2. The magnitude of price elasticity of demand directly affects the change in income resulting from the change in prices by the producer. Let's say that the price elasticity of professional baseball tickets is 0.8 if the ticket price is between 3,000 and 5,000 , and 1.2 if the ticket price is between 5,000 and 7,000 , and 2 if it is over 7,000 .
Currently, the admission fee is 5,000. How should the admission fee be adjusted to increase admission income?

Consider a multiplicative binomial model with N = 3, r = 0, u = 1.2, d = 0.8 and S 0 = 100. At time t = 1 when S 1 = 120 a (european) call option with maturity at T = 3 and struck at 100 is quoted at 25. Is that a fair value? If yes explain why? If not explain why and explicitly define an arbitrage strategy (you have to give details of the arbitrage strategy)

Consider a multiplicative binomial model with N = 3, r = 0, u = 1.2, d = 0.8 and S 0 = 100. At time t = 1 when S 1 = 120 a (european) call option with maturity at T = 3 and struck at 100 is quoted at 25. Is that a fair value? If yes explain why? If not explain why and explicitly define an arbitrage strategy (you have to give details of the arbitrage strategy)

500 hp, 600 V, 0.8 pf leading, 6-pole, delta-connected synchronous motor has X_S = 1.2 ohm and R_A = 0 ohm. Assume motor is lossless.

(a) Calculate E_A and I_A for 400 hp, 0.85 leading pf load.

(b) What is the torque?

(c) If |E_A| is increased by 20% for the 400 hp load, what are the new values of I_A and power factor?

8. It is required to produce an illumination of 100 lux in a factory hall 30 m by 15 m. Assume that the maintenance factor is 0.8, coefficient of utilization is 0.4 and efficiency of lamp is 14 lm/W. Suggest the suitable rating, the number of lamps and their possible arrangement. The sizes of the lamps available are 100, 250, 400 and 500 W.

ANS [40 lamps of 250 W in 5 rows]

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The lens and mirror are sperated by d=1.0 m and have focal lengths of 80.0 cm and 50.0 cm, respectively. An object is placed p=1.0 m to the left of the lens as shown.

a) Locate the final image, formed by light that has gone through the lens twice

b) Determine the overall magnification of the image.

c) is the final image inverted or upright?

ANS q=160 cm M= -0.8 Inverted

Consider an old-fashioned bicycle with a small wheel of radius 0.51 m and a large wheel of radius 0.8 m. Suppose the rider starts at rest, accelerates with a constant acceleration for 8 minutes to a velocity of magnitude 24.5 m/s. He maintains his velocity for 9.5 minutes and then decelerates, with constant deceleration, for 7.3 minutes. Find the total angle through which a point on the small wheel has turned.

Julia and Cate want to go bungee jumping. Julia goes first. She has a mass of m and uses a bungee cord with the length of L and unknown springiness. However, Cate is very hesitant to go and wants to calculate how far she will drop before she is pulled back up. She has a mass 0.8 times Julia's mass. How far will Cate go down?

**** Only Need answers for questions g and h****

Suppose that, in the absence of insurance, the daily demand for visits to a clinic is given by Qd = 200 – 0.5P, where c is the coinsurance rate and P is the price charged by the clinic.

a) Calculate the quantity demanded when P is $100.

b) Calculate daily revenues when P is $100.

Now assume that customers pay a coinsurance rate, c. You will need to modify the demand function to account for the coinsurance.

c) Calculate the quantity demanded when P is $100 and the coinsurance rate is 0.4.

d) Calculate the daily revenue for the values given in (c).

e) Calculate the quantity demanded when P is $100 and the coinsurance rate is 0.8.

f) Calculate the daily revenue for the values given in (e).

Assume the clinic’s daily capacity is 100 customers.

g) Calculate the price the clinic should set to exactly use its entire capacity when there is no coinsurance (i.e., the co-coverage rate is 1).

h) Calculate the price the clinic should set to exactly use its entire capacity when there is a coinsurance rate of 0.8

Answers:

1. 150
2. 15000
3. 110
4. 11000
5. 70
6. 7000