August 22, 2017

Missing Link

Characteristics of the market from supply perspective

  • Perfect competition
  • Monopoly
  • Oligopoly
  • Monopolistic competition

Conditions of perfect competition

  • For competitive market to be perfect, the following conditions must be satisfied.
  • The product of the market is identical for all the suppliers.
  • The firms are price takers.
  • There are no barriers to entry (or exit) into the market.
  • There is perfect information, i.e. no supplier possess any private information capable of affecting the prices.

Recap

  • Firm's objective is to maximize economic profit, which is equal to total revenue minus the total cost of production.
  • In the short run, the firm manipulate the only variable affecting the profits - the quantity of production.
  • In the long run, the firm also makes decisions on participation in the market, i.e. whether the firm enters or exits the market.

Price taking

  • Looking back at the equilibrium model, the only aggregate variables determined inside of the model were price (\(P\)) and quantity (\(Q\))
  • If the firm's share of the market is substantially small, the decision on the quantity of supply will not affect the total supply in the market.
  • At the same time, if competition is high and there are no transaction costs for the consumer to purchase item from a different supplier, then adjusting the price up would result in no product being purchased. We call this situation as perfectly elastic demand. It is reflected by horizontal demand curve.
  • In this case, the firm in the perfect competition market will have to accept the price established on the market.

Revenue in perfect competition market

  • One of the assumptions of the perfect competition is firm's inability to affect the prices on the market. In mathematical terms, we can write revenue function as \(TR=f(Q)=P*Q\).
  • We introduce marginal revenue (\(MR\)) - the change in total revenue that results from a one-unit increase in the quantity sold.
  • \[ MR=\frac{\Delta TR}{\Delta Q} \]
  • In perfect competition, marginal revenue equals price.
  • \[ MR=\frac{{TR}_2-{TR}_1}{Q_2-Q_1}=\frac{PQ_2-PQ_1}{Q_2-Q_1}=\frac{P(Q_2-Q_1)}{Q_2-Q_1}=P \]

Revenue graph

Profit-maximizing output

  • In order to maximize the profit, we need to find optimal \(Q\) that makes \(\Pi(TR,TC)\) maximal.
  • We know that \(\Pi(TR,TC)\) is maximized when distance between the \(TR\) and \(TC\) curves is the largest.
  • The points where \(TC=TR\) are called the break-even points. At these points, the economic profit is zero.
  • From "law of decreasing marginal returns", the total cost eventually increases faster than total revenue. This guarantees that we get the convergence in terms of optimal profit.

Profit-maximizing output cont.

Profit-maximizing output cont.

Finding optimal point

  • We know that all the cost and revenue functions can be expressed as a function of \(Q\), thus making the task of finding maximum profit equal to the task of finding the optimal \(Q\) that maximizes the profit.
  • We can observe that in the case of linear \(TR\), the slope of the tangent line to the optimal point on \(TC\) is equal to the slope of \(TR\) itself. This is the point where \(MC=MR\).
  • Intuitively, when \(MR>MC\), the revenue from selling one more unit exceeds the cost of producing that unit and an increase in output increases economic profit.
  • When \(MR < MC\), then the revenue from selling one more unit is less than the cost of producing that unit and a decrease in output increases economic profit.

Finding optimal point cont.

Example

  • Suppose total revenue function is given by \(TR=8Q\) and total cost function is \(TC=Q^2-2Q\).
  • Find the values of the functions \(TR\), \(MR\), \(TC\), \(MC\), \(\Pi\) for \(Q=\{0,1,2,3,4,5,6,7\}\) and draw the respective graphs.

Quiz

  • Sarah's Salmon Farm produces fish according to the function \(TR=10Q\), where \(P=10\). The total cost is given by \(TC=Q^2+10\), with average variable cost equal to \(AVC=7\). Find an optimal value of \(Q\) and corresponding profit (hint: consider the output \(Q=\{3,4,5,6,7\}\)).
  • Suppose price fell to 5. What would be the new \(Q\)?

