1. You are a manager working for Omni Consumer Products. Omni is a monopolist in the market for security devices and its marginal cost is zero for any quantity.  Omni faces a linear demand curve (i.e. the quantity demanded for its product is QD  = a − bP for some positive parameters a and b, where P is the price).  Omni is considering four possible prices for its product: P1 , P2 , P3 , and P4 . The quantity of Omni’s product that would be demanded is Q1  at price P1 , Q2  at price P2 , Q3  at P3 , and Q4  at P4 . It has been estimated that the price elasticity of demand is −2 at Q1 , − 1.5 at Q2 , − 1 at Q3 , and −0.8 at Q4 .

(a)  (2 marks) For each of the four prices P1 , P2 , P3 , and P4 , classify demand according

to its elasticity (e.g. elastic, inelastic) at the corresponding quantity demanded.

(b)  (2 marks) How do the four prices P1 , P2 , P3 , and P4  relate to each other? That is: state which price is the highest, which is the second highest, the third highest, and the smallest. Explain your answer.

(c)  (5 marks) Is Omni maximising its profits by setting the price to be P1 ? If so, explain why. If not, state how Omni can increase its profits.

(d)  (6 marks) If Omni is choosing only among the prices P2 , P3 , and P4 , what price would you advise Omni to choose? That is, which of these prices is associated with the highest profits? Explain your answer.

(e)  (2 marks) Assume that Omni follows your advice from part (d) and selects the price you recommended. What is the highest total fixed cost that allows Omni to enjoy non-negative economic profits?

(f)  (8 marks) In this part, Omni is free to choose any price.  After setting its price to the profit-maximising price level, Omni experiences an unexpected rise in the wage rate and its marginal cost increases. It now equals e for any quantity, where e is a small positive number. How does the increase in marginal cost affect Omni’s profit- maximising price:  does it increase or decrease?  Answer the same question for its profit-maximising quantity and its profit. Carefully justify your answers.

2. Under the Rug is a house-cleaning firm that uses only one input: labour. Under the Rug works with a large number of casual workers and can change the amount of labour em- ployed instantaneously. The market for house-cleaning services is perfectly competitive. Every day, Under the Rug incurs an administrative cost covering insurance, government registration costs, and membership fees for various professional associations. That cost is $60 and it is independent of the number of houses serviced. Under the Rug’s daily wage bill as a function of the number of houses cleaned in a given day is summarised in the table below. Under the Rug has no other costs.

(a)  (4 marks) Calculate Under the Rug’s short-run marginal cost, average variable cost, average fixed cost, and average total cost for each quantity between 1 and 6.

(b)  (3 marks) At what price in the market for cleaning services will Under the Rug earn exactly zero economic profits? Explain why.

(c)  (4 marks) What is the minimum price in the market for cleaning services at which Under the Rug will clean at least one house daily?  At what prices will Under the Rug shut down? Explain why.

(d)  (4 marks) Derive and draw the short-run supply curve of Under the Rug.  Explain how you arrived at your answer.

(e)  (3 marks) If the market price for house cleaning is $40, what is the profit-maximising number of houses cleaned by Under the Rug and what profits will it have?

(f)  (4 marks) Assuming that all firms in the market for house-cleaning services are identical and face the same cost schedule, what will the price of house-cleaning services be in the long-run equilibrium?   How many houses will Under the Rug clean? Explain your answer.

(g)  (3 marks) Continuing to assume that all firms in the market are identical, how many firms will operate in the house-cleaning market in the long run if daily inverse demand in the market is P  = 250 − QD /4 (where P is the price and QD   is the quantity demanded in number of houses to be cleaned)?

3. Crusty’s is a pizzeria with the following cost structure: its total fixed cost is $1200 per day, its total variable cost for producing q pizzas is  , and its marginal cost is  . The daily quantity demanded for Crusty’s pizzas is QD  = 900 − 30P, where P is the price of a Crusty’s pizza. The market for pizza is monopolistically competitive.

(a)  (3 marks) Explain which features of the market for pizza lead to its being monopo- listically competitive.

(b)  (7 marks) What are the profit-maximising quantity of pizzas that Crusty’s will pro- duce, the price it will charge, and its profits?

(c)  (2 marks) Does Crusty’s have market power? Explain how you know.

(d)  (3 marks) Is the market for pizza in a long-run equilibrium?  Explain why or why not.

(e)  (10 marks) Changes in the market for pizza cause the demand curve that Crusty’s is facing to change to QD  = 800 − 50P . What are the profit-maximising quantity of pizzas that Crusty’s will produce, the price it will charge, and its profits? Assuming that all pizzerias have the same costs and face identical demand, is the market for pizza in a long-run equilibrium? Explain why or why not.