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3. Suppose the Clean Springs Water Company has a monopoly on bottled water sales in California. If the price of tap water increases, what is the change in Clean Springs' profit-maximizing level of output, price, and profit? Explain in words and with a graph.

I would think that the output, price, and profit would increase. Since tap water being a substitutes to bottle water has a price increase. For the graph wouldn't the demand curve shift upward and where the MR curve and MC curve intersects would be shifted to the left.

2. Suppose that a natural monopolist was required by law to charge average total cost. On a diagram, label the price charged and the deadweight loss to society relative to marginal-cost pricing.

For 3) you are correct on all points except that, the intersection of the the new MR curve and the firm's MC curve would be up and to the right.

2) Good tough question. A graph will answer the questions. Start by drawing a demand curve and MR curve.
Now draw in an average cost curve. Because the firm is a natural monopoly, the average cost curve should be constantly declining over most, if not all, of the relevent possible outputs. (HOWEVER, trust me, the analysis will be much simplier if the AC curve has a minimum point somewhere under the demand curve.) Now draw a MC curve. The MC should be cut the AC curve at the AC's minimum point, and should continue to rise and cross the demand curve.

Do the standard monopoly model analysis, find the optimum quantity and price.

Now the tricky part. I interpret the phrase "required to charge ATC" means the monopolist must charge where ATC crosses the demand curve. Plz repost if your interpretation is different from mine. This point defines the final price and quantity. Deadweight loss becomes the triangle-looking area a) below MC, but b) above demand.

I hope this helps.
lotsa luck.

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