Micro Theory Honors - Formulas and things to know!

Numeraire

Set any price equal to 1

Monotonic preferences

more of either good is better — makes indifference curves negatively sloped

Perfect complements optimal condition

ax1 = bx2 — this is the kink point

Cobb-Douglas exponent equation

a = c/c+d while b = 1-a

MRS for Cobb-Douglas

-(c/d) x (x2/x1)

Perfect complements demanded amount

x1 = bm/(bp1 +ap2)

Change in m equation

Change in M = x1 x change in p1, new M = m + change in M

Budget constraint with endowment

p1x1 + p2x2 = p1w1 + p2w2

Labor supply

C = M + w[24-L]

Consumer surplus — continuous

v(x) - v(0) - px

Price elasticity of demand

(p/q) x (dq/dp)

Revenue

q(1+e) — if less than -1, it lowers revenue, in between -1 and 0, it raises, and at unit elasticity (-1), it is at its maximum

Marginal Revenue

p(1-1/|e|)

Income elasticity

(m/q)(change in q/change in m) — >0= normal, <0= inferior, 0<n<1= necessity, >1 = luxury

Aggregate excess demand for good i

(xiA - wiA) + (xiB-wiB) —> =0 per walras’ law

Two theorems

1. every competitive equilibrium is Pareto efficient

2. any Pareto efficient allocation can be reached as competitive equilibrium after suitably redistributing the initial endowments

Perfect Complements finding new x

x = m/px + yx, adjusting for kink — ie if y=5x, then put a 5 in front of y