Micro and macro doubts

[Chinni18]

Can someone help with this question:

Q.1 A poll conducted in the class of ECO revealed that 60 percents of students believe that Hong Kong should have minimum wage law. Consider a random sample of 10 students from the ECO class and count x; the number of students who support the minimum wage law.
How would we do this kind of question?

Q.2 In a (completely) fixed exchange rate system, the sum of current and capital account balances can be negative. (II) In a (completely) free i.e. floating exchange rate system, the sum of the two balances is zero.
Both statements are true. How?

Q.3 Three separate labs consider engaging in R&D for developing an anti-laziness pill (intended to used mainly by students like you). The value of the patent on this pill is estimated to be V = $240. If more than one firm discovers the patent, the firms equally share the prize (240/2 = $120 or 240/3 = $80).
Lab A: Cost of the lab is IA = $40, probability of discovery is 1/3.
Lab B: Cost of the lab is IB = $60, probability of discovery is 1/3.
Lab C: Cost of the lab is IC = $70, probability of discovery is 1/3.
What is the loss of firm C?

Q.4 The inverse market demand for Toaster-Phones in NYC is p = 36 — Q. The man¬ufacturer licenses a single dealer to sell this brand in NYC. Therefore, the dealer acts as a monopoly in the NYC market. The manufacturer sells each Toaster-Phone to the dealer for $d ≥ c, where c = $20 is the cost of producing one Toaster-Phone. In addition, the manufacturer may levy a fixed fee of $ f on the dealership. Consider a two-stage game in which in Stage I the manufacturer sets the per-unit price charged to the dealer d, and the fixed fee $ f. In Stage II the dealer determines the quantity sold as to maximize the dealership’s profit.
Compute the dealer’s price p, quantity sold Q, and profit as a function of d and f.
(Answer is (36+d)/2, [{(36-d)^2}/4] -f)

Thanks

[aditi5000]

Q.2 In a (completely) fixed exchange rate system, the sum of current and capital account balances can be negative. (II) In a (completely) free i.e. floating exchange rate system, the sum of the two balances is zero.
Both statements are true. How?

Hey the BOP always balances so especially in floating exchange rate system, the sum of the two balances is zero. whereas, in a fixed one, due to transactions of selling gold or foreign currencies etc, the BOP may run a negative balance.

Q.3 Three separate labs consider engaging in R&D for developing an anti-laziness pill (intended to used mainly by students like you). The value of the patent on this pill is estimated to be V = $240. If more than one firm discovers the patent, the firms equally share the prize (240/2 = $120 or 240/3 = $80).
Lab A: Cost of the lab is IA = $40, probability of discovery is 1/3.
Lab B: Cost of the lab is IB = $60, probability of discovery is 1/3.
Lab C: Cost of the lab is IC = $70, probability of discovery is 1/3.
What is the loss of firm C?

loss of c = loss when all discover+loss when 2 firms discover+ loss when c alone discovers
= 240(1/3*1/3*1/3*1/3 + 1/3*1/3*2/3*1/2 + 1/3*1/3*2/3*1/2 + 1/3*2/3*2/3*) - 70
the bold part is the probability of 3 firms discovering and 2 firms discovering respectively. Please share the answrs?

[aditi5000]

Q.4 The inverse market demand for Toaster-Phones in NYC is p = 36 — Q. The man¬ufacturer licenses a single dealer to sell this brand in NYC. Therefore, the dealer acts as a monopoly in the NYC market. The manufacturer sells each Toaster-Phone to the dealer for $d ≥ c, where c = $20 is the cost of producing one Toaster-Phone. In addition, the manufacturer may levy a fixed fee of $ f on the dealership. Consider a two-stage game in which in Stage I the manufacturer sets the per-unit price charged to the dealer d, and the fixed fee $ f. In Stage II the dealer determines the quantity sold as to maximize the dealership’s profit.
Compute the dealer’s price p, quantity sold Q, and profit as a function of d and f.
(Answer is (36+d)/2, [{(36-d)^2}/4] -f)

profit = tr-tc= pQ-(dQ) - f = 36Q — Q^2 -dQ-f
36-2Q-d=0
Q=36-d/2... p= 36- 36-d/2 = 36+d/2
profit = 36(36-d)/2 — (36-d)/2^2 -d(36-d)/2-f
i am getting the price you have mentioned as quantity..

[Chinni18]

Thanks aditi  The loss is firm C is 13 (answer). Thank you !

[Chinni18]

Ooh, I think that was what I did wrong. Got it now! Thanks aditi! As ritu says, you're a powerfuff girl  Thank you!!!

[aditi5000]

Hahahahaha Chinni  If I am a powerpuff girl, you are professor utonium! :)