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Question 1

Answer see lecture notes

(a) Explain the different scenarios that the International Energy Agency use in their World Energy Outlook. (4 marks)

(b) What has the impact of the COVID-19 pandemic on world energy demand. Briefly explain the IEA’s sustainable recovery plan. (5 marks)

(c) Explain why demand for electricity is expected to increase faster than overall energy demand over the next three decades. Why does it increase faster in the Sustainable Development Scenario compared to the Stated Policy scenario? Investment in Electricity flexibility is expected to be higher than investment in new capacity. Explain what flexibility is and why so much investment is needed for this. (6 marks)

(d) Describe current market conditions of the world oil market. What are the key drivers of supply currently? What are the key drivers of demand going forward? Explain why oil demand is expected to decrease steadily until 2050 in the Sustainable Development Scenario.          (5 marks)

Question 2 (20 Marks)

Consider a monopoly owner of a mine which can operate for two periods. Total mining costs are TC=50q₀ in the first period and TC=50q₁ in the second period  and the market demand curve is p_t =500-50q_t. There are 6 units of the resource R₀ to allocate across the two periods. The interest rate is r = 0.1.

i. Write down the Hotelling rule for the mining amounts q_t for a Monopoly. (2 marks)

MR1-MC1=(1+r)(MR0-MC0)

ii. Calculate the optimal mining amounts q_t , the prices p_t for both periods and the present value of the total profits. Comment on your results                                                                                     (8 marks)

(500-100q1-50=1.1(500-100q0-50)

(450-100(6-q00))=505-110q0

Q0=3.12, q1=2.88,

P0=344, p1=356

PV=Sum[(p-MC)/(1+r)^t]=(344-50)*3.12+(356-50)*2.88/(1.1)=1718

Comment: Scarcity forces Monopoly to mine less than they would like. Without scarcity they would mine MR=MC each period = 500-100q=50 q=4.5 each period. Profits are higher [2 marks for this]

iii. What is the mining path with R₀=20.  Would the present value of the profits of the monopolist increase if R₀ increases to 20 units. Explain why or why not? (2 marks)

See above

iv. Suppose now the government introduces a tax of $100 per unit. Calculate the new mining path and present value of the profits.  Does the profit increase or decrease (compared to ii)? Explain why.                                                                                                    (8 marks)

Hotelling is now (500-100q1-50-100)=1.1(500-100q0-50-100)

350-100(6-q0)=385-110q0

-250+100q0=385-110q0

Q0=3.02, q1=2.98

P+tax=500-100q, p=400-100q, p0=…….

Profits will be down as government takes a substantial proportion with the tax.

Question 3

Suppose in an electricity market the power generation plants have the following capacities and cost structure

Type	MC ($MWh)	Capacity (MW)	Fixed Cost
Hydro	0	3000	60
Coal	40	2000	40
CC Gas	120	1000	20
Gas Peaker	220	500	10

(a) Draw the competitive supply curve for the production of electric energy on this system (2 marks)

First 3000MW at price =zero

Next 2000MW at price of 40 and so on

(b) Assume that demand is 2500 Mw and is completely price inelastic in the very short run. What would be the spot price be in a perfectly competitive wholesale electricity market?                                          (2 marks)

P=0

(c) Assume that demand is 4000 Mw and is completely price inelastic in the very short run. What would be the spot price be in a perfectly competitive wholesale electricity market?                                                        (2 marks)

P=40

(d) Assume that demand equation is Q=7000-0.5p. Draw the demand and supply curves. What is the competitive market price?                                                                (6 marks)

Supply curve is vertical at q=6500

So 6500=7000-0.5p

p/2=500. P=$1000/MWh

(e) Now find the optimum capacity mix if demand can be curtailed at a price of $5000 if the base of the demand curve is above 6000MW. The load duration equation for the base of the demand curve is d(s)=6000-4000s (8 marks)

Hydro coal have 60=40+cf*40

Cf=0.5, so d(0.5)=4000MW =hydro

Coal/gas cf=0.25 so coal capacity=1000MW

Gas/peak=0.1, so peaker cap=600MW

10=dps(5000-220)

Dps=0.0021

D(0.0021)=5991.6 so peaker cap= 5991.6-5600=391.6MW

Question 4

(a) Explain why Geoff Bertram describes the NZ electricity market reforms - which saw a transition from a state controlled vertically integrated electricity system to the present market structure as a “failing experiment”. (10 marks)

See notes

(b) The New Zealand electricity market has a “dry year” problem. Explain what is meant by this and what key features of the New Zealand electricity market give rise to this problem. (4 marks)

