Microeconomics

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P=(0, )A rand we also know that 0=a−bP0 b−b∗a−bP −a −abℇ = = = = =−∞ii a−bP b∗a a−a 0a− b −bPℇ =We now know that when we have a linear demand curve ii a−bPa ℇ =−∞(0, )And elasticity in the point is iib −b∗0 0ℇ = = =0With the same reasoning we can say that in a point (a , 0) ii a−b∗0 aaℇ (0, )This means that if I compute from to I will find every value(a , 0)ii b−∞going from to0 aAn important point is , in this case price is ½ the reservation price and2 bquantity is ½ the intercept,b∗a a− −2 b 2ℇ = = =−1In this point ii b∗a aa− 2 b 235 | |ℇ >1when the demand is ELASTIC –> theℇ =−∞ iiii response of a quantity to a price change ismore than proportional, if we change price| |ℇ >1 by 10% quantity will change by more thanii 10% | |ℇ <10<when the demand

is RIGID –> theℇ =−1 iiii response of a quantity to a price change isless than proportional, if we change price by10% quantity will change by less than 10%| |ℇ <10< ii ℇ =0ii

We know that elasticity:elasticity is a pure number –> it does not depend on the way we use to measure- prices or quantities, this means that it does not matter whether we use € or,kg of lbs,whether the measure we’ll always get the same valueelasticity depends on other elements to be constant (i.e., other prices or- income) –> if we changeother variables there will be a shift of the demand curve(ceteris paribus,and the elasticity will change p.21)ℇwe can deduct that depends on the type of demanda b( )ex. let’s take a consumer w/ (Cobb-Douglas)=x ∗xu x , x1 2 1 2 a ∗ma+ bthe demand function for good 1 –> P 1 a ∗ma+bif we have 50 identical consumer the market demand will be let’s)50( P 1a )50(call Aa+b

A∗m¿ P 1So, would the market demand elasticity for good 1 be?d Q 1 ∗P A∗m −1= =Q A∗m∗P1d P 1 11 Pℇ = 111 Q 1 P−1−1 1Am∗(−1 )∗Pℇ = =−111 1 −1Am∗P 1This tells us that with a Cobb Douglas demand function and the correspondent−1demand curve the elasticity is always constant, and it is , it does notmatter what the price isThe elasticity measure also applies to other variables:36 ℇ = income elasticity, how much will the quantity of good change withi- ℑrespect to incomed q i ∗m with all the other variables constant we have twodmq ipossibilities: > 0 NORMAL goods (p.23)< 0 INFERIOR goods (p.23)ℇ = the effect on the quantity of good with respect to the change ini- ijprice of good jd q i ∗p jd p with all the other variables constant we have twojq ipossibilities:> 0 SUBSTITUTES goods (p.25)< 0 COMPLEMENTS goods (p.25)A∗mQ=let's take the

In the previous example, P 1A * m

THE MARKET 1ℇ = =1 if we m

First of all, a market is a "place" (not necessarily physical) where sellers/producers and buyers/consumers will meet so that in the market the quantity to be sold and the price at which to sell it will be decided. So, it is the place in which we have buyers, sellers and some outcome (that will be the price)

There are two sides to a market:

1 side -> we have buyers, can be summarized by the demand (D)

- The demand curve will summarize consumers' willingness to buy,

the demand curve tells us that with that specific price the consumer will be willing to buy that specific quantity of good.

2 side -> we have producers/suppliers (S)

- The supply curve will summarize producers' willingness to sell,

with the same reasoning the supply curve tells us that with that specific price on the market the producer will be willing to sell that specific quantity of good. As we can see

The main characteristic of the supply curve is that it is positively sloped. This is because if we increase the price, producers will be willing to sell more goods. It is the opposite of the demand curve.

MARKET EQUILIBRIUM = in case of what we call the "competitive market" A market in which there are many buyers and many consumers. The implication is no one in the market has the so-called market power = no one can decide the price. There also are two conditions:

• We should have a homogeneous product = all producers should produce the same type of good.
• There should be perfect information = To look at market equilibrium we need to know the equilibrium condition everybody knows everything about the = we have a market equilibrium when the quantity demanded at some price equals the quantity supplied at that same price. So, we have an equilibrium when there is a price at the market for which the quantity that the consumer wants to buy is exactly the same quantity that the producer wants to.

sell.D S=QQGraphically, the equilibrium is represented by point EBoth the demand and the supply curve areDex. =a−bPQ linearS =c +dPQ >0We also know that whilea , b , d c{ D =a−bPQ S => =a−bP=c+ dP=c +dPQ D S=QQbP−dP=a−c a−cE =P b+ d ETo find we canQsubstitute in either oneof the functionsE E=a−bQ Pa−cE =a−b( )Q b+d −ad +bcab−ad−ab+ bc E¿ =Qb+ d b+dD Sex. =40−P =−8+2Q Q PP Q P Q0 40 0 -838 40 0 10 1220 32{ D =40−PQS => 40−P=−8+2 P=−8+2Q P 40+ 8=3 PD S=QQ 3 P=48E =16PE E=40−PQ ¿ 40−16¿ 24E(24,16)Another possible way would be to take theexpression and substitute,a−c 40+ 8 48E = = = =16P b+ d 1+ 2 3( ) (−8∗1 )+40∗2−ad+ bc 80−8 72E = = = = =24Q b+ d 1+ 2 3 3When talking of the equilibrium we also have to talk about the STABILITY OF THEEQUILIBRIUMAn equilibrium is stable if when we are away from it,

There are market forces that will drive us back to it. Let's say we have a market equilibrium, let's also suppose we have a price (P), QH E H. In this case, we are far away from the equilibrium, with on the market > PP PH. The quantity that the consumer is willing to buy is different from the quantity (Q) DH H H that the consumer is willing to sell. In this situation, this means (Q) >¿Q QS S D that there is more supply than demand. For example, if and this means that of the 200 units that were = 200 = 100Q QS D produces only 100 will be sold –> there is a surplus, this brings to an incentive to reduce the price = there is a force pushing to decrease prices. If we have higher prices than the equilibrium price, the market will somehow take us back to it. In the same way, if the price is lower, customers would not be fully satisfied, and market forces would push up the prices. The MARKET SURPLUS is the measure of the total welfare of the market, it is composed by two sides.

A supply curve (S) - an equilibrium (E) - CS related to the demand curve - PS related to the supply curve - the MS - MARKET SURPLUS which is the sum between the CS and the PS.

Given the definition of the MS we can now say that the equilibrium is the point that will maximize the MS, there is no other price in the market that is able to make the total welfare of the market bigger than what we have with the competitive equilibrium.

Everything that leads us away from E, will reduce the total market surplus thus be negative for both producers and consumers.

What is the effect of putting a tax in the market?

First of all, there are two types of taxes:

Excise (paid by producers) -> put at producers' level

Sales (paid indirectly by the consumers) -> put at the consumers' level

We also know that taxes can be quantity taxes or ad-valorem (p.6).

Let's assume that we have a quantity tax -> the effect of this tax is that the prices paid by the producers

will not be the same prices received by the consumers. If we have an excise tax -> producers will have a price for the product but then, we have to add the tax S B so, in this case the price for the buyer will be +t=PP higher B if we have a sale tax -> consumers will pay price but then we have to pay a P tax to the government, so B S the producers will receive a lower price, -t =PP The idea is that the tax is somehow tra