Question

 (18 points) Demand Estimation and Profit Maximization.

 Firm A usually charges $200 for its product and sells 1530 units per week.  In a market experiment it raises it price to $215 and sells 1020 units per week.  

1. (3 points)  Assuming that firm A’s demand function is linear (i.e., Q(P)=a-bP), estimate its demand function.    

2. (3 points) Firm A has fixed costs of $16,634 per week and variable costs of $147 per unit.  What is its cost function?  

3. (3 points)  What is firm A’s profit function?  

4. (3 points)  Calculate the profit maximizing quantity, Q^*, that firm A should produce  

5. (3 points)  Calculate the profit maximizing price that firm A should charge

  6. (3 points) Calculate profits at the profit maximizing price