Notes on Deadweight Loss and Market Efficiency

Deadweight Loss

  • Total surplus is not maximized when there is a deviation from equilibrium quantity.
  • When total surplus is maximized, there are no gaps or deadweight losses.
  • Producing 2,750 units instead of the equilibrium quantity of 3,760 units results in a deadweight loss.

Willingness to Pay vs. Willingness to Accept

  • For a quantity less than the equilibrium, the willingness to pay is greater than the willingness to accept.
  • Willingness to pay is represented by the demand function, and willingness to accept by the supply function.
  • When willingness to pay exceeds willingness to accept, there are unexploited gains from trade.

Definition of Deadweight Loss

  • Deadweight loss is the loss from unexploited gains from trade.
  • Graphically, it is represented by the area of a small triangle.
  • Any deviation from the equilibrium quantity results in a deadweight loss.

Calculating Deadweight Loss

  • Deadweight loss is calculated as the area of the triangle formed by the deviation from equilibrium.
  • The formula for the area of a triangle is \frac{1}{2} \times base \times height
  • Example: If the base is 3760 - 2760 = 1000 and the height is 2.9 - 2.1 = 0.8, then the deadweight loss is \frac{1}{2} \times 1000 \times 0.8 = 400

Deviation from Equilibrium

  • Deviating from the equilibrium quantity, whether selling less or more, results in a deadweight loss.
  • The deadweight loss is the area of the triangle created by the difference between the demand and supply curves at the new quantity.

Overproduction

  • If 5,000 units are produced, the willingness to accept is greater than the willingness to pay.
  • This means the cost to produce exceeds what consumers are willing to pay.
  • Gains from trade are negative, resulting in a deadweight loss.

Deadweight Loss from Overproduction

  • The deadweight loss from overproduction is represented by the triangle formed on the graph.
  • The formula is \frac{1}{2} \times base \times height
  • Example: If the quantity is 5,000, price at demand curve is 1.9 and price at supply curve is 3, the deadweight loss can be calculated where the base is 3 - 1.9 = 1.1 and the height is 5000 - 3760 = 1240, which gives \frac{1}{2} \times 1.1 \times 1240 = 682

Efficiency of Competitive Markets

  • Equilibrium quantity in a perfectly competitive market is efficient.
  • Any deviation from the equilibrium leads to an inefficient outcome.
  • At equilibrium, total surplus is maximized, and there is no deadweight loss.
  • Competitive markets lead to efficient outcomes because incentives drive buyers and sellers to the efficient quantity.
  • Incentives lead to buyers and sellers to arrive at the efficient quantity through their own individual rational choices without any outside interference. Remember Adam Smith is visible.
  • Society allocates the efficient amount of scarce resources to the protection of this particular group.

Competitive Equilibrium

  • Competitive equilibrium is efficient because participants are price takers without market power, so price equals marginal cost.
  • The exchange of goods for money is governed by a complete contract between buyer and seller.
  • There are no effects on others besides the buyers and sellers.

Efficiency and Price Setting Firms

  • Perfectly competitive markets are efficient (price takers).
  • Monopolies and monopolistic firms: Is the outcome also efficient or not?

Monopoly Analysis

  • The demand curve represents willingness to pay.
  • Marginal cost is the cost to make an additional car, i.e., the derivative of the total cost function.
  • A firm can gain from trade if it can produce at a cost less than what a consumer is willing to pay.
  • Optimum point is where marginal revenue equals marginal cost.
  • In this example, the equilibrium price is 5.044 and the quantity is undefined.

Consumer and Producer Surplus in Monopoly

  • Consumer surplus is the area between the demand curve and the price.
  • Producer surplus is the area below the price but above the marginal cost curve.

Calculating Consumer Surplus

  • Given price is 5.044, Consumer surplus is: \frac{1}{2} \times 32 \times (8000 - 5044)

Producer surplus contributed by one unit

  • p - mc

Total Surplus

  • It is the consumer plus the producer surplus

Pareto Efficiency

  • There is no alternative allocation where someone is better off and nobody is worse off.
  • Point e is inefficient because of Pareto improvement.

Pareto Improvement

  • Some consumers would be willing to pay more than the firm's cost to produce.
  • If the firm produced another car and sold it at a price lower than $5.04 but higher than marginal cost, there would be a Pareto improvement.
  • Both the firm and consumer would be better off.

Additional Production

  • Suppose the firm sold cars to another 20 consumers for $3.08 without affecting the price of the first 32 cars.
  • Consumer surplus would increase, and the firm would also be better off.
  • The gains from trade are larger.
  • Sharing the deadly deadweight loss between producers and consumers is a Pareto improvement.

Firm Profit

  • Setting the price at $3.08 would maximize the total surplus but not the firm's profit.
  • The firm maximizes profits where marginal revenue equals marginal cost.
  • At the price of $5.04, the additional gains from trade will not be realized.
  • This creates a deadweight loss in total surplus relative to the Pareto efficient allocation.

Deadweight Loss Resulting from Monopolies

  • It is the area of the resulting monopoly equilibrium price and quantity

Market Power

  • Monopolies sell a differentiated product, meaning the firm has market power since it is the only firm producing that specific variety of their product.
  • Firms selling differentiated goods use their market power to set the price above their marginal cost.
  • This keeps the price high by producing a quantity that is too low relative to the Pareto efficient outcome.
  • These firms' profit-maximizing incentives do not lead to efficient outcomes.

Market Failure

  • Imperfect competition leads to an inefficient outcome.

Exercise - Kathy's Math Lessons

  • Kathy offers private math lessons (differentiated service).
  • The demand for her lessons: $QD = 200 - 2p$.
  • The opportunity costs of offering her lessons are given by the marginal cost: $MC = 40 + q$.

Task

  • Find the profit equilibrium price and quantity

Solution

  1. The profit maximizing condition is that Marginal Revenue equals Marginal Cost.
  2. Marginal Cost is present. However, Marginal Revenue is not. Therefore, solve for Marginal Revenue.
  3. We get total revenue by Price \times Quantity. Thus, we need to re-arrange the demand function to be in the form of Price.
  4. Rewriting QD = 200 - 2p in terms of P gives p = 100 - \frac{1}{2}q
  5. Next, as revenue = p \times q, we can conclude that the revenue function TR = (100 - \frac{1}{2}q) \times q which simplifies to 100q - \frac{1}{2}q^2
  6. Marginal revenue is the derivative of Total Revenue with respect to Quantity. Therefore, MR = 100 - q
  7. Here, we have the marginal cost (MC = 40 + q), we can equate the two functions together and solve for q
  8. 40 + q = 100 - q
  9. 2q = 60
  10. q = 30

Homework

  • Complete the Homework Assignment provided.