Price Quantity Demanded

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Q1. Illustrates the market for chocolate bars has the following demand and supply
schedules: [1.5 Marks]

Price Quantity Demanded Quantity Supplied
$3 111 26
$4 100 53
$5 80 80
$6 64 92
$7 51 111
$8 37 120

a. Graph the demand and supply curves. What is the equilibrium price and quantity in this market?
b. If the actual price in this market were above the equilibrium price, what would
drive the market toward the equilibrium?
c. If the actual price in this market were below the equilibrium price, what would
drive the market toward the equilibrium?

Q2. Illustrates the market for pizza is characterized by a downward-sloping demand curve
and an upward-sloping supply curve. [1.5 Marks]
a. Draw the competitive market equilibrium. Label the price, quantity, consumer
surplus, and producer surplus. Is there any deadweight loss? Explain.
b. Suppose that the government forces each pizzeria to pay a $1 tax on each pizza sold. Illustrate the effect of this tax on the pizza market, being sure to label the consumer surplus, producer surplus, government revenue, and deadweight loss. How does each area compare to the pre-tax case?
c. If the tax were removed, pizza eaters and sellers would be better off, but the
government would lose tax revenue. Suppose that consumers and producers voluntarily transferred some of their gains to the government. Could all parties (including the government) be better off than they were with a tax? Explain using the labeled areas in your graph
Q3. Suppose that a market is described by the following supply and demand equations:
[2 Marks]
QS = 2P
QD = 300 – P
a. Solve for the equilibrium price and the equilibrium quantity.
b. Suppose that a tax of T is placed on buyers, so the new demand equation is
QD = 300 – (P + T).
Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?

c. Tax revenue is T X Q. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 300.
d. The deadweight loss of a tax is the area of the triangle between the supply and
demand curves. Recalling that the area of a triangle is 1 ⁄2 x base x height, solve for deadweight loss as a function of T. Graph this relationship for T between 0 and 300. (Hint: Looking sideways, the base of the deadweight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.)
e. The government now levies a tax on this good of $200 per unit. Is this a good
policy? Why or why not? Can you propose a better policy?

 

Sample Solution

Ability to charge each cell up to its maximum safe voltage and discharge it down to its minimum safe voltage limits the battery pack capacity. Cell tolerance in the manufacturing processes gives them slight variations in how quickly they will charge and discharge. The BMS also balances the cells making sure that the battery pack is not limited to the capacity of the cell that gets emptied and filled quicker by using charge pumps or balancing resistors. They switch on and off to discharge off small amounts of power from small groups or individual cells and make sure that the maximum pack capacity can be exploited and not limited to the weakest cell capacity [8]. The BMS also protects the battery for example, by making sure it restricts the rate at which it is possible to charge the battery if it detects that the battery temperature is getting too high [8]. It is currently mandatory for all-electric racing motorbikes to be fitted with a BMS.

c. Electrical Machines

A typical AC motor consists of two parts; stator (with coils) and rotor. The stationary stator coils are supplied with AC current producing a rotating magnetic field and the rotor connected to the motor shaft given a torque by the rotating field as shown in figure 2 below. The stator of an induction motor is normally made from a laminated magnetic steel structure and has slots to hold the windings with each slot containing one or more copper coil conductors. These must be insulated between adjacent turns, the core and from other phases with each coil then connected to one of the three phases. Coils of the same phase are normally connected in series and depending on the direction of connection current can be reversed. For a 3-phase motor, the winding may be star or delta connected with the ends of the three windings terminated in the terminal box where 3-phase A.C. supply will be connected. The rotor construction can either be squirrel cage or wound rotor, but wound rotors can be expensive to manufacture hence they are hardly used in industrial applications.

Figure 4: 3 Phase Induction Motor
For a given power rating, the volume and therefore weight of an electric motor are proportionately reduced. This combined with the desire to reduce unsprung mass on the vehicle suspension dictates using a high-speed motor, coupled to the rear wheel via some mechanical reduction gearing [7]. The UoN racing electric motorbike uses a 3 phase GVM Parker Hannafin permanent magnet motor which can reach speeds of up to 10,500Rpm as shown in figure 1 [9]. Other motor models could have been chosen but the GVM motors from Parker are specifically dedicated for Mobile applications and specially designed for rugged atmospheres and harsh environments for traction, pump, auxiliaries, and steering. These motors are brushless synchronous servomotors, with permanent magnets which are made of rare e

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