Micro Flashcards
demand function in Cobb-Douglas economy
x for good 1=(aI)/p1; x for good 2 = (1-a)I/p2
weak vs strong Pareto efficiency
weak: ther is no feasible allocation x’ such that all agents strictly prefer x’ to x strong: there is no feasible allocation x’ such that all agents weakly prefer x’ to x, and some agents strictly prefers x’ to x generally, when we say sth is “Pareto efficient” we refer to its weak definition
weakness of the concept of PE
an allocation where one agent gets everything htere is in the economy and all other agents get nothing will be PE, assuming the agent who has everything is not satiated
non-satiation
There are diminishing returns to consuming more of a good, but you can never consume so much of it that having more incurs a disutility. Local nonsatiation is implied by monotonicity of preferences.
how to find PE allocations (in the Edgeworth box / two-person case)
fixing one agent’s utility function at a givenlevel and maximizing the other agent’s utility function s.t. this constraint MRS for both agents must be the same–>tangency condition
Pareto set
set of Pareto efficient points - these are the loci of tangencies drawn in the Edgeworth box; also known as the contract curve,since it gives the efficient set of contracts fr allocations
Walrasian equilibria vs. PE allocations
one-to-one correspeondence between the two each Walrasian equilibrium satisfies the FOC for utility maximization that the MRS between the two goods for each agent be equal to the price ratio between the two goods. Since all agents face the same price ratio at a Walrasian equilibrium–>all agents have same MRS. At any PE allocaiotn, the MRS must be equal across agents as well (bc moving from that point would make one person not optimal, i.e. worse off–>PE)
Walrasian equilibrium definition
an allocation-price pair(x,p) is a Walrasian equilibrium if the allocaiton is feasible, and each agent is making tan optimal choice from his budget set
First Theorem of Welfare Economics
if (x,p) is a Walrasian equilibrim, then x is PE
Second Theorem of Welfare Economics
every PE allocation is a Walrasian equilibrium
Pareto dominate & Pareto criterion
the allocation x’ is said to Pareto dominate x if everyone prefers x’ to x. If each individiual prefers x’ to x, it seems noncontroversia to asert tat x’ is better than x and any projects that move us from x to x’ should be undertaken. This is the Pareto criterion.
public vs. private goods & excludability vs rivalry in consumption
public vs private: The consumption of private goods only affects a single economic agent. Consider bread: You and I comsume different amounts of bread and, if I consume a particular loaf of bread, you are excluded from consuming the same loaf of bread.

Private consumption of a discrete public good
if consumer 1 buys the public good, he receives u(PG)-c utility, and if consumer 2 doesn’t want to buy the good he receives u(PG)>U(PG)-c utility. Thus, both consumers want to free ride and don’t buy the public good–>prisoner’s dilemma. The dominant strategy here is (don’t buy, don’t buy). Thus, the net result is that the good isn’t provided at all, even though it would be efficient to do so.
Voting for a discrete public good - case 1
The amount of a publci good is often determined by voting - will this generally result in an efficient provision?
Ex. 1: 3 consumers who vote to decide whether or not to provide a public good which costs $99 to privde. If a majortiy votes in favor of provision they will split the cst equally and each pay $33. The reservation prices of the three consumers are r1=90, r2=30, r3=30–>sum of reservation prices>cost of provision. But, in this case only 1 will votein favor because only he receives a net positive benefit if the good is provided–>problem with majority voting: only measures ordinal preferences for the public good, whereas the eficiency condition requires a comparison of WTP. 1 would be willing to compensate the other consumers to vote in favor, but that option might not be available.
Voting for a discrete public good (2)
different kind of voting: individuals state their WTP for the public good and the good will be provided if the sum of the stated WTP>c. If the cost shares are fixed–>no equilibrium. consider the example of three voters before: 1 is made better off if the good is provided, so he may as well announce an arbitratily large positive #. For 2&3 other way round
Voting for a discrete public good (3)
each person announces their WTP for the public good. If the sum of stated WTP≥c, the good will be provided and each person pays the amount he announced. In this case if provision of the public good is PE, then this is an equilibrium. Any set of announcements such that each agent’s announcement≤his reservation price and that sum up t the cost of the public good is an equilibrium. However, there are many other inefficient equilibria, e.g. all agents announcing 0 WTP for the public good will typically be an equilibrium.
