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Definition
| Anything that can function as a good or input. Eg labor/leisure |
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Definition
| The rules that must be followed to combine inputs to produce specific quantitites of goods |
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Definition
| How resources will be used and economy's output |
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Definition
| How to divide up the economy's output among agents for composition |
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| Formula for a an economy's set of feasible outcomes |
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Definition
| agents + resources + technology constraints + legal contraints |
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| Ricardian perspective in production of good i |
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Definition
| If L (fixed) is the only input, how much of good I will be produced if L_i is used to produce goods 1, 2. Results in production functions: q_1=F(L_1); q_2=G(L_2) |
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Definition
| Kaldor's justification for disagreeing with Robbins. Calculates the max tax each person could pay if policy (e.g. Corn Laws) is adopted, w/o making anyone worse off. Does NOT require that an anctual transfer be made. |
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Definition
| When at least someone ends up better off while no one ends up worse off. |
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Definition
| A set C is said to convex if when x, y ε C, then α x + (1−α) y ε C for all α less than 1 and greater than 0. |
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Definition
| Euclidean n space (En) is what’s called a metric space. A metric space consists of a set and a metric defined on that set. A metric is just a formula for calculating the distance between two elements of the set that it is defined on. So En is the set of all n-tuples, Rn = { (x1, x2, … , xn): xi ε R } with the distance between 2 n-tuples calculated this way: d(x, y) = { (y1 – x1)2 + . . . + (yn – xn)2 }^1/2 |
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Definition
| Now a function u( ∙ ) is said to be concave if this is true: for all x, y and λ € (0, 1), u(λ x + (1 –λ) y) > λ u(x) + (1 – λ) u(y) |
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| Note if a consumer’s utility function is concave, then… |
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Definition
| Note if a consumer’s utility function is concave, then their preferences are convex. |
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| Compensation chart columns |
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Definition
| Cost, benefit, tax, transfer, welfare change |
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| Three properties of preference ordering |
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Definition
| 1) For all X, Z € C, XPX (reflexive); 2) For all X,Z€C, either XPZ or ZPX or both/indifferent (completeness); 3) If XPZ and ZPY then XPY (transitivity) |
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| Three properties of Equivalence Relation (Indifference) |
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Definition
| 1) For all X€C, XIX (reflexive); 2) If XIZ then ZIX (symmetric); 3) If XIZ and ZIY then XIY (transitivity) |
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Definition
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| Who started consumer analysis |
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Definition
| Ragnar Frisch assumed consumers are rational, meaning 1) have different preference orderings and 2) use that P.O. to determine what specific market basket to purchase |
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| Who linked preference w utility |
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Definition
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| Whan can an ordinal untility function be transformed? |
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Definition
| When the transformation is monotanically increasing, aka F'(u)>0 |
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Definition
| If X* is a point of extreme value for F, a differentiable function, then F_1=F_2=…=F_n=0, then all functions partials evaluated at X*=0. A point of extreme value is max or min |
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| S.O.C. of a point of max value for a nxn function matrix |
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Definition
| If n is odd, the determinate is negative; if n is even, positive |
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| When to dispense of the S.O.C. |
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Definition
| Theorem: If a function is concave, then point of the F.O.C. are met will be a max value point |
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Definition
| F(x) is concave for all λ€(0,1) and all vectors X,Z, F(λX+(1-λ)Z)>λF(X)+(1-λ)F(Z) |
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Term
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Definition
| For a concave function the inequality is >= instead of > |
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| Relationship between consumers utility function and preferences |
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Definition
| If a consumers utility function is concave, then his/her preferences are convex; however, if preferences are convex it does NOT mean utility finction is concave, could be quasi concave. |
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Definition
| F(x) is QC if vectors X,Z and 0<λ<1, F(λX+(1-λ)Z)>min(F(X),F(Z)) <--the smaller of the two values |
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| Consumers Maximization Problem |
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Definition
| Maximize WRT u(X) such that P∙W=P∙X (inner product) |
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Definition
| F(x_1,…,x_n)+λG(x_1,…,x_n) where lambda is the lagrangian multiplier |
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| To max util the consumer must be consuming quants of n goods ST |
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Definition
| their marginal rates of substitution = ratios of prices |
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| Function v. Correspondence |
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Definition
| A function assigns 1ao1 element of y to each element in the set x, while a correspondence assigns more than 1 element in y to some elements in x |
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Definition
| Defined by a preference ordering and an initial endowment |
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Definition
| beta={X€C: P∙X=P∙W, X>=0} |
