1. ## Mathematical Economics

Q. Find Y ( dash on the top the Y) and C( dash on the top the C ) for the following functions:

Y=C+Io+Go
C=25+6y^(1/2)

where Io=16 , Go=14

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2. one more question

Q2) The market demand of a merchandise is given by p=150-45x. The merchandise is supplied by two duopolist with total cost functions:
C1=X1^2+13X1+45 and C2=13X2^2+11X2+100
Assume that the conjectural variations are zero.

1) show that the reaction curve of each dupolist and straight line.
2) If the total cost of each duopolist is same i.e. C=X^2+2X+50 , find the equilibrium output under duopoly and monopoly.
3) if the total cost of each duopolist is constant, find equilibrium output under duopoly and monopoly.

3. * 1) show that the reaction curve of each dupolist is a straight line.