Lecture 1- Logic; Functions; Foundations, Exponential, Logarithmic Flashcards
How do denote the price in equilibrium?
p* or pe (* at the top and e at the bottom)
How do denote A is sufficient for B or that A implies B etc for 2 statements A and B?
A⇒B- 3D looking arrow VERY important as 2D arrow signifies converging
How do denote that A is sufficient and necessary for B and that A implies and is implied by B etc for 2 statements A and B?
A ⇐⇒ B (double 3D arrow) OR A iff B
When writing solutions to for example algebraic equations what must you remember?
To show that solution is logically connected by placing the 3D arrow from the second line of reasoning- SEE WORD DOC IMAGE
How would verbally say the following:
1) y = f(x)
2) y = g(z)
3) U = u(C)
1) y depends on x
2) y depends on a
3) U depends on C
How would you algebraically write the demand function and what does it verbally mean? demand depends on price
q^D = f(p)
Demand depends on price
What is the main thing to remember about the linear functions of demand and supply?
The linear demand function will have a negative gradient as it is downwards facing
The linear supply function will have a positive gradient as it is upwards facing
How would you denote the linear demand function?
q^D = −ap+b
How would you denote the linear supply function?
q^S = cp+d
When is the market in equilibrium?
When q^D = q^S
How do denote the quantity in equilibrium?
q* or qe (* at the top and e at the bottom)
What are the equations of the inverse demand and supply functions?
Obtained by making p the subject of each of the linear demand and supply functions:
p = − 1/a(q^D) + b/a
p = 1/c(q^S) − d/c
What are some of most forgettable rules of logs?
1) logb (1) = 0 — log 1 of any base is always 0
2) logb (b) = 1 — when the base and log number are equal the answer is always 1
3) b^logb (A) = A — b^logb cancel each other
When trying to prove the function y = b^x what must you remember?
1) Take logs of both sides
2) Make sure you take logs with base b so that you xlogb (b) which means that x multiplied by 1 equals just x
How would you separate log10 (ab) ^-cx?
log (a) +log (b)^−cx
