Case Problem:

General Remark: You should limit yourself to the price/cost/quantity that appears in the table.

Except for Step 11, all the answers should be numbers only.

Background: Fireland County has two industries.

The first industry contains many power plants.

The power plants are identical and provide perfectly substitutable electricity used only by the

second industry. The second industry has only one firm, Cloud.ai. Cloud. ai takes electricity as

input and provides cloud computing services. Cloud.ai has substantial market power and faces a

downward-sloping demand curve.

Part 1: Fill in the table below

Step 1. The demand for Cloud.ai's service is given in the spreadsheet (attached). To produce one

unit of service, Cloud.ai has to input one unit of electricity (and that is the only cost). Suppose

the current electricity price is $4 per unit, answer the questions below:

1) What is the optimal price for Cloud.ai's service?

2) What is the corresponding marginal revenue?

3) What is the optimal quantity for Cloud.ai?

4) What is the Profit for Cloud.ai?

Step 1 Table: Cloud.ai production

Quantity	Price	Elasticity	MR	TC	MC	Profit
0	$10.00
400	$8.00
420	$7.90
440	$7.80
460	$7.70
480	$7.60
500	$7.50
520	$7.40
540	$7.30
560	$7.20
580	$7.10
600	$7.00
620	$6.90
640	$6.80

Step 2. Please fill in the table below

Curently, all power plants use coal as input. The cost structure of each coal plant

Is given in the spreadsheet (attached). Answer the following questions:

1) Given the cost structure, what is the minimum average cost?

Step 2 table: Fire plant production

Quantity	Fixed Cost	Variable Cost	Total Cost	Average Cost	Marginal cost
0	$40.0	$ -
5	$40.0	$7.5
10	$40.0	$20.0
15	$40.0	$37.5
20	$40.0	$60.0
25	$40.0	$87.5
30	$40.0	$120.0
35	$40.0	$157.5
40	$40.0	$200.0

Step 3. Please fill in the table below

We now consider the equilibrium. Assume that when Cloud. ai chooses a price-quantity pair to produce, the electricity market instantaneously reaches long term equilibrium (coal plants freely enter and exit). Now, answer the following questions:

1) Since the electricity market reaches a long-term equilibrium, the electricity price is determined solely by the technology of the coal plant. What is the electricity price equal to?

2) Given this electricity price, What is the optimal quantity for Cloud.ai?

3) Finally, what is the number of coal plants?

Step 3 table: Cloud.ai production

Quantity	Price	Revenue	TC	MC	Profit
0	$10.00
400	$8.00
420	$7.90
440	$7.80
460	$7.70
480	$7.60
500	$7.50
520	$7.40
540	$7.30
560	$7.20
580	$7.10
600	$7.00
620	$6.90
640	$6.80

Step 4. Welfare analysis. (Consumer surplus calculation formula given below)

It costs the Fireland County government $3/unit of electricity to clean up the pollution caused by the coal plants. Given the equilibrium that we calculated in Step 3, answer the following:

1) What is the profit for the coal plants?

2) What is the profit for Cloud.ai?

3) What is the consumer surplus?

(Please refer to the consumer surplus calculator in the spreadsheet. Simplify put the optimal quantity of Cloud.ai to the calculator.)

4) What is the environmental cost to clean up?

5) If we define the total surplus as "the sum of all the profits" plus "consumer surplus" minus "cleaning cost," what is the total surplus?

Welfare analysis - Consumer surplus calculator

CS_Quantity
Consumer Surplus	CS_Quantity*(CS_Quantity/400)
Total Surplus	Coal plant profit + Cloud.ai profit + Consumer surplus + Environmental cost

Part 2

The Fireland County government has decided to incentivize coal plants to transform into solar plants. The cost structure of a solar plant is given in the spreadsheet.

Step 5 Please fill in the table below:

The cost structure of each solar plant is given in the spreadsheet. Answer the questions below.

1) Given the cost structure, what is the minimum average cost?

The Clean Air Act provides a dollar amount rebate to Cloud. ai when Cloud.ai sells certified

products manufactured using clean energy. Specifically, if the rebate is $A, then when a

consumer pays $P, Cloud.ai receives $P+$A.

For example, to sell the quantity of 400, the price to charge to the consumer is $10, as seen in

Step 2. With the rebate of $3, the revenue per unit ("the effective price") for Cloud.ai is $10+$3=$13.

Step 5 Table: Solar Plant Production

Quantity	Fixed Cost	Variable cost	Total cost	Average Cost	Marginal Cost
0	$90.00	$ -
5	$90.00	$7.5
10	$90.00	$20.0
15	$90.00	$37.5
20	$90.00	$60.0
25	$90.00	$87.5
30	$90.00	$120
35	$90.00	$157.5
40	$90.00	$200.0

Step 6. Please fill in the table below

Assume that the current rebate is $3. We consider the equilibrium when Cloud.ai buys electricity from solar plants. Same as in Step 3, when Cloud.ai chooses a price-quantity pair to produce, the electricity market instantaneously reaches a long-term equilibrium (solar plants freely enter and exit). Answer the questions below:

1) Since the electricity market reaches a long-term equilibrium, the electricity price

is determined solely by the technology of the solar plant. What is the electricity price equal to?

2) Given this electricity price and the government program, what is the optimal quantity for

Cloud.ai?

3) Finally, what is the number of solar plants?

Step 6 Table: Cloud.ai energy production

Government incentives	rebate	$3.00
Quantity	Effective price	Revenue	MR	TC	MC	Profit
0
400
420
440
460
480
500
520
540
560
580
600
620
640

Step 7. Given the equilibrium that we calculated in Step 6,

1) What is the profit of the solar plants?

2) What is the profit for Cloud.ai?

3) What is the consumer surplus? (Again, use the calculator.)

4) What is the cost of the program to the government?

5) If we define the total surplus as "the sum of all the profits" plus "consumer surplus" minus "the program cost for the government", what is the total surplus?

Step 7 table : Welfare analysis.

CS_Quantity
Consumer Surplus	CS_Quantity*(CS_Quantity/400)
Total Surplus	Solar plant profit + Cloud.ai profit + Consumer surplus + Government cost

Step 8. Comparing its profits between Step 3 and Step 7, will Cloud.ai switch the technology from coal to solar?

A. Yes.

B. No

To obtain a higher total surplus, which rebate level will the Fireland County goverment choose?

A. $O.

B. $3.

Part 3

The Fireland County government tries to find the optimal policy under different objectives.

Step 9. Suppose the goal is to minimize government spending while incentivizing Cloud.ai to switch to clean energy. Then,

A) What should the government set the rebate per unit equal to?

Step 10. Suppose the goal is to maximize the total social surplus via changing the rebate. Then, what should the government set the rebate per unit equal to?

Suppose the government is now considering offering a more complicated incentive scheme: a percentage credit and a dollar amount rebate per unit. When the credit is A % and the rebate is $B, if the consumer pays $P for one unit of the Cloud.ai service, Cloud.ai receives (1+A%)*$P+$B per unit.

Step 11. Suppose the goal is to minimize the government spending under the constraints that (i) Cloud.ai will switch to the clean energy and (ii) Couldai's production level is no less than the one in Step 9. If both the credit and rebate must be non-

negative, which one of the following is correct?

A. The government should only use the percentage credit.

B. The government should only use the dollar rebate.

C. The government should use both the percentage credit and dollar amount rebate.

D. The choice between the percentage credit and dollar rebate does not matter. Only the

difference between the consumer's payment $P and Cloud.ai's revenue (1+A%)*$P+$B matters.