Week 2 - Economic Applications of Derivatives

Question 1

Given a demand equation in terms of Q (Q=…), describe to determine at what value of p profit is maximized.

Answer 1

1. Solve equation so it is in terms of q, not p
2. Multiple by q to get the total revenue (TR)
3. Find the derivative of TR to get MR
4. Set equal to MC (marginal cost)
5. Plug in q into the price function to solve for price (this is the price for profit to be maximized)

Question 2

What is the elasticity of demand?

Answer 2

How strongly do changes in price cause quantity demanded to change
E(p) = - % change in quantity demanded / % change in price = - p*f’(p)/f(p)

Question 3

Describe an independent variable vs a dependent variable

Answer 3

Independent: often y; this is the variable that is determined by the equation when the dependent variable changes (ex: What is price at different quantities). Note that the demand function is often written in terms of quantity (so p=…) and therefore the inverse demand function must be solved for.
Dependent: input

Question 4

If elasticity of demand (E(p)) = 1/3, what does that mean?

Answer 4

Demand is inelastic

For every 1% increas in price, demand decreases by 1/3%

Question 5

What does an elastic demand tell us?

Answer 5

% change in demand is greater than the % change in price (ratio is > 1)

Question 6

With a total revenue function, visually, at what parts of the graph is demand elastic or inelastic

Answer 6

Elastic where TR is increasing, inelastic where revenue is decreasing