and total production cost is € TC = TCp + TCn a) Write the total revenue (TR) an
ID: 1196801 • Letter: A
Question
and total production cost is € TC = TCp + TCn
a) Write the total revenue (TR) and profit (?) functions when Con Ed price discriminates.
b)Find the quantity of electricity produced during peak hours and non-peak hours that maximizes profit when Con Ed price discriminates. Prove that you have found the maximum. What are peak hours price, non-peak hours price, and maximum ??
c) Find the demand function when Con Ed no longer price discriminates.
d) Write the total revenue (TR) and profit (?) functions when Con Ed does not price discriminate.
e) Find the quantity of electricity produced that maximizes profit when Con Ed does not price discriminate. Prove that you have found the maximum. What is the price and maximum ??
Explanation / Answer
a) TR = Price*Quantity
When the company disriminates price,
TR = TR from peak hours + TR from non peak hours = (p*Pp + nPn)
The above is TR function.
Profit = TR - TC
when it discriminates prices,
Profit = (TR from price discriminates) - TC from peak hours - TC from non peak hours
= (p*Pp + nPn) - 10 - 30P - 10 - 30n
= p*Pn + nPn - 30(P+n) - 20
The above is profit function.
b) Quantity and Price from Peak Hours:
TR = 526p - 8p2
MR = dTR/dp = 526 - 16p
MC = dTC/dp = 30
equating MR and MC
526 - 16p = 30
p = 16.533 = 17 units of electicity will be supplied during peak hours
and Pp = 526 - 8*17 = $390 will be charge.
Quantity and price for non peak hours:
TR = 114n - 2n2
MR = dTR/dn = 114 - 4n
MC = dTC/dp = 30
equating MR and MC
114 - 4n = 30
n = 10.5 = 11 units of electicity will be supplied during non peak hours
and Pn = 114 - 2*11 = $92 will be charge.
Profit = p*Pn + nPn - 30(P+n) - 20 = 17*390 + 11*92 - 30(17+11) - 20 = $6782.
Thus it supplies total of 17+11 = 28 units
d) When the company does not discriminate:
Total demand = demand of peak hour + demand of non peak hour = 526-8q + 114-2q = 640 - 10 q
where q = n+p
Total Cost = Cost of peak hour + Cost of non peak hour = 20 + 60q
TR = P*q = P(640 - 10 q) where p is same price for non peak and peak hours.
Profit = TR - TC = q(640 - 10 q) - 20 - 60q = 640q - 10q2 - 20 - 60 q
e) Quantity and price when it does not discriminate:
MR = dTR/dq = -20q + 640
MC = dTC/dq = d(20+60q)/dq = 60
equating MR and MC
-20q + 640 = 60
q = 29 units of electicity will be supplied
p = 640-10(29) = $350.
q =
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