ECON 101 Tutorial: Week 1
Shane Murphy
s.murphy5@lancaster.ac.uk
Office Hours: Monday 3:00-4:00 – LUMS C86
Outline
•
•
•
•
Introduction
Roll Call
Problems
Discussion
Exercise 10
Chocolate Bar demand and supply can be described:
Qd = 1600 – 300p
Qs = 1400 + 700p
Calculate the equilibrium price and quantity.
Exercise 10
Qd = 1600 – 300p
Qs = 1400 + 700p
Equlibrium in supply and demand is where the supply
and demand curves intersect.
Set
Qs = Qd
1400 + 700p = 1600 – 300p
-1400 + 300p = -1400 + 300p
1000p = 200
p = 0.2
Qs = 1400 + 700p = 1400 + 700(0.2) = 1400 + 140 = 1540
Check Qd = 1600 – 300p
Calculus: first derivative of polynomial
The slope of a function can be calculated at any point
y taking its first derivative and evaluating at that
point.
Remember the rule for taking the first derivative of a
polynomial:
y = xn => dy/dx = nxn-1
y = w + z => dy/dx = dw/dx + dz/dx
So for example:
y = 3x2 + 5x + 2
dy/dx = 6x + 5
Exercise 10
Graph: Qd = 1600 – 300p
Qs = 1400 + 700p
Exercise 10
Slope: Qd = 1600 – 300p
Qd:
Δy = Δp = 1
Δx = ΔQd = -300
So slope is
Δy/Δx = -1/300
Qs = 1400 + 700p
Using calculus, rewrite demand as:
p = f(Q) = 1600/300 – Qd/300
dy/dx = dp/dQ = -1/300
Exercise 10
Slope: Qd = 1600 – 300p
Qs:
Δy = Δp = 1
Δx = ΔQd = 700
So slope is
Δy/Δx = 1/700
Qs = 1400 + 700p
Using calculus, rewrite demand as:
p = f(Q) = 1400/700 + Qd/700
dy/dx = dp/dQ = 1/700
Exercise 9
Draw the Demand
and Supply Curve:
What is the equilibrium
quantity and price?
Q = 30,000
P = 30
Exercise 9
Your team plans to increase total capacity in its
stadium by 5,000 seats. What admission price should
it charge?
Between 20 and 30 (probably 25)
Discussion Points
What is economics?
Is scarcity more important in today than in 1950?
Give an example of an economic model?