30. Crusty Cakes sells donuts in Eastown and Westown. It's total costs are given by TC = 10(QE + QW). The demand in each neighborhood is given by QE = 100 - 2PE and QW = 100 - PW. If Crusty price discriminates between the two neighborhoods, how much are its maximized profits?

Total Maximized Profit = $2612.5

Explanation:

given data

Total Cost TC = 10(QE + QW)

QE = 100 - 2PE

QW = 100 - PW

solution

we consider here Q is = QE + QW

so total cost  TC = 10 Q

we first derive it Marginal Cost by taking derivative of TC w.r.t Q  that is

MC =    

MC = 10

so when crusty practice price discrimination then it will different marginal revenue from each market is

QE = 100 - 2PE

and

Total Revenue from market E is

E = TRE = QE × PE

E =  100PE - 2PE²

and

Marginal Revenue from E is

E  = MRE =  

E = 100 - 4PE

and

now we put MRE = MC

100 - 4PE = 10

PE =  $22.5

and here QE will be

QE = 100 - 2PE

QE = 100 - 45

QE = 55 units

and

TRE = 55  × 22.5

TRE = $1237.5

and

now Considering second neighborhood W

QW = 100 - PW

so here

TRW = 100PW - PW²

and

MRW = 100 - 2PW

now we equating MRW with MC

so it will be

100 - 2PW = 10

PW = $45

and

Q = 100 - PW

Q = 100-45

Q = 55 units

so

TRW = 55 × 45

TRW = $2475

so here

Total Revenue will be

Total Revenue = TRE + TRW

Total Revenue = $1237.5 + $2475

Total Revenue = $3712.5

and

Total Cost will be

Total Cost  = 10(55+55)

Total Cost  = $1100

and

Total Maximized Profit  will be

Total Maximized Profit = TR -TC

Total Maximized Profit = $3712.5 - $1100

Total Maximized Profit = $2612.5

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