Ardinator
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-Done-
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Ardinator
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Any help?
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js93
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(Original post by Ardinator)
Any help?
I will do one at a time.

Q will equal the sum of QH and QL.

Ph is simply the given demand function
Ph=20-5Qh, as these people are willing to pay the market price.

QL=Q-QH

Rearrange the given demand function to get Q=... and sub into the above to yield:

QL=4-1/5P-QH

The P we are talking about here is PL:

Hence,

QL=4-1/5PL-QH

Rearranging yields:

PL=20-5QL-5QH

The profit function will be PLQL+PHQH-MCL-MCH-FC

MC denotes marginal costs, FC is fixed costs

Hence:

profit=((20-5QL-5QH)QL+(20-5QH)QH-5QL-5QH-15)

Max profit w.r.t QL and QH:

MAX wrt Qh:
20-10QH-5QL-5=0

MAX wrt QL:
20-5QH-10QL-5 = 0

solve simultaneously to yield:

QH=QL=1

Sub QH into PH=...

sub QL into PL=...

Hence:

PL = 10

PH = 15
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js93
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(Original post by Ardinator)
Any help?
Economics profit is (15*1)+(10*1)-(5*1)-(5*1)-15 = )
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js93
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(Original post by Ardinator)
Any help?
If only one price can be charged the firm will set MR=MC

R=PQ

hence R=20Q-5Q^2

MR=20-10Q

MC=5

equating yields:


10Q=15

Q=3/2


sub in to find price


P = 12.5

Find profit.

(12.5)(3/2)-(5*1.5)-15 = -3.75

So the firm is worse off
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js93
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(Original post by Ardinator)
Any help?
Work out the consumer surpluses of the two options.

Firstly when there is one price.

The demand curve cuts the Y axis at P=20.....(when Q=0)

Hence the consumer surplus for one price is:

((20-12.5)*1.5)/2 = 5.625

When there is two prices.

CS for PH:

((20-15)*1)/2 = 2.5

CS for PL:

((15-10)*1)/2 = 2.5

CS for PL and PH is 5.

Therefore consumers are worse off with the price discrimination as their CS is smaller than in the single price case
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Ardinator
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(Original post by js93)
Work out the consumer surpluses of the two options.

Firstly when there is one price.

The demand curve cuts the Y axis at P=20.....(when Q=0)

Hence the consumer surplus for one price is:

((20-12.5)*1.5)/2 = 5.625

When there is two prices.

CS for PH:

((20-15)*1)/2 = 2.5

CS for PL:

((15-10)*1)/2 = 2.5

CS for PL and PH is 5.

Therefore consumers are worse off with the price discrimination as their CS is smaller than in the single price case
Thanks a lot mate, your help is really really appreciated!
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