Efficient provision of a continuous public good
amount of public good: f(g1+g2) and the utility of agent i is Ui(f(g1+g2),wi-gi)
the condition for eficiency in the case of continuous provision of the publci goodis that the sum of marginal WTP = marginal cost of provision
Private provision of a continuous public good
Supose that each agent independently decides how much he wants to contribute to the public good. If agent 1 thinks that agent 2 will contribute g2, then 1’s utility maximization problem is maxg1 u1(g1+g2,w1-g1) such that g1≥0. The constrain is a natural restriction in this case; it says that 1 can voluntarily incerase the amount of the public good, but he cannot unilateraly decrease it
reservation price
A reservation is a limit on the price of a good or a service. On the demand side, it is the highest price that a buyer is willing to pay; on the supply side, it is the lowest price at which a seller is willing to sell a good or service.
Isoquants
gives all input bundles that produce exactly y units of output
Properties:
- An Isoquant Slopes Downward from Left to Right: This implies that the Isoquant is a negatively sloped curve. This is because when the quantify of factor K (capital) is increased, the quantity of L (labor) must be reduced so as to keep the same level of output.
- An Isoquant that Lies Above and to the Right of Another Represents a Higher Output Level: It means a higher isoquant represents higher level of output.
- Isoquants Cannot Cut Each Other:
If two isoquant are drawn to intersect each other, then it is a negation of the property that higher Isoquant represents higher level of output to a lower Isoquant. The intersection at point E shows that the same factor combination can produce 100 units as well as 200 units. But this is quite absurd. How can the same level of factor combination produce two different levels of output, when the technique of production remains unchanged.
- Isoquants are Convex to the Origin: This property implies that the marginal significance of one factor in terms of another factor diminishes along an ISO product curve. In other words, the isoquants are convex to the origin due to diminishing marginal rate of substitution.
monotone preferences
In economics, an agent’s preferences are said to be weakly monotonic if, given a consumption bundle, the agent prefers all consumption bundles that have more of all goods.
Much of consumer theory relies on a weaker assumption, local nonsatiation.
IC curves
gives all input bundles that produce exactly y units of output
Properties:
- Negatively-sloped: The indifference curves must slope down from left to right. This means that an indifference curve is negatively sloped. It slopes downward because as the consumer increases the consumption of X commodity, he has to give up certain units of Y commodity in order to maintain the same level of satisfaction.
- Convex to the origin: This is equivalent to saying that as the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes of X for Y along an indifference curve. As the consumer moves from A to B to C to D, the willingness to substitute good X for good Y diminishes. This means that as the amount of good X is increased by equal amounts, that of good Y diminishes by smaller amounts.
- Indifference Curve Cannot Intersect Each Other: Given the definition of indifference curve and the assumptions behind it, the indifference curves cannot intersect each other. It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible.
- Don’t touch the axes: One of the basic assumptions of indifference curves is that the consumer purchases combinations of different commodities. He is not supposed to purchase only one commodity. In that case indifference curve will touch one axis. This violates the basic assumption of indifference curves.
Leontief utilities
Leontief utility functions represent complementary goods. For example:
Suppose x is the number of left shoes and y the number of right shoes. A consumer can only use pairs of shoes. Hence, his utility is min(x,y)
Properties:
- A consumer with a Leontief utility function has the following properties:
- The preferences are weakly monotone but not strongly monotone: having a larger quantity of a single good does not increase utility, but having a larger quantity of all goods does.
- The preferences are weakly convex, but not strictly convex: a mix of two equivalent bundles may be either equivalent to or better than the original bundles.
MRTS
The rate at which one factor can be substituted for another while holding the level of output constant.