Question 1) The demand for petrol in NZ is given by Q_D=150-25P and supply is given by Q_S=60+20P . Price is in dollars per litre and quantity is in million litres per year. Calculate the equilibrium market price and quantity. [2 marks]

Equilibrium condition:

Q_D= Q_S  

150-25P= 60+20P

150-60= 20P+ 25P

150-60= 20P+ 25P

90= 45P

P=90/45  

P=2

Putting P = 2 in supply equation

Q_S=60+20P

Q_S=60+20(2)

Q_S=60+40

Q_S=100

Equilibrium market price is 2 and equilibrium market quantity is 100.

Now assume that government imposes a tax on supply of $1 per litre. Calculate the impact of the $1 petrol tax on:

The price consumers pay & the change in quantity. [2 marks]

Since government imposes $1 tax in supply:

P^*=P-1

Where,

P = market price

P* = price suppliers receive

t = tax suppliers pay

Q_S=60+20(P-1)

Q_S=60+20P-20

Q_S=40+20P

Now again applying equilibrium condition,

Q_D= Q_S  

150-25P= 40+20P

150-40= 20P+ 25P

150-40= 20P+ 25P

110= 45P

P=110/45  

P=2.44

Putting P = 2.44 in supply equation

Q_S=40+20P

Q_S=40+20(2.44)

Q_S=40+48.89

Q_S=88.89

Now, the consumers pay 2.44 and change in quantity is 88.89.

Annual revenue from the tax. [2 marks]

TR=Tax Revenue=Q ×t

TR= 88.89 ×1

TR= 88.89

The deadweight loss arising from the tax. [2 marks]

Deadweight loss=1/2  ×change in price ×change in quantity

Deadweight loss=1/2  ×(2.44-2) ×(100-88.89)

Deadweight loss=1/2  ×(0.44)×(11.11)

Deadweight loss=1/2  ×(4.8884)

Deadweight loss=2.4442

Illustrate your results using a suitably labelled graph. [2 marks]

Question 2) The demand for gas is Q_D=150-25P. The supply of gas is

Q_S= 60+20P

P of Gas = 2

Q_s  of Gas = 100

Suppose the government imposes a price ceiling of $1 in the market.

What is the size of the shortage in the market with the price ceiling? Calculate the producer surplus. [2 marks]

If the ceiling price is $1, consumers demand 120 units of Gas, but producers supply 80 units of gas only. The excess demand or size of shortage is 40 units of gas that is represented by horizontal distance in the above figure between W and X.

size of shortage=X-W

 size of shortage=120-80

size of shortage=40

The producer surplus is represented by triangular area i.e. above the supply curve and below the $1 ceiling price. The area of producer surplus is represented as SWZ:

producer surplus=1/2  ×80 ×(1-0.2)

producer surplus=1/2  ×80 ×0.8

producer surplus=1/2  ×64

producer surplus=32

Calculate the consumer surplus, assuming that gas is purchased at $6. [2 marks]

consumer surplus=1/2  ×80 ×(2.4-1)+1/2  ×80 × (6-2.4)

consumer surplus=56+144

consumer surplus=200

Calculate the net benefits of the price ceiling. [2 marks]

net benefit=producer surplus+consumer surplus

net benefit=32+200

net benefit=232

Calculate the deadweight loss. [2 marks]

Consumer surplus =1/2  ×100 ×(6-2) 

Consumer surplus =1/2  ×400 

Consumer surplus =200 

producer surplus =1/2  ×100 ×(2-0.2)

Consumer surplus =1/2  ×180

Consumer surplus =90

net benefit=producer surplus+consumer surplus

net benefit=90+200

net benefit=290

deadweight loss=net benefit before ceiling-net benefit after ceiling

deadweight loss=290-232

deadweight loss=58

Illustrate your results using a suitably labelled graph. [2 marks]

Question 4) The market demand for petrol is  Q=339-P where P is cents per litre and Q is millions of litres. There are two petrol retail outlets (X & Z), each has constant marginal cost and average cost of 147 cents per litre.

Marginal Cost=MC=147

Average Cost=AC=147

If X & Z is a monopoly, calculate the profit maximising output and market price. Illustrate your result in a suitably labelled diagram. [5 marks]

Q=339-P

From Above

P=339-Q

In monopoly market

P=MR

MC  = 147

Equilibrium condition:

MR=MC

339-Q=147 

339-147=Q

192=Q

Q=192

Putting Q into monopoly demand equation

P=339-Q

P=339-192

P=147

Profit maximization output is 192 and market price is 147

Now assume the market is a duopoly, firm X and firm Z. Find the Nash-Cournot equilibrium and illustrate your results in a suitably labelled graph. [10 marks]

P=339-Q

C1 = 147

C2 = 1477

P=339-(q1+q2)

TR=[334-(q1+q2)]  ×q1

= (334-q1-q2)  ×q1

=334q1-〖q1〗^2-q1q2

π_1=334q1-〖q1〗^2-q1q2-q1

∂π1/∂q1  =334 – 2q1 – q2 – 1

=333-2q1-q2

2q1=333-q2

q1=(333-q2)/2

q1=166.5-0.5q2

TR2=[334-(q1+q2)]  ×q2

= (334-q1-q2)  ×q2

=334q2-q1q2- 〖q2〗^2

TR2=334q2-q1q2-q2^2

π_2=334q2-〖q2〗^2-q1q2-q2

∂π2/∂q2  =334 – 2q2 – q1  – 1

=333-2q2-q1

2q2=333-q1

q2=(333-q1)/2

q2=166.5-0.5q1

Putting q2 in q1

q1=166.5-0.5(166.5-0.5q1)

=166.5-83.25+0.25q1

q1-0.25q1=83.25

0.75q1=83.25

q1=111

Similarly

q2=111

Equilibrium price

P=339-Q

P^*=339-111

P^*=228

In cournot-nash equilibrium output for both is 111 and price is 228.

Using the results in (a) and (b) above, and the market demand curve, illustrate the market price in the case of monopoly, duopoly, and perfect competition. Note: to derive the competitive solution assume identical firms with AC = MC. [5 marks]

Monopoly market price= 147

Duopoly market price=228

In perfect competition:

P=MC=147

Question 5) You live at 92 Grange Road, Mt Eden (of course you do not!). Dr Kiti Suomalainen at the Energy Centre has developed a solar tool for estimating the generation potential and return to investment (link below). For the questions below, do not change any of the following investment parameters: annual consumption, investment cost, value at year 15, economic life, & maintenance. You are only interested in the viability of your investment in solar./

Assuming electricity price PE = NZ$0.27/kWh, a buy-back price PB = NZ$0.08/kWh and self- consumption QS = 20%, would you invest in solar PV? Why/why not? [10 marks]

P_e=   0.27

P_b  =  0.08

Q_s=   20 %  =  0.2

Q_s  =  10 (P+  1)

0.2 =  10 (P+1)

P =  0.98

I would invest in the solar PV.

Holding PE & PB constant, is there a level of QS that would make the investment break even? Bearing in mind the solar generation profile, is this feasible? [10 marks]

C_s  =   P_e/E  =  0.27/0.08  =  3.37  

Using the results from (b) above, what size battery would improve the performance of the solar PV system? If a battery would help balance solar generated electricity with consumption what would the price of a battery have to be in order to break even? [10 marks]

The solar panels can be connected through parallel and series combination to increase the efficiency of the system. according to the results of part b it can be concluded that the balance of generated electricity consumption can be analyzed and maintained. In case of enhancing the battery capability of generating the electricity the PV system can be improved.