# 2. Budget constraint (2016)

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 Universidad Universidad Pompeu Fabra (UPF) Grado International Business Economics - 1º curso Asignatura Microeconomics I Año del apunte 2016 Páginas 5 Fecha de subida 27/04/2016 Descargas 8 Puntuación media Subido por avillagrasa

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Resumen del libro completado con apuntes de clase.

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avillagrasa II.
1st year IBE - 3rd Term Microeconomics I Budget constraint Index The budget constraint ...................................................................................................... 2 Two goods are often enough........................................................................................ 2 Properties of the budget set............................................................................................. 2 Changes in the budget line ............................................................................................... 3 Changes in income ........................................................................................................ 3 Changes in price............................................................................................................ 3 Changes in prices and income ...................................................................................... 4 The numeraire .................................................................................................................. 3 Taxes, subsidies and Rationing .......................................... ¡Error! Marcador no definido.
Taxes ............................................................................................................................. 4 Subsidies ....................................................................................................................... 4 Lump-sum ..................................................................................................................... 4 Rationing constraints .................................................................................................... 5 Rationing constraints and taxes ................................................................................... 5 Summary ........................................................................................................................... 5 1 avillagrasa 1st year IBE - 3rd Term Microeconomics I The budget constraint Consumption bundle (X): is the quantity of good 1 (x1) and good 2(x2) that the consumer can consume.
Each good has a given price, and we have a determined quantity of money, which constrains us. Therefore, we are constrained to spend less on out bundle than the money we have (m). So we are constrained by our preferences and income.
Budget set: it represents all the affordable bundles  p1x1 + p2x2 ≤ m Budget line: it is the maximum we can afford  p1x1 + p2x2 = m Two goods are often enough Usually we will only use a bundle with two goods. However, we can think of it as representing all the goods we can choose. Good 1 can be the good we are interested in studying, while good 2 can represent everything else we could buy with that money.
Under this assumption we can think of good 2 (x 2) as being only money (p2=1). It is a composite good.
Properties of the budget set As we have seen, the budget line (constraint) is represented by p1x1 + p2x2 ≤ m, so we can plot it and obtain a downward sloping line with slope -p1/p2 because it corresponds to the change we have to make in quantity of good 1 to get good 2 (substitution).
The slope is the rate at which the market is willing to substitute good 1 for good 2. It has a negative sign because if you want to consume more of good 1 you will have to consume less of good 2 and vice versa. The slope can also be interpreted as the 2 avillagrasa 1st year IBE - 3rd Term Microeconomics I opportunity cost of consuming good 1, because is the consumption we have to give up from good 2. However this is not quite true in real life.
The numeraire The budget line is defined by two prices and one income. However, we can peg 1 one of the prices or the income dividing everything by it. At the end, we will get an equivalent expression of the budget constraint but with one of its components (m or p2) equal to one.
When one of the prices is set to 1 we call it the numeraire price. It is the price relative to which we’re measuring the other price and the income. It can be useful as then we don’t need to care about one of the prices.
Changes in the budget line Changes in income When the income changes there is a parallel shift outward (if there’s an increase in income) or inward (if there’s a reduction in income). The slope doesn’t change.
Changes in price If prices change - keeping the same income - the slope changes. If the price of good 1 increases, the slope increases too, thus we have a steeper line. We can draw it to see it clearer. If good 2 doesn’t change its price, if we use all our money to buy it, we will get the same quantity. However, if we use all my money to buy good 1, as it is more expensive, we can buy less quantity.
1 Fijar 3 avillagrasa 1st year IBE - 3rd Term Microeconomics I Changes in both prices When both prices increase the same, the curve shifts inwards. It is the same as reducing the income.
Changes in prices and income If prices go up and income goes down, for example, first of all we know that the line will shift inwards (the interceptions2 are at a lower point). Also, if price 2 increases more than price 1 (slope decreases) the line will become flatter and if the price 1 increases more than price 2 (slope increases) it will become steeper.
Fiscal policy Taxes Quantity taxes: It acts like a higher price. Therefore the budget line gets steeper.
Value or ad valorem taxes: The consumer pays the price (p 1) plus an interest depending on the price that goes to the government. He ends up paying (1+i)·p1.
Subsidies Quantity subsidy: It acts like a lower price. Therefore the budget line gets flatter. The price is p1 - s (s=subsidy).
Value or ad valorem subsidies: The consumer pays the price (p1) minus an interest depending on the price that is given by the government. He ends up paying (1-s)·p1.
Lump-sum It can be a tax or a subsidy. If it’s a tax the government will take away an amount of money regardless of the individual behaviour. It is like a reduction on income, so it 2 The quantity of good 1 I will get if I got 0 of good 2 and vice versa 4 avillagrasa 1st year IBE - 3rd Term Microeconomics I shifts the budget line inwards. A lump-sum subsidy acts in the opposite way, shifting the line outwards.
Rationing constraints It consists on the government fixing a maximum consumption of a good. It is used during wars, for example.
Rationing constraints and taxes We might want people to consume less than a determined quantity of a good. What we can do is to impose a tax only to be paid if the quantity is exceeded. Because of this the line becomes steeper for quantities greater than the one set by the government.
Summary      The budget set consists on all the bundles of goods that the consumer can afford at a given price and income.
The budget line is p1x1 + p2x2 = m and its slope is -p1/p2.
Changes in income shift the budget line.
Increases in p1 make the line steeper and increases in p2 make it flatter.
Taxes, subsidies and rationing change the slope and/or position of the budget line, as they act as changes in prices.
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