Question

14. Residents of a village by the sea pick oysters to find pearls. This is a rare kind, so the entire world production of this type of pearl comes from this village. The inverse demand of this pearl in the market is p(q) = 1000−q. The total cost function for finding q number of pearls is C(q) = q 2 . Assume that no person in this village is allowed to extract more than one pearl from the sea. If people of this village are independently making decisions on whether or not to search for pearls, what will be the price of a single pearl be in the market?

(a) 500

(b) 750

(c) 1000

(d) 1500

15. (Continued from the previous problem.) Now assume that the leader of the village determines the number of pearls to be extracted from the sea. What is the price in the market then?

(a) 500

(b) 750

(c) 1000

(d) 1500

16. (Continued from the previous problem.) Assume the leader requires each person who finds a pearl to pay an extraction fee of f to the village. How much should f be such that the number of pearls extracted is equal to the socially optimal number.

(a) 500

(b) 750

(c) 1000

(d) 1500

17. (Continued from the previous problem.) Villagers searching for pearls causes disruption in the marine eco-system, which makes the color of the water turn from blue to brown/green. This, consequently, leads to a decrease in the number of tourists coming to visit the village. Assume that profits from tourism are Π(y, q) = 600y − yq − y 2 where y is the amount invested in tourism. What is the socially optimal number of pearls to be extracted in this case?

(a) 500

(b) 200

(c) 600

(d) 1000

18. (Continued from the previous problem.) Assume the leader of the village gives the rights to search for pearls in the sea to the people who benefit from tourism. So now every villager who extracts a pearl has to pay p to these people. What is p in a competitive equilibrium?

(a) 500

(b) 200

(c) 600

(d) 1000

The answer of 18. is C, how can I get it?

Answer 1

as per first 4 is answerd

a] answer option [a] is correct

if every person is making decisions individually the n the extraction will be up to the points where

=0

pq - c[q] =0

[1000 -q ] q- q2   =0

1000 q - 2q2 =0

1000 =2 q

q = 500

B ] correct answer is [b]

if the leader decide the number he will maximize the profit such that

/ q [1000 q - 2q2 ] = 0

1000 - 4q =0

q =250 [social optimum

p[q] =750

c] the correct answers is [a]

after extraction cost f the profit of each villagers in

= pq -cq -f

1000q - 2q2 -f

for  =0 ; 1000 q - 2q2 -f =0

at q =250 ; 1000 [ 250 ] - 2 [250 ]2 -f

f =125000

as each person is allowed to extract only one pear;s then per person f in 125000 / 250 = 500  

d ] correct option [ b ]

in social optimum me level the villagers maximize joint profit from tourism and pearls

= [ y , q ] +  [q]

= 600 y -yq - y2 +1000 q - 2q2

/ q = 600 -q -2y =0 ----------------------------------[1]

/ q = -y + 1000 - 4q = 0 ----------------------------[2]

from 1 ; q = 600 - 2y =0 -------------- [3]

substitution [3] in [2] ;

- y +1000 -4 [600 - 2y ] =0

-y + 1000 -2400 +8y =0

-1400 +7y =0

y =200

q =600 -2 [200 ]= 200