demand for two markets are p1=15-q1 and p2=25-2q2 .THE monopolist Tc is c=5+3(q1+q2). what are price,output,profits and Mr if a,the monopolist can price discriminate b,the law forbids(prohibits)chrging different pricesin the two regions
Economics
answer
yes
To find the price, output, profits, and marginal revenue (MR), we need to analyze two scenarios:
a) Price Discrimination:
In this scenario, the monopolist can charge different prices in the two regions.
1. Price and Output:
To determine the price and output in each market, we need to set the marginal cost (MC) equal to the marginal revenue (MR).
MC = MR
Since TC = 5 + 3(q1 + q2), MC = dTC/d(q1 + q2) = 3.
In Market 1:
MC = MR = 3
15 - q1 = 3
q1 = 12
p1 = 15 - q1 = 15 - 12 = 3
In Market 2:
MC = MR = 3
25 - 2q2 = 3
2q2 = 25 - 3
q2 = 22 / 2 = 11
p2 = 25 - 2q2 = 25 - (2 * 11) = 25 - 22 = 3
Therefore, in both markets, the monopolist charges a price of 3 and the output in Market 1 is 12 units (q1 = 12) while the output in Market 2 is 11 units (q2 = 11).
2. Profits:
To calculate the profits, we need to subtract the total cost (TC) from the total revenue (TR) in each market.
Total Revenue in Market 1:
TR1 = p1 * q1 = 3 * 12 = 36
Total Revenue in Market 2:
TR2 = p2 * q2 = 3 * 11 = 33
Total Cost:
TC = 5 + 3(q1 + q2) = 5 + 3(12 + 11) = 5 + 3(23) = 5 + 69 = 74
Profits:
Profit = TR - TC
Profit = (TR1 + TR2) - TC
Profit = (36 + 33) - 74
Profit = 69 - 74
Profit = -5
In this scenario, the monopolist incurs a loss of 5 units.
b) Charging Same Price in Both Regions:
In this scenario, the law prohibits the monopolist from charging different prices in the two regions.
1. Price and Output:
Since the monopolist can't price discriminate, they need to set one price for both markets. To determine the price and output, we'll use the total revenue (TR) equation.
Total Revenue:
TR = p(q1 + q2)
MC = MR = dTR/d(q1 + q2)
MC = dTR/d(q1 + q2) = 3
Given p = 15 - q1 = 25 - 2q2, we can substitute the value of p into the total revenue equation.
TR = (15 - q1)(q1 + q2)
Apply the derivative:
dTR/d(q1 + q2) = (15 - q1) - (15 - q1) - 2q2
MC = MR = 3
15 - q1 - 2q2 = 3
12 - q1 - 2q2 = 0
q1 = 12 - 2q2
Now, substitute the value of q1 into p:
p = 15 - (12 - 2q2)
p = 15 - 12 + 2q2
p = 3 + 2q2
Since p1 = p2 (charging the same price in both markets), we can equate their expressions:
3 + 2q2 = 25 - 2q2
4q2 = 22
q2 = 22/4 = 5.5
Substituting q2 into the expression for p, we can find p1 = p2:
p = 3 + 2(5.5)
p = 3 + 11
p = 14
Therefore, in both markets, the monopolist charges a price of 14, and the output in Market 1 is determined by substituting q2 into the equation q1 = 12 - 2q2:
q1 = 12 - 2(5.5)
q1 = 12 - 11
q1 = 1
2. Profits:
Total Revenue:
TR = p * (q1 + q2)
TR = 14 * (1 + 5.5)
TR = 14 * 6.5
TR = 91
Total Cost:
TC = 5 + 3(q1 + q2)
TC = 5 + 3(1 + 5.5)
TC = 5 + 3(6.5)
TC = 5 + 19.5
TC = 24.5
Profits:
Profit = TR - TC
Profit = 91 - 24.5
Profit = 66.5
In this scenario, the monopolist earns a profit of 66.5 units.
To summarize:
a) With price discrimination, the monopolist charges a price of 3, produces 12 units in Market 1 and 11 units in Market 2, and incurs a loss of 5 units.
b) Without price discrimination, the monopolist charges a price of 14, produces 1 unit in Market 1 and 5.5 units in Market 2, and earns a profit of 66.5 units.