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Definition
| 1) Choose a unit measure (ie particular market basket aX_m) 2) Suppose for all X€C there's a positive real # ST X I aX_n (scalar distribution) 3) Then the utility of X is defined to be a, u(x)=a |
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| Profit max formulas for competative and monopolistic markets |
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Definition
| Competative: pi(q)=pq-c(q); Monopoly: pi(q)=p(q)q-c(q). Then max pi(q) ST q>0 |
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| Formula for a rational consumer's utility max |
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Definition
| Max u(x) WRT x ST x€beta (beta=consumer's budget set) |
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Definition
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| Example slope of a country's PPF for 2 goods |
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Definition
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Definition
| marginal utility of wealth, ie how u(x*) increases as a consumer's wealth increases, CP |
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| Total differential of the utility function |
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Definition
| du = u_1dx_1 + u_2dx_2 + … + u_ndx_n |
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Definition
| 1) differentiate utility function WRT 2 goods, 2) Set differential = 0, 3) Solve for dx_j/dx_i = MRS "x_j for x_i" |
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| Formula for MRS_Apples,Oranges |
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Definition
| MRS_A,O = -dO/dA = MU_A(A,O)/MU_O(A,O) |
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Definition
| If f is a continuous function and B is a compact set, then the max (or min) of f(x):x€B has a solution |
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Definition
| In E^n, a set is compact iff it's closed and bounded |
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Definition
| E_(i,p_j) = (dx_i/dp_j)(p_j/x_i) |
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| Second Theorem to test concavity |
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Definition
| A function is concave if grad F(x)∙(y-x)>F(y)+F(x) |
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Term
| If F(x) is concave, grad f(x*) = ? |
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Definition
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Term
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Definition
| if F(x) is cont & concave and B is compact & CONVEX then max F(x), x€B has a unique solution |
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Definition
| Ludwig Otto Hesse called it the "functional determinants" and is not to be confused with a Jacobian maxtrix of first derivatives. |
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Term
| Compensated demand function (aka?, And when to use?) |
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Definition
| A compensated demand function shows how the quantity of a good demanded changes as prices change with the consumer's utility level held constant. Also known as Hicksian demand function. They are a solution to the minimization problem. |
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Term
| Who is credited with adding indifference curves to consumer decision making? |
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Definition
| John Hicks and Wilfredo Pareto |
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| Formula for a compensation demand function |
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Definition
| u_0=u(x(p_0,Y_0)) where u_0 is a level of utility, p_0 is specific prices, Y_0 is specific income. Then min (WRT x) p ∙ x ST u(x)=u_0 |
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| Three axioms of consumer demand |
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Definition
| 1) x_i ^c (p,u_0) = x_i(p,e(p,Y_0)) 2) dx_i ^c / dp_i <0 3) dx_i ^c / dp_j = dx_j ^c / dp_i [note: e is income for when the consumer is compensated for price changes] |
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Term
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Definition
| If G is twice differentiable with continuous partials, then G_ij=G_ji |
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Term
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Definition
| A non-market good is any good such that an agent's consumption of that good is not solely determined by a market transaction |
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Term
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Definition
| Suppose that x(p,Y,z), where z is vector of non-market goods, is the solution to max u(x,z) WRT x ST Y=p ∙ x. Then the change in maximum utility WRT z equals the partial derivative of u WRT z. |
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| Demand function homogenous of degree 0 (relation to elasticities?) |
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Definition
| x_i(p,y)=x_i(tp,ty) for all t,p,y>0. Also, the total sum of elasticities equals 0 |
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Term
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Definition
| Anything increses max u, e.g. non-market goods. u(x(p,y,z),z)=v(p,y,z) |
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Term
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Definition
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| Formula for willingness to pay (WTP) to go fromp_1 to p'_1 |
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Definition
| w(p'_1) = w(p_1) - integral [p_1,p'_1] x_1 dp |
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| Ordinary demand function (aka?) |
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Definition
| x(p,y) (aka Marshallian function) |
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| Aggregate production function formula |
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Definition
| Y*=F(N*), where N* is full employment and Y* is full employment output |
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Term
| Cobb-Douglass Production Function |
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Definition
| Y=A(K^a)(HL)^(1-a), K to represent the physical capital stock, L to represent labor, H to represent human capital, and A to represent technology (including natural resources) |
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Term
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Definition
| M_0=k_hatP*Y*, where M_0 is the money supply, k hat is nominal value or captial, Y* is F(N*) the full output resulting from full employment. The Cambridge equation formally represents the Cambridge cash-balance theory, an alternative approach to the classical quantity theory of money. The Cambridge equation focuses on money demand instead of money supply. The theories also differ in explaining the movement of money: In the classical version, associated with Irving Fisher, money moves at a fixed rate and serves only as a medium of exchange while in the Cambridge approach money acts as a store of value and its movement depends on the desirability of holding cash. |
