functions

A = P(1+ x/100)^n

C = c + b(y)
Slope = Marginal propensity to consume (MPC)

S = So + S(y)

r = ro - r(i)

Y = C + I
C = consumption = a + by
I = investment
C + I = Expenditure

D(p) = a - bp
Demand is an inverse function of price
As price increase QD decreases
Negative function

S(p) = c +dp
Supply is proportional to price
positive function
c = minimum supply price = intercept

π = TR - TC
π = EP
TR = Price x quantity (P x Q)
TC = Total fixed cost + total variable cost

when TR-TC>0 it means positive economic profit
TR=TC breakeven pointor normal profit
TR<TC economic losses

O = 1/w

wage increase leads to decrease in output

L = (W/P)

log100 = log(10)^2 = 2
ln1 = 0
log0.1 = log10^-1 = -1
lne^-1 = -lne = -1
lnx/y = lnx - lny
ln(xy) = lnx + lny
lne^x = x and x = e^lnx

change in total cost / change in quantity

change in total cost / change in quantity

change in total utility / change in quantity

change in total production due to one additional unit of labor

EP = TR - TC
dEP / dQ = dTR / dQ - dTC/dQ = 0
= MR - MC = 0
MR = MC

y = f(l)
dY/dL = y'

dTB/dQ - dTC/dQ = MB -MC = 0
MB = MC

Differentiate to solve

relative rate of change = f'(x) / f(x)
percantage rate of change = f'(x) / f(x) * 100

d(uv)/dx = vu' + uv'

dy/dx = (vu' - uv') / v^2

dy/dx = dy/du * du/dx

maximum is always < 0 ---> concave function
minimum is always > 0 ---> convex function

revert back total when economically interpreting second derivitives. e.g marginal utility is maximum means that total utility is maximised

Marginal utility
marginal benefit
margianl demand
marginal supply
marginal tax rate

change in total utility due to one additional unit of x keeping everything else constant

utility - rate at which you substitute y for x keeping total utility constant |negative shows opportunity cost| (slope = Marginal rate of substitution MRS)
Production - (Marginal rate of technical substitution MRTS)

y = x(f'(x)) / f(x)

f(x) exists
lim f(x) exists
limf(x) = f(a) (x-->a)

f(b) - f(a) / b - a

f(x + h) - f(x) / h

MAX
EP = TR - TC
d(ep) / dQ = (dTR / dQ) - (dTC / dQ) = MR - MC = 0
MR = MC ---> Pmax
first order condition are the necessary conditions that tell us about the slope of the function
take second derivative and if < 0 means maximum
second order conditions are the sufficient conditions that will guarentee that a function is a max or min
you can maximise TB and compare MB & MC, you should continue production etc until MB = MC

MIN
TC = wl (wage x labor)
TC'q = MC
second order condition (second derivitave ) TC''qq > 0 for min

total cost / quantity

pluggin in what the variable is = to in differentiation back into the original function

plug in positive and negative values into the second derivative, if signs change it is a point of inflection

when one variable is a function of the other and the first variable depends on the second

or

formal definition - a function assigns each input number an output number

-b/2a

y=ax^2 + bx + c