Question

Use one of the following methods to solve: five step approach or profit function max

Given: P = 12 -.01 Q and TC = 90 + 2Q
Find profit max P, Q, TR, TC, profit and elasticity

Answer 1

Given :

Solution is done using profit maximization method-

"A firm maximzes it's profits at an output level where marginal revenue equates marginal cost and after that profit maximizing output level marginal cost is rising."

Total revenue (TR)

So,

Marginal revenue (MR)

So,

Marginal Cost (MC)

So,

First profit maximizing condition:  

  

  

  

  

Put Q=500 in to get value of P-------------------

P=7

Second profit maximizing condition is to check whether marginal cost increases with increase in Q after Q=500 i.e. to check whether ----------------------

Second condition is satisfied which prove that profits of the firm are maximized at P=7 and Q=500.

Put Q=500 in -----------------------

Put Q=500 in

Let elasticity be defined by and this is calculated using formula

putting values of P and MC imply

Answer : P=$7

Q=500 units

TR= $3,500

TC=$1,090

Profits=$2,410

Elasticity= -1.4