Here is a linear demand function: 0.3Q = 12 - 3P.Find its price function by inverting the demand function. Then find its total revenue function by multiplying through by Q. EXAMPLE:The linear demand function Q = 400 -250P inverts into the price function P = 1.6 -0.004Q. Multiplying this by Q gives its total revenue function TR = 1.6Q -0.004Q². This skill will be useful in assignment 4. Show the algebra involved.

 

a. Derive the price function from the demand function 0.3Q = 12 - 3P:

P=

b. Derive the total revenue function (TR) from your price function found in (a.):

TR =

2. Evaluate the following TR function: TR = 4Q - 0.1Q². EXAMPLE: When Q = 20, TR = $40.

a. When Q = 10, TR = $____ b. When Q = 40, TR = $_____

3. Evaluate the following expression. Y = 5X² +4X +6 EXAMPLE:When X = 2, Y = 34.

a. When X = 0, Y = ___ b. When X = 1, Y = ___

c. When X = 2, Y = ___ d. When X = 4, Y = ___