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:

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 2. 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 3. 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 4. 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 sprcadsheet. 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?

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. 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 6. 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 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 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

Remark: Prefilled tables are not provided for this part. To facilitate answering the questions you

may answer with your own tables in tab "Extra sheets for Part 3". If you wish to create the demand

curve beyond the given data points, please maintain the assumption that the demand is linear.

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.

Step 1: Cloud.ai production Step 2: fire plant production Step 5: solar plant production Quantit Fixed Variable Average Variable Average Marginal Quantity Price Elasticity Revenue MR TC MC Profi Cost cost Total Cost Cost Marginal Cost Quantity Fixed Cost cost Total Cost Cost Cost 0 $10.00 $ 40.0 $ 30.0 $ - 400 $ 8.00 40.0 7.5 90.0 7.5 420 $ 7.90 40.0 0.0 90.0 $ 20.0 0 $ 7.80 40.0 37. 90.0 $ 37.5 460 $ 40.0 60.0 90.0 60.0 $ 7.60 $ 40.0 87.5 90.0 87.5 500 $ 7.50 $ 40.0 120.0 90.0 120.0 520 $ 7.40 $ 40.0 157.5 90.0 $ 157.5 $ 7.30 40 $ 40.0 $ 200.0 90.0 $ 200.0 560 $ 7.20 580 $ 7.10 600 $ 7.00 620 $ 6.90 Step 6: Cloud.ai clean energy production 640 $ 6.80 Step 3: Cloud.ai production Governemnt incentives rebate $ 3.00 Quantity Price Revenue TC MC Profi Quantity Effective Price Revenue MR MC Profit $ 10.00 400 $ 400 420 $ 7.90 420 140 $ 7.80 440 460 $ 7.70 460 480 $ 7.60 480 500 $ 7.50 500 520 $ 7.40 520 540 $ 7.30 540 560 1 $ 7.20 560 580 $ 7.10 580 500 $ 7.00 600 6.90 620 640 $ 6.80 640 Step 4: Welfare analysis Step 7: Welfare analysis Consumer surplus calculator Consumer surplus calculator Quantity Quantity er Consumer surplus surplus Coal plant profit Solar plant profit Could. ai profit Could. ai profit Consumer surplus Consumer surplus Enviromental cost Government cost Total surplus Total surplus