#OK to post homework
#George Spahn, 2-6-2022, Assignment 4

# 5 
# The monopoly is best. Since we are trying to maximize combined profits,
# we can think of both company as a single company, which does the best
# when the total produced is A/2

# 6

# i 


# See hw5GeorgeSpahn.txt , problem 6
# We look at s1, set d[1]=d, and multiply by A, to get
# A/(d+1)

#ii

# By the previous part, we know that player 2 will produce (A-q1)/(d+1)
# Thus player 1 has utility function
ut1 := q[1]*(A - q[1] - (A - q[1])/(1 + d))^d:
# Setting the derivative equal to 0.
s := solve(diff(utp1,q[1])=0,q[1]):
# s = A/(1 + d)
# q1 = A/(1 + d)
# q2 = (A - A/(1 + d))/(1 + d) 
# q2 = A*d/(1 + d)^2


# iii

# See hw5GeorgeSpahn.txt , problem 5
# We set d[1] = d[2] = d, and multiply by A, to get
# both players produce A/(d+2)