Answer to Question #207824 in Microeconomics for Shahjan hosen

Question

Total revenue and cost function of competitive firm are as follows

R=1400Q

C=Q^3-60Q²+1500Q+1800

1. Calculate the amount of profit contribution.
2. What is break-even level of output?
3. Determine the output level corresponding to 500 unit profit.

Answer 1

Solution:

1.). Amount of profit contribution:

Profit contribution = TR – VC

TR = 1400Q

VC = Q³ - 60Q²+1500Q

First determine Q:

Set MR = MC

MR = 1400

MC = 2Q² - 120Q + 1500

1400 = 2Q² - 120Q + 1500

Q = 59

Profit contribution = 1400(59) – (59³ – 60(59²) + 1500(59)

Profit contribution = 82,600 – 85,019 = (2,419)

 

2.). At break-even: TR = TC

1400Q = Q³ - 60Q²+1500Q + 1800

Q = 7 units

 

3.). Output level corresponding to 500-unit profit:

1400Q = Q³ - 60Q²+1500Q + 1800 + 500

Q = 8 Units

 

Output level corresponding to 500-unit profit = 8 units