MICROECONOMICS – QUIZ 2

The SLUTSKY equation provides insight into the own price effect (p1). But more specifically, it allows us to understand why the demand curve does not always slope downwards (i.e.: why it doesn't always have a (-) sign); and also why the change in price can have an impact on the consumption of other goods.

We aim to DECOMPOSE the slutsky equation into two parts that allow us to understand the total effect of a price change. The total effect is constituted by the Substitution Effect (SE) and the Income Effect (IE). The first decomposition is the SE, and the second decomposition is the IE.

The substitution effect is defined as the change in demand due to the change in the rate of exchange between x1 and x2. The change in the rate of exchange is due to a change in own price (p1). Furthermore, the SUBSTITUTION EFFECT ALWAYS HAS A NEGATIVE (-) SIGN. This means that the relationship between the rate of exchange (price) and the change in demand (quantity of x1) is inverse. In other words, when the price of a good increases, we will see a decrease in the quantity of said good consumed and vice versa. Naturally, then, the SE gives the slope of the demand curve when looking at the equation in its entirety.

BE SURE to draw this as the first effect on the graph relative to the original budget constraint. The income effect is drawn last on the new budget constraint given new prices.

Income effect is the second decomposition of the Slutsky equation whereby a price change (either increase or decrease) impacts the consumer's income in terms of purchase power. What this means is that while there may not be a change in real income (we're not actually giving the consumer more money), the consumer can still either purchase less or more of a good based on the change in pricing of said good. Meaning, that with a change in price and change in purchasing power, the demand of the good in question is also changed.

It is important to note that while SE always has a (-) negative sign, for INCOME EFFECT the sign (or relationship) of the effect to demand depends on whether or not we are dealing with an inferior good or with a normal good.

When we are dealing with a NORMAL good, the sign of the income effect is always (+).

when we are dealing and in INFERIOR good, the sign of the IE is always (-).

THIS MEANS: that for a normal good (+) , the income effect will decrease with a price increase and demand decrease.

and for an INFERIOR good (-): when the price increases, the demand increases, and the income effect DECREASES.

The Slutsky equation is important for public policy because when we make changes to prices via tax programs, for example, we know that the consumer will behave differently based on the new prices they have to face. Therefore, the insight that the slutsky equation gives us on the price effect allows us to change policies SUCH AS income taxing and minimum waging BASED on the implications of the income and substitution effects.

EX:
If we are dealing with a normal good, and the government decides to add a tax to said good, we can see how the IE and SE will pivot and shift to the left, leaving the consumer on a new budget constraint, and thus, with a new bundle on a lower indifference cure. The consumption pattern has shifted.

Your purchasing power is defined based on the relationship between the set income you have, and the changing prices that the consumer faces. For example, your purchasing power will increase when the price of a good decreases - meaning, that you can actually buy more a good with the same set income you initially had - i.e.: you have more purchasing power with your set income.

The law of demand simply defines the TOTAL EFFECT of the slutsky identity whereby the IE and the SE both have a negative sign i.e: both negatively related to the price change, and thus result in a demand curve that has a negative slope.

An Endowment is the amount of two goods that a consumer owns before entering the market. A consumer's endowment determines if they will be a net seller of a product or a net buyer.

denoted by (x1-w1) or (x2-w2).

WE ADD THIS ^ TO THE NEW SLUTSKY EQUATION - ENDOWMENT ENDS UP DENOTING A SPECIFIC INCOME EFFECT. THAT IS, THE ENDOWMENT INCOME EFFECT.

Consumer is a NET BUYER if the sign is (+) i.e.: (x1-w1) is greater than 0

Consumer is a NET SELLER if the sign is (-) i.e.: (x1-w1)<0 is less than 0.

The BUDGET CONSTRAINT FOR THE ENDOWMENT:

p1x1+p2x2=p1w1+p2w2

This one is used for graphing

OR

p1(x1-w1)+p2(x2-w2) = 0

This one is useful for denoting the consumer's adjustment to a new optimal point based on their initial endowments.

1) MRS (x1,x2 optimal) : P1/P2

2) p1(x1-w1)+p2(x2-w2)=0

A net buyer is a consumer who has an endowment of a good and the prices in the market go down, which result in the consumer buying more of that good - in other words, the consumer is better off.

The endowment sign is POSITIVE for a net buyer, meaning that a net buyer's total effect is NEGATIVE. meaning that for a normal good when the price decreases the consumer will buy more of it -> strictly referencing the TOTAL effect even though the income effect is positive.

A net seller is a consumer who has an initial endowment where the price goes up, and the consumer is left better off because you want to sell your good to make a profit on it. Conversely, if the price goes down then the net seller is worse off because the value of the endowment decreases.

The TOTAL effect of the net seller is AMBIGUOUS. The income effect for the net seller is positive, while the endowment effect (x1-w1) is negative. this is why we are left with an ambiguous total effect because we don't know which sign the total effect will take - i.e.: which, between SE and IE will overtake which.

The labour supply model can be described as the total hours a worker is willing to work given a wage rate. Within the labour supply model, the endowment that a worker has "prior" to entering the labour market is simply their time.

The public policy implication of the labour supply model is multifaceted as most of us interact regularly with the labour market in order to sustain ourselves. For example, when implementing a benefit package in order to life single parents over the poverty line, and to get them to enter the labour market, the government has to decide if it would be a better incentive for them to receive a compensation for their child care cost, or if it would be better for them to receive a lump sum for the cost of childcare. As it turns out, it is better to compensate them a fraction of their child care costs in order to render it more affordable, so as to both incentivize and enable entrance into the labour market, while also maintaining that they are able to work and earn and not have all their income go towards child care - as one example.

