Question

3. A water utility has total cost function given by TC = 800 + 40Q where Q is the quantity of water sold. Suppose demand is given by P = 100 - Q. The utility is the sole provider of water. (a) What is the average total cost curve for this utility? (b) If the monopoly is unregulated, what single price will it set? (c) Show that the intersection of demand and average total cost with the largest Q occurs at Q = 40. (d) Draw this market i.e. draw the demand curve, marginal cost curve, and average total cost curve). (e) If the water utility is forced to adopt marginal cost pricing, what will its losses be? Show the losses on your diagram from part (d). (f) If the firm is forced to adopt average total cost pricing, what price would it charge? What would be its profits?

I need help mainly with d, e and f, if you can please draw a graph. Let me know if additional info is needed, thanks.

Answer 1

Given, Cost function, TC = 800 + 40Q

Demand function, P = 100 - Q

Refer the attached picture below for the values used to draw graph

MC Q 0 10 20 30 40 50 40 40 40 40 Demand ATC 100 90 120 80 80 70 66.67| 60 60 50 56 40 53.33 30 51.43 2050 10 48.89 0 | 48 60 40 40 40 70 40 80 90 100 40 40

Refer the attached picture for the graph

140 0 10 20 80 90 100 30 40 — Demand 50 60 — ATC — 70 MC

E. When the price is set equal to MC = $ 40. Then the firms will end up selling 60 units and at this output level the ATC = $ 53.33.

Loss = 60 × 40 - 60 × 53.33 = 60 ×(-13.33) = - $ 799.80

Loss = - $ 800 (Approximately).

Refer the attached picture (I am really sorry I have done this picture manually as I don't have access to graphing tool). The picture you can use for drawing the graph just for reference

140 Loss 0 10 20 80 90 100 30 40 — Demand 50 60 70 — ATC — MC

Please pardon for the manual graph.

F. If the firm is forced to charge ATC then it should charge $ 60 per unit and sell 40 units. Because at this level the ATC = Price.

Profit = 40 × 60 - 40 × 60 = 0

Please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.