Microeconomics Semester 2 Flashcards
What is a consumers consumption bundle?
This is the quantity of the two different goods that a consumer will choose.
A consumers affordable consumption bundle describes the bundle of goods that does costs no more than m, the consumers income/budget.
What is required to understand a consumer demand for goods?
1) The goods (a description of all feasible choices
2) A description of preferences (how the consumer views two particular goods)
3) A description of economic circumstances (the prices)
What would we do if there are more than two goods in the consumption bundle?
Although we will only have to deal with two goods, if we did have more than this then we can let the price of the second good be equal to 1. Therefore, when you get the budget constraint expression, it will be made up of demand for good 1, and then demand for all other goods.
In this case we call good 2 the composite good, which is also known as a numeraire good.
How do we graph budget constraints?
This is done by getting the point where the consumption bundle equals the budget (known as the budget line). Then re-arrange to get good 2 on the y-axis, and plot. Using this re-arranged formula, we can analyse the impact of changes in prices, as well as changes in the budget. E.g an increase in income will cause a parallel shift of the budget line.
The slope of the budget line is the rate at which we are willing to substitute good 1 for good 2, or in other words, the opportunity cost of consuming good 1.
What is the benefit of having a numeriare price?
When we do this, there will be one less price to worry about, which can make analysis of the budget and bundles easier.
What external factors could impact a budget line in real life economics?
-Rationing (if there is a limit to the quantity available of one good, the budget line will become vertical (or horizontal) after a specific amount in the bundle.
-Taxes and subsidies will impact the slope of the budget line.
-Taxes, subsidies and rationing can also be combined, such as having a tax applied after a specific quantity of a good has been purchased.
What is significant about optional choice with perfectly balanced inflation?
When all prices and budgets are raised at the same rate, there will be no change in anybodies optimal choice, and the budget set won’t change, everything has been multiplied by the same amount.
What is the endowment bundle?
This is the quantity of goods than an individual has before they enter the market.
When there is an endowment bundle, the income (m) that we had previously can be replaced by this bundle, because the consumer can always ‘afford’ their bundle or less, but cannot leave the market with excess of what their endowment was worth.
What is important to consider graphically when there is an endowment bundle in the budget line?
Whenever there is a change in the conditions of the budget prices, the budget line must still travel through the point where the endowment lies, this is because the maximum the consumer can obtain from trade must equal their original endowment,
What complications come with budget constraints overtime?
-The introduction of time allows for the possible of prices to change due to inflation.
-To make things easier, we will assume borrowers and savers will have equal interest rates.
What is the difference between a discount factor and discount rate?
The discount rate is just r (the interest rate), but the discount factor is (1/1+r). With each time period, the discount factor is to the power of as many periods as there have been, so this shows that the further into the future consumption occurs, the less value it holds.
What does pi and rho symbolise in the imtertemporal budget constraint?
-Pi symbolises Increaae I’m priced over a period (initially period 1).
-Rho is interpreted as the real interest rate, which is the interest rate taking inflation into account
-So, with inflation the new budget constraint will be: c1 = (1+ rho)(m0 - c0) + m1.
-However, if inflation is zero, then the real interest rate is equal to the nominal interest rate.
Look at lecture 1 slides to see this graphically
What is a real life example of budget constraints?
The consumption-leisure budget constraint:
We can make a budget as follows:
pC = S + wL with time constraints L + R = T. p = price of consumption (C), S is savings and w is wage of labour (L). R is then leisure and T is total time.
Before entering the labour market, L will be zero, so T = R, and from this we can derive an endowment bundle.
Through re-arranging, we then end up with C = (pC’ + wR’)/p - w/p
What is a consumption bundle?
This is a complete list of the goods and services that are involved in the choice problem we are investigating. The word “complete” deserves emphasis: when you analyze a consumer’s choice problem, make sure that you include all of the appropriate goods in the definition of the consumption bundle
What are the 3 types of preferences we need to know between two bundles?
-You can strictly prefer another bundle (>), this means they would choose one bundle over another, given the opportunity.
-You can weakly prefer another bundle (<~)
-you can be indifferent between two bundles (~), if you would be just as satisfied with either bundle.
-When we make assumptions about preferences, use weakly prefer, so we are as general as possible with our assumptions.
What are the assumptions we make about preferences?
-Comleteness
-Reflexivity
-Transivity
-Convexity
What does completeness mean in preferences?