Much of NZ generation is hydro (around 60%). Storage lakes have limited capacity (about 6 weeks at normal operation). NZ market isn’t connected to other markets so reliant on own generation. Lakes are generally low in winter as much precipitation falls as snow. If the inflows are low leading up to winter there may not be enough storage for normal operations. In this case water is scarce and the price of electricity goes up and more thermal generation. If this continues there is a danger that rationing may be needed

(c) The New Zealand Government recently completed an Electricity Price Review. Explain why they thought it was needed. And describe two of their recommendations. An economist from the University of Auckland suggested that market power was one reason why prices are high. Briefly explain his approach. Why did the Electricity Price Review disagree with his findings?    (6 marks)

Electricity prices for residential customers have gone up dramatically –around 59% in last 20 years. Recommendations various answers. The Economist used an computer agent based model to calculate profits compared to a competitive model and found these were substantial. The EPR suggested that it was better to look at long run marginal costs and concluded there were no market power problems.

Question 5

Suppose that the sustainable harvest for a fishery depends on the effort level E as follows:

Y(E)=10E-0.1E² where Y(E) is the sustainable fish harvest measured in tonnes. The price of

fish is $200/tonne and the unit cost of harvest is $800 per unit of effort.

(a)  Find the open access equilibrium (that is E and Y).  Use a suitable diagram to show the open access equilibrium. (6 marks)

Open access TC=TR

800E=200(10E-0.1E^2)

4=(10-0.1E), E=6/.1=60. Show revenue curve which has maximum at 10-0.2E=0 E=50, equals zero at E=0, and 100

Diag shows where straight line of TC intercepts the revenue curve to the right of max.

(b)  The government decides they will manage the fishery so that sustainable harvest is the maximum possible. Calculate what this harvest level is. (2 marks).

Maximum is when E=50, Y=250

They decide to use a catch limit for the fishery equal to the maximum sustainable harvest. The fishing season finishes as soon as the catch limit is reached. Explain what is likely to happen and why this an inefficient policy. Illustrate using a suitable diagram. (3 marks)

There will be a race to get catch which pushes osts up until TC=TR at E=50. TC line swivels to the left

(c)  A policy advisor to the government explains that a tax on effort is a better policy to achieve the government’s aim in (b) above. Calculate what the tax should be.                           (3 marks)

Need (800+t)E=200Y(E)

At E=50 Y€=250

So 800+t=200*250/50

800+t=1000

T=200

(d)  The policy advisor argues that it is possible to achieve further efficiency gains with a different tax. What is the tax they suggest and what is the efficiency gain compared to (c) above?  (6 marks)

Most efficient is when MR=MC which is E=30, tax should be $600

Question 6

(a) Suppose there are two sectors in the NZ economy –transport, electricity and agriculture. The marginal abatement cure for transport is MAC_T=10X_T and for electricity it is MAC_E=5X_E. Initial emissions for electricity are 10 Mt, and for transport 30Mt. Total emissions are 40Mt. X is emission reductions for the different sectors.

(i)Derive and draw the economy wide marginal abatement curve. [hint. remember the most any sector can abate emissions is up to total initial emissions]. Note points of interest on your graph.                             (5 marks)

Up until XE=10 we have X=XE+XT=MAC/10+MAC/5=3MAC/10

MAC=10X/3

After XE=10 or MAC=50 and X=15

have X=10+MAC/10

MAC=10X-100

(ii) What carbon tax would be needed to ensure a 75% reduction in emissions?    (2 marks)

If X=30 then MAC=200 which is the carbon tax needed

(iii) What is the abatement for each sector to achieve for the this 75% reduction in emissions. (2 marks)

If MAC =200 XE=10

And XT=200/10=20

(iv) Calculate the total cost of this 75% reduction in emissions.                                  (2 marks)

TC=area under curves for electricity =0.5*10*50=250 for transport =0.5*200*20=2000

Total =2250

(v) Suppose the government decided that each sector had to achieve a 75% emission cut. So electricity emissions would be abated by 7.5Mt and transport would abate by 22.5Mt.  Calculate the total costs for this policy.                                                                       (2 marks)

At XE=7.5 MAC =5*7.5=140.625

At XT=22.5, MAC=225 =2531.25 total=2672

(vi) What is the difference in total costs between (iv) and (v). Comment on your results.                (2 marks)

Difference =422. The most efficient abatement uses up as much cheap abatement as possible which is XE=10 then the rest with more expensive transport

(vii) Now suppose that an analysis of the marginal benefits for carbon emission abatement is   MB=560-10X. Calculate the optimum amount of abatement, the carbon tax which would ensure this level of abatement and illustrate with a diagram.                  (5 marks)

560-10X=10X-100

20X=660, X=33