Problem 1: Suppose that a firm has a demand function of P = 100 - 0.01Q and a total cost function of TC = 50Q + 30000 ($)

1. What are functions of total revenue (TR), marginal revenue (MR), marginal cost (MC), variable cost (VC), average variable cost (AVC), fixed cost (FC), average fixed cost (AFC), and average total cost (ATC)?

2. Identify quantity and price to maximize total revenue? What is the maximum total revenue (TR max)?

3. Identify optimal output level (Q* ) that give the firm maximum profit ? What is maximum profit of the firm?

4. Assume that the government imposes a tax of 10$ per unit sold, identify optimal output level (Q* ) and price level (P*) that give the firm maximum profit ?

Problem 2: A monopolist has total cost function of TC= Q2 + 40 Q + 8000, and demand function of P= 500- Q

a. What is price and optimal output level that gives this firm maximum total revenue and maximum total profit? Calculate maximum total revenue and maximum total profit of the firm?

b. What is Lener indicator (L) to measure market structure ? What is dead weight loss (DWL) created by this monopolist?

c. Identify consumer surplus (CS), Producer surplus (PS) at the optimal output level?

d. What is price level to maximizes quantity without loss?

e. Draw a graph to show the above results.