We assume that any two bundles can be compared. A preference will always be either indifferent with another bundle, or weakly preferred.
What is reflexivity?
This is when we assume that a bundle is at least as good as itself.
What is transivity in preferences?
In a set of bundles, there has always got to be one bundle which is the best choice, therefore this means we must always be able to rank bundles based on the satisfaction they provides.
If a consumer prefers bundle X to Y and Y to Z. They can’t then prefer bundle Z to X, as this would mean there’s no best option.
What does an indifference curve show?
This shows all the consumption bundles that a consumer is indifferent between. All bundles on and above the curve are weakly preferred.
It is essentially for this reason indifference curves cannot cross each other, or there would be a contradiction of preferences.
What will I difference curves look like if two goods are perfect substitutes?
This will mean consumers are willing to substitute one good for another at a constant rate, this may not always be a 1:1 ratio, but that is the simplest model.
The indifference curves will be linear and downwards sloping, with a constant slope as they have a constant MRS.
What will I difference curves look like for perfect complements?
These are goods that will always be consumed in fixed proportions. This doesn’t necessarily have to be in a 1:1 ratio, however. MRS will be zero of infinity.
Their indifference curves will be L-shaped, as more of one good is pointless without the necessary ratio also of the other good. The utility will be equal to the minimum of the bundle.
What do indifference curves look like for bad goods?
This is a commodity the consumer doesn’t like. In this case, the indifference curve would be upwards sloping when there is one bad good, and one ‘good’ good.
If there is a neutral instead of a bad good, the indifference curve will be vertical or horizontal.
What happens when we consider satiation in an indifference curve?
Sometime if there is a overall best bundle for the consumers, and the closer they are to this in terms of their own preference, the better of they assume themselves to be.
This occurs when too much of a good makes it become a “bad’ and there will be circular indifference curve around the bliss/satiation point.
What is a discrete good?
This is a good which only comes in discrete (whole) units, they will have kinked indifference curves for each whole unit consumed.
What do we assume with “well behaved indifference curves’?
-More is better (talking about goods, not bads). This is called monotnicity, as long as both bundles have at least as much of one good, then the bundle with more of another good will be preferred.
-Average are preferred to extremes, the weighted average of two bundles on the same indifference curve will be at least as good or strictly preferred to the two more extremes. This will apply for any weighting between 0 and 1.
What does monotonicity imply about the shape of indifference curves?
It implies that they would have a negative slope, as moving up will be to a better position, and down to a worse position, if one good remains equal, so moving to an indifferent position will mean moving up and left or down and right.
What does the assumption averages are preferred to extremes mean geometrically? What is strict convexity?
It means the set of bundles weakly preferred to the original bundle will be a convex set.
We want to assume well-behaved goods are convex because for the most part, these goods will be consumed together.
Strict convexity means the weighted average is strictly preferred to two extremes. A perfect substitute would not be strictly convex.
What is the marginal rate of substitution?
This is the rate at which the consumer is just willing to substitute one good for the other. The MRS is equal to the negative of the gradient of the indifference curve. Therefore we consider MRS to be positive.
This isn’t the same as what they have to pay, as this related to prices, not preferences.
What is the diminishing marginal rate of substitution?
The amount of good 2 a consumer is willing to give up for more of good 1 will reduce as the quantity of good 1 consumed increases, as we now already have more of that good.
If not strictly convex, this assumption may not hold.
What is utility?
Utility is thought of as the only way by classical economists to describe preferences.
What is ordinal utility?
The only property of a utility assignment that is important is how it orders the bundles of goods. The magnitude of the utility function is only important insofar as it ranks the different consumption bundles; the size of the utility difference between any two consumption bundles doesn’t matter, and is arbitrary.
What is monotonic transformation?
Since only the ranking of the bundles matters, there can be no unique way to assign utilities to bundles of goods. If we can find one way to assign utility numbers to bundles of goods, we can find an infinite number of ways to do it. If
U(x1, x2) represents a way to assign utility numbers to the bundles , then multiplying by 2 (or any other positive number) is just as good a way to assign utilities
We typically represent these transformations by a function. Graphically, these transformations is just relabelling indifference curves.
What is a budget share?
Expenditure/income.
The cobb Douglas utility function will represent a budget share if the two powers of the two goods add up to 1.
What is a quasi-linear utility?
This is where the increase in utility will be linear for one good, and non-linear for the other good.
