DSE 2009 Doubt

[Manvendra]

DSE 2009

A monopoly faces the demand curve P = 8 - Q .The monopoly has a constant unit cost equal to 5 for Q <= 2 and a constant unit cost equal to 3 for Q > 2. Its profit maximizing output equals :
 a) 3/2
b) 2
c) 5/2
d) Both 3/2 and 5/2

In the above question if we apply MR = MC , we get 3/2 and 5/2 as the profit maximizing quantities . But if we calculate the profits separately we find that the profit when Q = 5/2 is greater than when Q= 3/2.



So what should be the correct option.

[ritu]

hello manvendra:)
profits are coming out to be same ie.2.25 in both the cases....
when q=2.5...then u calculate profits this way
upto 2 units profits are (5.5-5)*2
then for remaining 0.5 unit....(5.5-3)*0.5...[price is same coz its not a discriminating monopolist case]
so total profits are 2.25 ,the same as u get for q=1.5....(6.5-5)*1.5=2.25

hope u got the point!:)

[s]

hi ritu can u please elaborate how u calculated the profit of monopolist when q=5/2..i am going terribly wrong somewhr...
upto 2 units i calculated profit=8*2-4-10=2 and for remaining 0.5 units profit=8*0.5-0.25-1.5=9/4

[ritu]

hi s:)
when monopolist produces 2.5 units ,u first calculate the price from dd functn which wud be P=8-2.5=5.5....now no matter what is the cost of each unit produced price wud be 5.5 only as he is not a discriminating monopolist...

now upto 2 units, applicable MC IS 5 SO FIRST PART OF PROFIT IS (P-ATC)*Q
since mc is constant ,ac is also constant at 5 .so profit=(5.5-5)*2=1


for second part of profits 0.5 units are left which is produced at a MC of 3....and hence AC=3
profits are (5.5-3)*0.5=1.25

adding the two parts of profit u get 1+1.25=2.25

hope u understood it now:)

[ritu]

nd manvendra correct option is d:)

[s]

thanks a lot ritu :)

[Manvendra]

Hi Ritu ..

Thanks a lot :)