Temporary shutdown decision

  • When firm decides to shut down temporarily, it receives no revenue and incurs no variable costs. The firm still incurs fixed costs. The total economic loss is equal to total fixed cost.
  • When firm decides to produce, it receives revenue and incurs both fixed costs and variable costs. The final result (profit or loss) depends on the structure of the cost functions.
  • If total revenue exceeds total variable cost, the firm's economic loss is less than total fixed cost. It makes production more feasible than a shutdown.
  • But if total revenue is less than total variable cost, the firm's economic loss will exceed total fixed cost. It makes shutting down the production more profitable than any production level (that is \(Q>0\)).
  • The point at which firm is indifferent between the options is called shutdown point. This point is reached when the price equal minimum average variable cost.

The firm's short-run supply curve

  • We know that in perfect competitive market \(P=MR\).
  • We know that marginal revenue is a function of \(Q\).
  • We know that the firm is optimizing its profit by setting \(Q\) in such a way such that \(P=MC\).
  • Using all the above, we can create an individual supply function by varying the market price and recalculating the optimal decision \(Q\) that leads to this price.

The firm's short-run supply curve cont.

Short-run equilibrium

  • What can we say about profit function from a market equilibrium? If demand is high, then would that result in large profit for firms?
  • We can build an equilibrium from an individual level optimization, but we cannot reconstruct the individual levels from an aggregate market.
  • In the short term, there are three potential scenarios in an equilibrium: firms make zero, positive, or negative economic profit.
  • The rectangle that is formed by axes, \(MR\), and a point of \(ATC\) curve represent the total economic profit for the firm.
  • If \(MR\) lies above \(ATC\) the profit is positive, otherwise the profit is negative.

Short-run equilibrium in normal times

Short-run equilibrium in good times

Short-run equilibrium in bad times

Example

  • Consider the total cost given by \(TC=\frac{1}{3}Q^3+Q+1\) with marginal cost given by \(MC=Q^2+1\). Draw the \(MC\), \(ATC\), and \(AVC\) curve.
  • What would be the supply curve for this market? Find total profit for the \(P=5\).

Transition to the long run

  • In the long run, each firm can make a decision to enter and exit the market.
  • Our main assumption is an infinite number of firms that exist beyond the market.
  • Depending on situation on the market in the short run, the firms outside of market can make decision to enter the market.
  • At the same, firms in the market decide whether they want to continue operate under short run conditions.

The effects of entry and exit

  • Economic loss is an incentive for firms to exit a market, but as they do so, the price increases and the economic loss of each remaining firm decreases.
  • Economic profit is an incentive for new firms to enter a market, but as they do so, the price falls and the economic profit of each existing firm decreases.
  • At some point, we arrive at long run equilibrium - a situation, where no firms enter or exit the market. Economic profit in this case is zero!

The efficiency of perfect competition

  • Perfect competition is known to be efficient (or Pareto efficient). The efficiency is a situation that maximizes a benefit of all agents.
  • As a side effect, the efficiency implies there are no other market allocations that more efficient than perfect competition.
  • We consider the efficiency in terms of consumer and producer surpluses.
  • Consumer surplus is a difference in the amount spent between maximum price that he/she is willing to pay and what he/she actually pays in equilibrium.
  • Producer surplus is a sum of supplier's economic profit and fixed cost.

Example

  • Suppose demand function for the market is given by \(P=10-\frac{1}{10}Q\). There are 10 identical firms in the market with following cost functions:
  • \[ TC=\frac{1}{2}q^2+2q+10\\ MC=q+2 \]
  • Find a short-run equilibrium. What would be economic profit of the firms?
  • Assuming the production for each firm remains the same, how many firms have entered/exited the market?

Quiz

  • Consider the total cost given by \(TC=\frac{1}{2}q^2+q+10\) with marginal cost given by \(MC=q+1\). Draw the \(MC\), and \(AVC\) curve.
  • What would be the supply curve for this market?
  • Suppose demand is given by \(P=3-\frac{1}{6}Q\), where \(Q=6\). How many identical firms are in the market?
  • What is the number of firms in the long run?

Wrap up

  • We considered a market of perfect competition and constructed the supply curve using the individual supplier's optimization plan.
  • We showed how short run equilibrium is related to short run cost curves and derived the conditions for the firms to remain in the market.
  • We found the long run equilibrium for the perfect competition market and showed how firm's decision to enter/exit market affects economic profit.