Advanced Microeconomics - Consumer Theory (Marshallian and Hicksian Demand), Adverse Selection and Moral Hazard in the Case of Insurance
Question 1: Consumer Theory
1.1:
In both the Marshallian and Hicksian consumer optimisation problems, it is assumed that consumers are supposed to be rational. The main focus of these problems are cost minimisation and utility maximisation, which play a huge part in consumer demand, but in real life, these are not the only problems that are considered. Also, it is assumed that every consumer’s indifference curve for two goods would be the same – they are very generalised models, and do not take into account other factors. For example, not many consumers would spend their entire budget on said goods – one thing to consider would be a consumer’s marginal propensity to consume and save. Though both of the problems provide a framework and model of consumer decisions, they are not plausible when applying them to real-life terms, because we have imperfect knowledge.
1.2:
The expression given in the question, is the rearranged derivative of the Hicksian demand being equal to the Marshallian demand, when income from the budget constraint is equal to minimised expenditure, whereby m=ep, μ. This is given by: dDdp= dHdp- dDdm . dedp using m = e.
Shephard’s Lemma provides us an alternative way of deriving Hicksian demand functions, using e. It is given by: dedp= x*
It is important to note that e is strictly increasing in p, due to Shephard’s Lemma, and x* >0,by assumption. Substituting this into the above expression gives: dDdp= dHdp- dDdm x*
This expression now represents a complete law of demand, as it has combined both Marshallian and Hicksian demand, whereby income from the budget constraint of Marshallian demand, is equal to minimised expenditure of Hicksian demand. Therefore, it has maximised utility and minimised cost simultaneously, to create an optimal quantity of demand in x*.
The first term, dDdp, means that Marshallian demand (maximising utility) increases, relative to the price of the good. dHdp represents the Hicksian part of the expression,
1.1:
In both the Marshallian and Hicksian consumer optimisation problems, it is assumed that consumers are supposed to be rational. The main focus of these problems are cost minimisation and utility maximisation, which play a huge part in consumer demand, but in real life, these are not the only problems that are considered. Also, it is assumed that every consumer’s indifference curve for two goods would be the same – they are very generalised models, and do not take into account other factors. For example, not many consumers would spend their entire budget on said goods – one thing to consider would be a consumer’s marginal propensity to consume and save. Though both of the problems provide a framework and model of consumer decisions, they are not plausible when applying them to real-life terms, because we have imperfect knowledge.
1.2:
The expression given in the question, is the rearranged derivative of the Hicksian demand being equal to the Marshallian demand, when income from the budget constraint is equal to minimised expenditure, whereby m=ep, μ. This is given by: dDdp= dHdp- dDdm . dedp using m = e.
Shephard’s Lemma provides us an alternative way of deriving Hicksian demand functions, using e. It is given by: dedp= x*
It is important to note that e is strictly increasing in p, due to Shephard’s Lemma, and x* >0,by assumption. Substituting this into the above expression gives: dDdp= dHdp- dDdm x*
This expression now represents a complete law of demand, as it has combined both Marshallian and Hicksian demand, whereby income from the budget constraint of Marshallian demand, is equal to minimised expenditure of Hicksian demand. Therefore, it has maximised utility and minimised cost simultaneously, to create an optimal quantity of demand in x*.
The first term, dDdp, means that Marshallian demand (maximising utility) increases, relative to the price of the good. dHdp represents the Hicksian part of the expression,