02_HW_EEE598
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Apr 3, 2024
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Homework 02
EEE 598 – Electric Energy Markets Professor Kory W. Hedman
Homework 2: Due by 5pm AZ time, Tuesday, January 30. Price Takers: 1) 30 Points
There are two firms (producers) in the market and they are price takers. Total Cost Function
for firm 1: 0.3(Q
1
)
2
+ 30Q
1
+ 150
Total Cost Function
for firm 2: 0.25(Q
2
)
2
+ 40Q
2
+ 100
Each firm has a minimum capacity of 0 but no maximum capacity; note that Q stands for quantity and P below stands for price. Note that, if the unit is not producing anything, it does not incur the fixed cost (no-load cost) term.
The inverse demand curve for the market is: P = 400 – 0.9Q = 400 – 0.9(Q
1
+ Q
2
). a) What is the inverse supply curve for the entire market? When calculating this curve, make sure you account for the minimum capacity of the firms. If the price is too low, firms produce nothing, not a negative quantity. (note that you may have a non-smooth curve). Draw it.
b) What is the market clearing price for this market? What is the market quantity?
c) Calculate the Consumer Surplus (CS), the Producer Surplus (PS), and the Social Welfare (SW).
Monopoly:
2) 35 Points
Take the information from problem 1 above. Assume that these two firms now act as a monopoly (a single entity owns both units and acts as a monopoly in this market). You can assume that both units will produce.
a) What is the marginal revenue? Draw the marginal cost curve (supply curve), the demand curve, and the marginal revenue curve. b) What is the market clearing price for this market with this monopoly? What is the market quantity? Does the resulting marginal revenue equal marginal cost? c) Calculate the Consumer Surplus (CS), the Producer Surplus (PS), the Social Welfare (SW), and the Deadweight loss. Label these on your drawing from part (a) above. Page 1 of 2
Homework 02
Cournot Equilibrium:
3) 35 Points
Take the information from problem 1 above. Assume that these two firms now act based on the Cournot model. Each firm has complete information (knows the other firm’s cost curve and they know the demand curve). You can assume that both firms will be producing.
a) Calculate and write down the best response function for each firm.
b) What is the market clearing price for this market with this Cournot competition between these two firms? What is the market quantity?
c) Calculate the Consumer Surplus (CS), the Producer Surplus (PS), the Social Welfare (SW), and the Deadweight loss. Compare and comment on these values as compared to the values for problems 1 and 2.
Page 2 of 2
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