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| 2 classical propositions in aggregate production function |
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Definition
| 1) a flexible real wage will allow for full employment and 2) money is neutral, only having nominal effects |
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Term
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Definition
| E_P,M=dP/dM(M/P)=1 (by Cramer's Rule) |
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| Pessemistic elasticity conditions |
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Definition
| 1) investment demand is highly inelastic 2) money demand is highly elastic (liquidity trap) |
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Term
| Chararacteristic of agregate production function |
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Definition
| Increase in inputs results in an increase of outputs, but at a diminising marginal rate |
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Definition
| Dis/equilibrium in 1 market will cause dis/equilibrium in the other (Clower disagrees & says Kaynesian economics is price thoery without Walras' law) |
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Definition
| Consumers go to labor market before goods market |
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Definition
| Says fiscal policy does NOT jumpstart economy bc households reduce spending when observing an increase in government spending that will inevitably lead to an increase in taxation |
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Term
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Definition
| Aka perpetuity, valued at 1/i |
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Term
| Money-financed fiscal expenditure |
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Definition
| delta Y / delta G = 1/t, assuming no crowding out |
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Term
| Bond-financed fiscal expenditure |
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Definition
| delta Y / delta G = [1+(1-t)(dB/dG)]/t |
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Term
| Government budget restraint |
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Definition
| B+G-T(Y+B) = (dB/i)/p + (dM/p) |
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Term
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Definition
| Invesmentment Saving - Liquidity Preference Money Supply Model explains the decisions by investors between the amount of money available and interest rate |
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Definition
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Term
| Effective v notional demand |
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Definition
| Effective demand is the demand for a product or service which occurs when purchasers are constrained in a different market while notional demand demand when purchasers are NOT constrained in any other market. |
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Term
| Blinder's formulas for a change in the money,bond supply |
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Definition
M^dot = G+B_bar-T[F(M,B_bar,K_bar) + B_bar]
B^dot = H(M_bar,B,K_bar){G+B-T[F(M_bar,B,K_bar)+B]} |
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| Stability condition under pure money, bond finance |
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Definition
SCMF: tF_M > 0
SCBF: tF_B > 1-t |
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| Blinder's formulas for government income, interest equilibrium |
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Definition
Income: Y(t)=F(M,B,K_bar,G)
Interest: r(t)=H(M,B,K_bar,G) |
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Term
| What does a dot over a function mean |
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Definition
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Term
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Definition
| Y=nominal national income, P=the price index implicit in estimating national income in constant prices, y=national income in constant prices |
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| Properties of Phillips Curve |
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Definition
| 1) downward sloping 2) convexed 3) intertemporal instability |
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Term
| Expectations-augmented Phillips Curve |
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Definition
| pi = pi^e - λ(u-u_bar) where pi^e is expected inflation (with e as notation NOT a power), λ captures deviation in unemployment's impact on inflation, and u_bar is the natural rate of unemployment |
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Term
| Long-run equilibrium of Expectations-augmented Phillips Curve |
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Definition
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Term
| Assumptions of Clower's Kaynesian Model |
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Definition
| 1) There exists 2 markets: product and labor, 2) Households supply labor and demand product, 3) Firms demand labor and supply product, 4) Market sequence is important, households first go to labor market THEN product market |
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Term
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Definition
| "Supply creates its own demand" ie a surplus of output is created bc there is deamand for some other good or money |
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Term
| Quantity theory of money (aka?) |
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Definition
| MV_bar=PY_bar (aka Fisher equation) |
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Term
| 4 Foundations of Classical Macroeconomics |
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Definition
| 1) Say's Law, 2) The quantity theory of money, 3) The real theory of interest, 4) Wage and price flexibility |
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Term
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Definition
| R=r+pi^e where R is nominal interest rate, r is the real interest rate and pi^e is expected rate of inflation. |
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| Kaynes 2 classical postulates |
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Definition
| 1) Real wage equals the marginal product of labor 2) The utility of the real wage when a given volume of labor is employed equals the marginal disutility of that amount of employment |
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