When this is the case, each indifference curve will be a vertical translate of the rest of the indifference curves for the quasi linear utility function.
What is the optimal choice for a consumer?
The optimal choice for a consumer will occur when the consumer reaches the highest possible indifference curve they can, based on their budget line.
Can optimum choice occur where all consumption goes towards one good in the bundle?
Yes, in some cases (such as substitute goods), there will be a boundary optimum, rather than an interior optimum solution. When this is the case, there will not necessarily be the tangent of the two lines being equal.
What is needed to ensure that a optimal choice is sufficient?
Having the tangent of the indifference curve equal to the budget constraint will be necessary when there is an interior solution, but that by itself won’t be sufficient. It will also be necessary to obtain the second order condition of the indifference curve, as doing so will allow to ensure the S.O.C is negative, and hence we have definitely found a maximum point where the indifference curve is convex, not concave.
What is the demand function?
The demand function is the function that relates the optimal choice (the quantities demanded) to the different values of price and incomes. We write demand functions as depending on both prices and income.
How do we find the optimal choice bundle when dealing with perfect substitutes?
1) If p2 > p1, then the indifference curve will be steeper than the budget line, and hence consumers will spend all their money on good 1.
2) If the opposite, then consumers will spend all their money on good 2.
3) If p2 = p1, then there will be a whole range of optimal choices, and we cannot confirm which one will be taken.
Look at lecture notes for how to do this mathematically.
How do we find the optimal choice of perfect compliments?
Optimal choice must always lie on the diagonal, where the consumer is purchasing an equal amount of both goods, regardless of what the prices are.
See lecture slides for how to do this mathematically.
What are some other examples of unusual optimal choices?
-With neutrals and bads, consumers will spend all of their money of the good they like, and won’t want to spend any on the neutral or bad good.
-With discrete goods (which can only be purchased in integer units), the optimal choice depends on the price of discrete good 1, where good 2 represents everything else. We can use diagram analysis to analyse this.
-In the rare case of a concave preference, consumers will spend everything on either one good or another one.
How does optimal choice work with the cobb-Douglas example?
Cobb Douglas preferences have a convenient property, which is that their quantities demanded of both goods will me make up of a combination of income/price of that good.
-This is done by rewriting the budget constraint with x2 being the subject, and then substituting this into the utility function to derive it in terms of good 1, and hence then solve for the quantity of good 1 demanded, which can be used to then get the quantity of good two.
See slides for how to do this, with a method which can be memorised, as you may still be asked to carry it out in the exam.
How do we calculate MRS?
MRS is just a ratio of the marginal utility with respect to good 1, over the marginal utility with respect to good 2.
What is important to consider when we talk about normal and inferior goods?
-Just because for one person on a specific income a good would be considered an inferior good, this doesn’t mean that everyone would consider it to be an inferior good, someone on a lower income would consider it a normal good.
What is an income offer curve?
An income offer curve is a line which will connect all the different optimal choices as income, m, varies.
What is an Engel curve?
An Engel curve will show how the quantity of a good purchased (x axis) will vary depending on income (y axis). The gradient of the slope will be equal to the price of the good. Usually, the Engel curve will be a linear line.
What are homothetic preferences?
A homothetic preference is a preference where if you prefer the original bundle to another bundle, then when both bundles quantities are changed then you will still prefer the original bundle to the new bundle, despite the change in income impacting the quantity of the goods you can consume.
What will the Engel curve look like for quasi linear preferences?
It will be curving upwards to a point, and then after that it will just be a vertical straight line. This is because the good will be consumers more as income rises, up to a point where it will then no longer be beneficial to consume more of the good, e,g once you have enough income to brush your teeth twice a day, you don’t need to buy more toothpaste after that.
What is a price offer curve?
This is a curve which shows how the quantity of two goods will change as prices change rather than income. -For an ordinary good, is x1 (x-axis) falls or rises in price, then the price offer curve will be horizontal.
-For a griffin good, if the price of the good falls or rises in price, the change in in quantity demanded will reflect the change in price, so the price offer curve will be vertical.
What will the quantity demanded of x1 in bundle (x1, x2) look like if the goods are perfect substitutes?
If p1>p2, then zero of x1 will be consumed. If P1 = P2, then any amount of the good p1 could be consumed, and as p1<p2, more and more of x1 will be consumed (in a convex manner), until the price reaches zero.
