must be in the range where MC is increasing.

Short-run Profit-Maximization- Perfect competition
  1. Find the MC.
  2. If the price the product sells for is greater than MC, produce this unit.
  3. Check the next unit (is price > marginal cost?)
  4. Don't produce the next unit if marginal cost is > price. Get as close to where p=MC as possible without producing any units which decrease profits.
  5. Check to see that the revenues at the best output cover STVC (TR>STVC or p>SVC). If not, shutdown-- produce zero.
    • Shutdown will result in losses equal to total fixed costs.
    • Producing anything would cause even larger losses of TFC + (TVC-TR).

Example
Output01234567
TVC020355478110150196
MC--20151924324046

TFC = 50

How many units of output should the firm produce

  1. if the price is $42?
  2. if the price is 33?
  3. if the price is 25?
  4. if the price is 17?

Question 1 Answer
Output01234567
TVC020355478110150196
MC--20151924324046
MR--42424242424242

MR>MC for units 1, 2, 3, 4, 5, 6, but not 7. Therefore produce 6 units unless shutdown is better.

  • TR = 42 x 6 =252 which is greater than TVC (150). The firm produces instead of shutting down.
  • At Q = 5, profit would be 50. Producing the 6th unit adds 2 to profits (42-40). Profit = 252-150-50 = 52.
  • AT Q=7, profit = 48 ($4 less because MC>MR by 4).

Question 3 Answer
  • Following the MR>MC rule, the firm produces units 1, 2, 3, and 4. Unit 5 won't be produced as MR (25) < MC (32).
  • Total revenue (4 x 25) = 100 which exceeds TVC of 78. The firm produces instead of shutting down.
  • Profit = 100-78-50 = -28. The firm is operating at a loss. If it shutdown, however, its profits would be -50, an even larger loss. Keep losses to a minimum by producing 4. Sometimes a small loss is the best you can do in the short run.

Answer- Question 4
  • When price = 17, the firm should shut down. TR is always less than total variable costs (or, equivalently, price is less than average variable costs)
  • Output01234567
    TVC020355478110150196
    TR01734516885102119
    Profits
    if TFC=50
    -50-53-51-54-60-75-98-127
  • Producing anyoutput leads to additional losses (TVC-TR) on top of the 50 in fixed costs the firm loses in shutting down.

Fixed costs
  • How would the answers to the problem change if fixed costs equalled 100 instead of 50?
  • Answer: There'd be no change in the short run. Fixed costs don't affect marginal cost, total variable cost, or revenues and therefore are irrelevant to short-run decision making.
    • Fixed costs stay the same whatever the firm does so they can't affect which option is best.
    • Fixed costs DO change the amount of profit the firm receives.
  • In the long run these costs do matter.

Marginal Cost and Supply
  • The compettive firm's supply curve is the same as its marginal cost curve from MC's intesection with AVC.
    • Higher prices induce the firm to move out along its MC curve to where MC equals the now higher price.
  • The section of the MC curve below the intersection is not part of the firm's supply curve because at prices this low, the firm would shutdown because it's not covering its variable costs.
  • Diminishing retuns is the cause of the upward slope to the firm's marginal cost curve and therefore the reason the firm's short-run supply curve is upward-sloping.

Real Life Applications
  • Edison
  • Baking
  • Airlines
  • Apples
  • Others


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