In the labour supply model, the conditions for optimality are as follows:

a) MRS: w/p
Where w is the equivalent of price, and p is the consumption price.

and b) pc+wl=wT+m } this is just the new budget constraint for the labour supply model.

Leisure in the labour supply model is defined as the time a worker spends outside of the labour market, and therefore the time spent not earning a wage. Wage can be considered the price of leisure in this model, because when we opt for leisure time over work, each hour of leisure costs the amount of wage we would be making if we were working.

WRITE OUT THE SLUTSKY EQUATION FOR PRICE EFFECT IN THE LABOUR MODEL - PRICE EFFECT IS WAGE EFFECT FOR THE ABOVE REASONS.

The net income effect is the first income effect including the endowment income effect. The sign for the net income effect is always the opposite of what it would be based on whether its a normal or inferior good.

meaning, that if it's a normal good and has a (+) sign, then the net income effect sign will be a (-). This is because in the labour supply model, the endowment (of time) overpower the first Income Effect because we are always net sellers of time - the worker cannot buy more time.

THE AMOUNT OF THE GOOD THAT THE CONSUMER ACTUALLY ENDS UP CONSUMING; HOW MUCH IS TAKEN HOME FROM THE MARKET.

THE DIFFERENCE BETWEEN WHAT THE CONSUMER ENDS UP TAKING HOME FROM THE MARKET, AND THE INITIAL ENDOWMENT OF GOODS.

price elasticity measures the responsiveness of demand to changes in price. I.e.: how do consumers demand of a good change when the price changes. For this, Elasticity is measured in three different ways:

1) |E| = 1 means that the demand is UNIT elastic
2) |E| >1 demand is elastic, which means that consumers are very responsive or reactive to a change in price.
3) |E| <1 demand is inelastic which means that consumers are not very reactive to a change in price.

elasticity equation is as follows:

E= P1/X1 x (DX1/DP1)

If demand is inelastic, an increase in price ultimately results in an increase in revenue because consumers will buy the product regardless of price. Think here, cigarettes. Addiction to the product means consumers are inelastic.

DRAW OUT THE GRAPH SHOWING EACH OF THESE POINTS.

This is just the change in revenue with a change in quantity.

consumer surplus is a measure of the benefits a consumer derives from buying a good at a particular price. At any price/quantity combination, the consumer surplus will be above the demand curve, and below the price line. It can also be understood as the difference between what the consumer is willing to pay for a good and what the consumer actually ends up paying.

Those consumers that are on the demand curve exactly are called MARGINAL consumers- that means, they spend their reservation price on the good. Everyone else is able to purchase the good at a price lower than their reservation price.

This is important for public policy analysis because it provides insight into any governments policies for example, taxes quotas and other restrictions which will often impact the prices paid by the consumer.

The producer surplus, on the other hand, is related to the supply curve. Given any combination of price and quantity, the producer surplus will appear above the supply curve and below the price line. For the producer, the reservation price is the lower possible price that they will agree to sell at. Therefore, their marginal producer is the producer who is on the supply curve and has to sell for their lowest possible price point.

So ALL suppliers that are above the supply curve and below the price line are able to make more money than they would at their reservation price.

NEW PRICES (SLOPE), SAME INDIFFERENCE CURVE. (In other words, draw the tangent line ON the old indifference curve and not on the new one.

THIS is used to compensate the consumer for any price changes so that they remain on the same indifference curve. An example of this would be gst or income tax returns. our incomes and products are taxed, but at the end of the year if the government sees that our incomes our low, they will return that money to us, moving us from a worse off position, back to our original position.

ORIGINAL SLOPE (PRICES) AND NEW INDIFFERENCE CURVE.

HERE YOU WANT TO DRAW YOUR TANGENCY ON THE NEW INDIFFERENCE CURVE.

With equivalent variations, the its the income we take (via price increasing) or the income we give (via price decreasing) to a consumer so that they attain a new indifference curve facing the original relative prices (meaning the same slope).

We say the income variation is equivalent then, so the price change.

CV AND EV are not always equal unless its on a quasi liner preference.

The production function is a way of representing feasible methods of converting inputs to outputs. Input and output combinations are called production sets.

Defined as:

f (tx1,tx2) = t . f (x1,x2)
and example is the production function of fixed proportions where the function looks like

y=f(x1,x2) = min [ax1.,bx2]

f(tx1,tx2)>t.f(x1,x2)
An example of this would be the

COBB DOUGLAS PREFERENCE- this is because when you are squaring the scale it increases more than if you were to simply double it.

f(tx1,tx2)<f.t(x1,x2)

An example would be the perfect substitutes production function.

THE RATE AT WHICH WE ADJUST X2 AS WE CHANGE X1 TO KEEP Y CONSTANT - MOVING ALONG AN ISOQUANT KEEPS Y AT A CONSTANT OF 0.

THIS IS RELATED TO THE DIMINISHING MARGIAL PRODUCT WHICH MOVES DOWN AN ISOQUANT AND DELINEATES AN INCREMENTAL OUTPUT FOR CERTAIN INPUTS EVENTUALLY DECREASE- HOLDING ONE INPUT CONSTANT.

LONG RUN : ALL FACTORS ARE VARIABLE

SHORT RUN: AT LEAST ONE FACTOR IS FIXED.