3
1. Consumer preferences
The consumer in this model will choose between two goods, meaning a consumer will have a basket of goods (e.g. 2 units of food and 3 units of another good).
The consumer’s problem is figure out the optimal composition of goods in their baskets.
We will approximate this basket in our model with a concept known as the market basket.
Market basket – a list of specific quantities of one or more goods.
When a consumer decides one basket is better than another, we represent her preferences using a preference relation.
When a consumer strictly prefers A to B, we represent this as A ≻ B.
On the other hand, if we write A ≽ B, this represents a weak preference relation.
If a consumer likes A and B equally well, they are indifferent between them. This is represented as A ∼ B.
Assumptions about consumer preferences and preference relations:
- Completeness – consumers can compare and rank all possible market baskets. For all consumption baskets A and B, either A ≻ B, B ≻ A or A ∼ B. The consumer must prefer one over the other or be indifferent between them.
- Transitivity – this has four parts:
1) If A ≻ B and B ≻ C, then A ≻ C.
2) If A ∼ B and B ∼ C, then A ∼ C.
3) If A ≻ B and B ∼ C, then A ≻ C.
4) If A ∼ B and B ≻ C, then A ≻ C.
This assumption rules out ‘irrational’ preference cycles.
- More is better – consumers prefer consuming more of a good to consuming less.
Suppose that basket A has more of both food and other goods than basket B. It must be the case that A ≻ B.
- Convexity – indifference curves exhibit diminishing MRS.
Consumers tend to stay away from extreme consumption baskets where there is, say, 90%
of food and 10% of the other. This assumption implies that the average of two baskets is preferred as opposed to the extremes.
Indifference curves
Indifference curves can be used to rank multiple market baskets.
An indifference curve represents all combinations of market baskets that provide a consumer with the same level of satisfaction.
Consider the basket A below.
Consuming less of both food and the other good, therefore, A cannot also lie in this region.
Any basket here has more of both goods relative to A. Thus, any point here must be preferred to A and cannot be on the same indifference curve that includes A.
Therefore, an indifference curve that includes A must go through the unshaded regions.
17 Income and substitution effects
A fall in the price of a good has two effects:
1. Consumers will tend to buy more of the good that has become cheaper and less of those goods that are now relatively more expensive. This response to a change in the relative prices of goods is called the substitution effect.
2. Because one of the goods is now cheaper, consumers enjoy an increase in real purchasing power.
They are better off because they can buy the same amount of the good for less money, and thus have money left over for additional purchases. The change in demand resulting from this change in real purchasing power is called the income effect.
Substitution effect – change in consumption of a good associated with a change in its price, with the level of utility held constant
Income effect – change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant
Suppose the Australian government enacts a new per-unit tax on petrol. The aim is to lower petrol
consumption by increasing its price. Clearly this will lower the utility of those Australians that buy petrol. As a result, suppose the Australian government agrees to provide a yearly rebate to all households compensating them for the utility loss. One would expect the rebate to completely negate the consumption effects of the tax. However, it turns out that petrol consumption could still decrease in Australia.
A tax on petrol will have two effects:
Substitution effect – the rate at which one can exchange petrol for another good will change
Income effect – the total purchasing power of a consumer’s income will change
Consider the diagram below, where G refers to petrol and O refers to other goods.
The slope of the budget line is −𝑃𝑃𝐺
𝑂.
An increase in 𝑃𝐺 due to the tax will pivot the budget line inwards and lower consumption of G from 𝐺1 to 𝐺3.
An imaginary line (purple) that is parallel to the new
budget line and tangent to 𝑢1 is drawn to separate the income and substitution effect.
With this budget line, we’re holding utility constant at the original level.
Because the move from 𝐺1 to 𝐺2 keeps the consumer on the same indifference curve, it reflects the effect of a change in relative prices alone.
Therefore, the move from 𝐺1 to 𝐺2 represents the substitution effect.
Now consider the move from 𝐺2 to 𝐺3. Notice that relative prices are the same (because budget constraints are parallel). Therefore, the only difference between the optimal baskets (𝐺2, 𝑂2) and (𝐺3, 𝑂1) is the level of income.
Therefore, the move from 𝐺2 to 𝐺3 represents the income effect.
Total effect of a price change = substitution effect (SE) + income effect (IE)
36 Law of diminishing returns
When production functions are always concave, it implies that output is increasing in L but at a decreasing rate. That is,
𝑑𝑀𝑃𝐿 𝑑𝐿 < 0
Long-run – the amount of time needed to make all production inputs variable.
In the long-run, it is unrealistic to assume that capital will be fixed.
In this setup, a firm can produce its output in a variety of ways by combining different amounts of labour and capital. When various combinations of inputs can produce the same level of output, we call such combinations production techniques.
Consider the following long-run production function:
𝑞 = 𝐹(𝐿, 𝐾)
In this case, the marginal production of labour (𝑀𝑃𝐿) is the change in output resulting from one additional worker being hired and with no changes to capital.
Similarly, the marginal production of capital (𝑀𝑃𝐾) is the change in output resulting from one additional capital being used and with no changes to labour.
Isoquants
We can use isoquants to denote a set of efficient
production techniques that result in the same quantity of output.
Isoquants in the theory of the firm is similar to indifference curves in the theory of the consumer.
However, utility is an ordinal measure. This is different to output (q), which is a cardinal measure.
For example, a q = 6 isoquant represents twice the amount of output as a q = 3 isoquant.
Substitution among inputs
Recall that in consumer theory, there is the concept of marginal rate of substitution (MRS).
The 𝑀𝑅𝑆𝑋𝑌 of X for Y is the amount of Y that a consumer is willing to give up to acquire one unit of X.
The MRS is equal to –1 times the slope of the indifference curve.
In the theory of the firm, there is an analogous concept.
Note that the slope of each isoquant indicates how one input can be traded off against another, holding output constant.
We refer to the magnitude of the slope of the isoquant as the marginal rate of technical substitution (MRTS).
The MRTS of L for K is the amount of K that must be reduced in order to increase L by one unit, holding output constant.
MRTS and marginal products
Suppose L use has increased and K use has decreased between these points. The additional output from the increased labour use, ∆𝐿, is:
𝑀𝑃𝐿×∆𝐿 The decrease in output from the decreased capital use is:
𝑀𝑃𝐾×∆𝐾
where this product is a negative number
