Question

7. Show analytically that the necessary condition for the profit maximization of a monopolist that
supplies his output in two separate markets with two different demand functions is
MR1 = MR2 = MC.

I please for the clear explanation :)

Answer 1

As we know in a single market Monopolist sell where MR=MC,

Because if MR >MC , means selling additional unit gives more revenue than it cost.so it sell more.

If MR<MC , means selling additional unit gives less revenue than it cost .,so it Decrease its Production.

If there are two market, the firm will keep selling in that market till ,the Marginal revenue ( Revenue from selling additional unit) is from second market is higher.

If MR1>MR2, means selling additional unit in market 1 gives more revenue than selling it in market 2 ,so firm Increase selling in market 1 and Decrease selling in market 2 ,by doing this MR1 Decreases and MR2 Increases and firm reach at equilibrium at MR1=MR2.

If MR1<MR2 ,then selling additional unit in market 2 gives more revenue than selling it in market 1 ,so firm Increase selling in market 2 and Decrease selling in market 1 ,by doing this MR2 Decreases and MR1 Increases and firm reach at equilibrium at MR1=MR2.

So it is clear firm equilibrium will be at MR1=MR2

If MR1=MR2>MC, means selling additional unit gives more revenue than it cost,so firm sell more QUANTITY so that MC Increase and MR Decrease and firm reach equilibrium at MR1=MR2=MC

If MR1=MR2<MC,means selling additional unit gives less revenue than it cost,so firm reduce Production so that MR Increase and MC Decrease and firm reach equilibrium at MR1=MR2=MC