Two assumptions of Market

1. Perfect Competititive : all participants of market should be price-takers
2. No Externalities
   • corrective tax : directive approach to solve externality
   • market function : indirective approach to solve externality

1. Modeling the Consumers

1. Indiviudal Demand

While farmers sell different types of fruit and vegetables on this market, today you are looking at the apples.

The number of apples you purchase depends on their current price. Such curves show what the price should be for a consumer to purchase a certain amount of a particular $good$ or $commodity$.

2. Surplus

Let us suppse that when you get to the market, the prices is $0.40 per apple. At this price, you decide to buy six apples.

Value	Quantity	Price	Surplus
Fisrt apple	1	$1.00	$1.00
Second apple	1	$0.80	$0.80
Next four apples	4	$0.60	$2.40
Gross Surplus			$4.20

We can define the red colored area as gross surplus of consumer. It can be decomposed into two differnet parts net consumer's surplus, expense of purchasing the goods.

Net consumer's surplus means Extra Value that you get from being able to buy all the apples at the same market price, even though the value you attach to some of them is higher than the market price.

3. Demand and Inverse Demand Functions

Some consumers would pay much more for the same number of apples whie others buy apples only when they are cheap.

If we aggregate the demand characteristics of a sufficiently large number of consumers, the discontinuities introduced by the individual decisions are smoothed away

• If $q$ denotes the quantity purchased and $\pi$ the price of the commodity, we can write:
  $\pi=D^{-1}(q)$
• If we look at the same curve from the other direction, we have the demand function for the commodity
  $q=D(\pi)$
• For most, if not all, practical commodities, the demand function is downward sloping

  The amount consumed decreases as the price increases.

• Demand curve gives the marginal value that consumers attach to the commodity.
• Their marginal willingness to pay decreases as their consumption increases.
  
• The concept of net surplus is much more important than the calculation of an absolute value for this quantity.

  Calculating the absolute value of the net surplus is quite difficult because the inverse demand function is not known accurately.

• If the market price is $\pi_1$, the consumer purchase a quantity $q_1$ and the net surplus is equal to the shaded area.
• If the market price increases to $\pi_2$, the consumption level decreases to $q_2$ and the consumers' net surplus is reduced to the roughly triangular area labeled A.

  Two effects contribute to this reduction in net surplus.

  • First, because the price is higher, consumption decreases from $q_1$ to $q_2$. This loss of the net surplus or welfare is equal to the area labeled C.
  • Second, because consumers have to pay a higher price for the quantity $q_2$ that they still purchase, they losd an additional amount of welfare represented by the area labeled B.

4. Elasticity of Demand

• Increasing the price of a commodity even by a small amount will clearly decrease the demand.
• But by how much?
• elasticity : the concept of same products between the demand for commodity $i$ and the price of commodity $i$.
  $\epsilon=\frac{\frac{dq}{q}}{\frac{d\pi}{\pi}}=\frac{\pi}{q}\frac{dp}{d\pi}$
• cross-elasticity : the concept of substitute products between the demand for commodity $i$ and the price of commodity $j$.
  $\epsilon=\frac{\frac{dq_i}{q_i}}{\frac{d\pi_j}{\pi_j}}=\frac{\pi_j}{q_i}\frac{dp_i}{d\pi_j}$
• While the elasticity of a commodity to its own price is always negative
• Cross-elasticities between substitute products are positive because an increase in the price of one will spur the demand for the other.

  If two commodities are complements a change in the demand for one will be accompanied by a similar change in the demand for the other.

  • Electiricy and electric heaters are clearly complements.
  • The cross-elasticities of complementary commodities are negative.

2. Modeling the Producers

1. Opportunity cost

• We also argued that the consumption level is such that the marginal benefit that consumers get from this commodity is equal to the price that they have to pay to obtain it. A similar argument can be used to develop our model of the producers.
• Generally opportunity cost could be summurized as biggest cost by making choice when you decide

2. Supply and Inverse Supply Functions

• If the market price for apples is higher, our producer may decide that if is worthwhile to increase the quantity of apples that she brings to the market.
  
• Inverse supply function : $\pi = S^{-1}(q)$
• Supply function : $q=S(\pi)$
  
• The marginal producer is the producer whose opportunity cost is equal to the market price.
• Extramarginal production : production that could become worthwhile if the market price were to increase.
• Inframarginal production : the opportunity cost of the production exist below the market price

3. Producer's Revenue

• Producer's Revenue : The red colored area at point $(\pi_1, q_1)$
  
• Producer's Net Surplus : Upper area of the supply curve and lower area of the $\pi_1$
  

4. Elasticity of Supply

• price elasticity : change of amount of the supply by change of price
  $\epsilon=\frac{\frac{dq}{q}}{\frac{d\pi}{\pi}}=\frac{\pi}{q}\frac{dq}{d\pi}$
• The elasticity of supply is always positive.
• It will usually be higher in the long run than in the short run because suppliers have more opportunities to increase the means of production.

3. Market Equilibrium

• We will make the assumption that each supplier or consumer cannot affect the price by its individual actions.

  All market participants take the price as given

• Then, the market is said to be perfectly competitive market
• Equilibrium price or market clearing price : $\pi^*$
  • The quantity would be decided by following fomula : $D(\pi^*)=S(\pi^*)$
• Equilibrim also can befined in terms of the inverse demand function and inverse supply function.
  • $D^{-1}(q^*)=S^{-1}(q^*)$

• If the market price is $\pi_1 < \pi^*$ where the demand is greater than the supply

  • Some suppliers will inevitably realize that there are some unsatisfied customers
  • The traded quantity will increases and so will the price until the equilibrium conditions are reached.

• If the market price is $\pi_2 > \pi^*$ where the supply is greater than the demand.

  • Some suppliers are left with goods for which they cannot find buyers.
  • They will reduce their production until the amount that producers are willing to sell is equal to the amount that consumers are willing to buy.

4. Pareto Efficiency

• Pareto efficient : if the benefit derived by any of the parties can be increased only by reducing the benefit enjoyed by one of the other parties.
• The equilibrium situation in a competitive market is Pareto efficient in terms of both the quantity of goods exchanged and the allocation of these goods.
  
• There is someone willing to sell extra units of the good considered at ta price $\pi_1$ that is less than the price $pi_2$
• Thus, if the total amount traded is less thant the equilibrium $q^*$, the situation is not Pareto efficient
• Also, any amount in excess of the equilibrium value is not Pareto efficient

  In a competitive market, all units of a given commodity are traded at the same price and this price represents the marginal rate of substitution between this good and all other goods.

5. Global Welfare and Deadweight Loss

• Consumer's surplus : A + B + E

• Producer's surplus : C + D + F

  External intervention sometives prevents the price of good from settling at the equilibrium value that would result from a free and competitive market

• If this price is set at a value $\pi_2$ that is higher than the competitive market clearing price $\pi^*$

• consumers reduce their consumption from $q^*$ to $q$.

  • Consumers' surplus shrinks : A + B + E
  • Producers' surplus : B + C + D

• If the government could enforce a maximum price for a good. Price set at a value $\pi_1$

  • Consumers' surplus shrinks : A + B + C
  • Producers' surplus : D

• Deadweight Loss : E + F