What is the price elasticity of demand

Question

Solve the following:

Q1. Determine the partial derivatives with respect to all of the variables in the following functions:

a.TC=200+20Q₁+30Q₂+0.4Q₁Q₂Q₃

dtc/dq₁ = 20+0.4Q1

dtc/dq₂ = 30+0.4Q2

dtc/dq₃ = 0.4Q3

b.Qa=5P_a^-3.0Y^0.5P_b^0.2

Q2. A company hires you as the marketing consultant to estimate the demand function for its product. You have concluded the demand function is

Q=200P^-2.5

Where Q is the quantity demanded per capita per month, P is the product's price (in dollars).

a. What is the price elasticity of demand?

b. Suppose you propose the selling price to be $200, what will be the associated marginal revenue?