Question

In a rural county, the demand for water is QD = 1000 − 100p.

The local public utility has a total cost of C(q) = 800 + q

In a rural county, the demand for water is Q” = 1000 - 100p. The local public utility has a total cost of C(q) = 800+9 1. Explain why this company can be considered as a natural monopoly? 2. Find the profit maximizing output and price when the public utility company charges the same price to all customers. 3. Because the community thinks water should be available to all, the county decides to set a price ceiling for water. Which price of water would maximize the total surplus? What would be the quantity of water produced at that price. 4. On a graph, draw the profit maximizing solution, the socially optimal solution and the deadweight loss created by the monopoly. What are the profits or losses made by the firm in the two scenarios? 5. Because of the price ceiling, the firm is threatening to shut down. As a consequence, the county is willing to raise the price ceiling to 2$. Will the firm keep operating in this scenario? Compute the deadweight loss with this new price.

Answer 1

falls Natural monopoly occurs where average cost of products over the wide range of output. (6 - 800t a AC - 800 to 7 when I rises, the value of AC S Hence, It decreases, is = a Case 800 + of natural Monopoly. e (0) = sooth MC = d 1800+B) 8 = 1000 - 10ol 7 PP 10 - TR - (10-18 x Q. TR = 1016- 18 MR = 1o- la Me - I 100 50 UUUUUUUUU MR = MC 10-18 = I - so 7 100 P= 10- 1 x 450 3 10 - 4.5 5.5 9 = 0% 1 soxq = 450 butput would be produced at competitive е – умс To- 100" 9 = 8 = [p = tools goo 7710 DOL Monopoly profit= 5.5 - 5.5x450 - 800 - 4501 = 1225 socially optimal Mi = 900 x1 - 800-900 = 1-800 loss 750 goo DWL = - 0.5XBXH 0.5*(49)(4.5) = 110125

Farlier price Coiling was I, but now reised to $2. pe = iom - Im x2 = 100 - 200 (p=2J r= 800x2 - 800 - 800 = 1600 - 800-B 0 0 - LOT Normal profit, DWL DWL 0.5X BH = 6.5x 100 x - sol 1 MC . to 800 from will continue produce 900 firm is carning normal profit. 0