What is a feasible allocation?
An allocation (x1A, x2A, x1B, x2B) is feasible if
x1A + x1B = w1A + w1B
x2A + x2B = wBA + w2B
What is a Pareto efficient allocation?
A feasible allocation (x1A, x2A, x1B,x2B) is Pareto efficient when there is no feasible allocation (x1'A, x2'A, x1'B,x2'B) such that UA(x1'A, x2'A) ≥ UA(x1A, x2A) and UB(x1'B,x2'B) ≥ UB(x1B,x2B), with strict inequality for at least one consumer.
What is the contract curve?
The contract curve is the set of all Pareto efficient allocations.
What maximization problem do Pareto efficient allocations solve?
max(x1, x2) uA
s.t. uB = u
x1a + x1b = omega1A + om1B
x2a + x2b = om2A + om2B for some utility u in B's utility possibility set.
Why must Pareto efficient allocations solve that maximization problem?

If it did not solve the max, there would exist another allocation x' satisfying uB(x') = uB(x), which would mean uA(x') > uA(x). Impossible under PE.

If some nonPE x' Pareto dominates x, it cannot solve the max.

If the inequality for B is actually an equality, then the inequality for A must be strict, and hence xA cannot solve the maximization problem.
Explain why a feasible allocation is PE iff the MRSA = MRSB.

Use the max problem for PE for allocation and find FOCs.

Rearranging FOCs will yield MRSa = (L/L) = MRSb

Conversely, if already has MRSa = MRSb, one can define (L/L) to solve the PE max problem.
What is a competitive equilibrium?

CE defines an allocation and prices such that

Consumers maximize utility taking p as given.

Firms maximize profit taking p and w as given.

Markets clear. (Resource constraints  consumption = endowment + production)
Is every allocation in the contract curve a competitive equilibrium allocation?
No. Any allocation in the contract curve that gives less utility to A than his endowment cannot by a CE, by revealed preference.
The endowment is always affordable.
Is every allocation in the contract curve a CE when a social planner can use lump sum taxes and subsidies?
Yes. By the Second Welfare theorem, any allocation in the contract curve is a competitive equilibrium allocation provided the social planner taxes/subsidizes the consumers using purely redistributive lump sum taxes/ subsidies.
TRS is equal to the slope of what?
The TRS equals the slope of the isoquant.
marginal product of factor 1/ marginal product of factor 2 = ?
TRS
What does the reservation price for the kth unit measure?
The reservation price for the kth unit measures consumer’s marginal willingness to pay for an extra unit when he has k – 1 units already.
How does one find market demand?
– add inverse demands horizontally
– properly account for zero demands
If p(q) is the inverse demand function, what is the price elasticity of demand?
E = p/q * (dq/dp)
What does elasticity depend on?
In general, how many and how close substitutes a good has.
When is E inelastic?
When absolute value of E is less than one.
What elasticity must demand have for increasing revenue with an increase in price?
inelastic
What does a consumer effectively pay with a quantity tax?
pd = ps + t
What is the relation between feasible allocations and Edgeworth boxes?
Feasible allocations can be viewed as points in the Edgeworth box.
When is a feasible allocation Pareto Efficient?
A feasible allocation is Pareto efficient if there does not exist a feasible allocation x' that Pareto dominates x.
What are isoquants?
Set of input combinations (x1, x2) with f (x1, x2) = y upper bar, for given y upper bar. (constant output)
What is the law of diminishing marginal product?
We expect that the marginal product of a factor will diminish as we get more and more of that factor.
MC equals the derivative of ___
The cost function C(Y). That's why, when maximizing profits in a simple case, the FOC is that price = c'(Y) = MC.
What are two exceptions to the p = MC as defining the inverse supply curve?

Declining MC. Then if you increase y, you can get more profit.

Shutdown Condition. If AVC are greater than P, you're better off shutting down.
What does Walras' law state?
The value of aggregate excess demand is zero.
Why, in a Pareto efficient allocation, must production be in the PPF?
If production were not in the PPF, then it is possible to produce weakly more of both goods and strictly more of at least one good, without violating the technological constraints and the resource constraints. Then, we can give the extra units produced to a single consumer to obtain a Pareto improvement.
What is a price offer curve?
All the optimal choices of a consumer at different prices.
What is the formula for profit maximization of a firm?