Energy Engineering - Energy Economics

Natural monopoly

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Question 1. In a natural monopoly, a firm serves two groups of customers with different demand profiles. For group 1, the demand curve is: p1=10 -q1 For group 2, the demand curve is: p2=8-8q2 The total cost function for the utility is TC(q 1,q2)=100+2q 1+2q 2 The price set by the monopolist are p 1=5 and p 2=4. Do these prices meet the second best Ramsey solution? Question 2. A electricity utility serves two groups of customers with different dema nd profile. For group 1, the demand curve is: p1=10 0-q1 For group 2, the demand curve is: p2=60 -q2/2 The total cost function for the utility is TC(q 1,q2)=100+2q 1+2q 2 An independent agency wants to meet a breakeven constraint to encourage a firm to produce for both types of consumers . What should be the price s in this case? What is the welfare in this case? Demonstrate that the welfare is the maximum possible if prices are linear (i.e. without any 2 parts tariff) . Question 3. A monopolist faces a demand curve: p= 300 -5q. The total costs function is TC(q)= 100 0+5q2. Determine the price and quantity at the equilibrium. Quantify the deadweight loss and the monopolist profit. How your answers change if the monopolist introduces a two part tariff if you know that the monopolist has 100 customers ? Question 4. The demand for electricity is Q d =5 -Pp in peak periods and Q n =4 -2P n in off -peak periods. Variable cost is 0.25 per unit of output per period and capital cost capacity are 0.75 per unit of capacity per day. Capacity costs are sunk and cannot be adjusted between periods. (a) Find the optimal capacity, peak price and off -pea k price if the firm sets the prices. (b) Find the optimal capacity, peak price and off -peak price if an independent agency sets the prices. (c) Compare the welfare in the two cases. Consider a market with market demand given by function: p(q) = 10 – 2q. In this market there is one single firm with a Total Cost ( TC ) function equal to: TC (q) = 4q+q 2. • What is the market equilibrium (price and quantity)? Illustrate your answer graphical ly. • How the welfare changes after a tax is imposed on the firm, equal to t = 3 for each unit of quantity produced. Firm 1 produces a clean good, x, and firm 2 produces a polluting one, y, associated with 1 unit of harmful emissions for any unit of good produced. The total cost functions of the firms are: ������ (�)=5 �+2 �2 +�2 ������(�) = 4 � + 3 �2 Assuming perfect competition, the market prices of the two goods are px = 21 and py = 40. Find the profit maximizing quantities for the two firms, x* and y* . Calculate the welfare in this case. How the answer changes , if firm 2 pay s firm 1 for any emission ?