Microeconomics

It has been estimated that the world demand for wheat can be represented by thefunction P = 80 - 2Q. It has been further found that the countries supplying thismarket have marginal cost curves which when summed together are given by theequation MC = 5 + Q

What price and output levels will prevail in the world market if a free marketsituation exists?

why "The sum of the individual MC curves of producers is the supply curve"?In monopoly they are lacking of supply curve??

Here the Total Revenue(TR)= P.Q =Q(80-2Q)=80Q-2Q2 ………………….(1)
We have theMR by differentiating equqtion in respect to Q.Therfore
d(P.Q)/dQ = 80-2.2.Q = 80-4Q
We know MC=5+Q……………….(2)
At the equilibrium, we have-
MR=MC
Hence, 80-4Q = 5+Q…………………(3)
Or -4Q+Q = 5-80
-3Q= -75
3Q =75
Q=75/3= 25
Again, putting the value of Q in equation (1),we have
25.P=80.25-2*25
=2000-50=1950
P=1950/25=78

The supply curve is the locus of the points representing the amount supplied by the producers at different prices. Under perfect competition the AR=MR curve is a horizontal straight line. So we have unique relationship between the quantity supplied with and the price. Thus under perfect competition the MC curve represent the supply curve the firm .We have the market supply curve by summing up the supply curves of the firms. But under monopoly such unique relationship is absent as the quantity supplied depend on the AR and MR and those curves are downward sloping. So supply curve is lacking under monopoly.

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