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
To find the price, output, profits, and marginal revenue (MR), we need to analyze the monopolist's behavior under the given conditions.
a) Price Discrimination:
Price discrimination occurs when a monopolist charges different prices to different groups of customers. In this case, the monopolist can charge different prices in the two regions, allowing us to calculate the outcomes separately for each market.
For Market 1:
Demand: p1 = 15 - q1
Total Cost: Tc = 5 + 3q1
To find the monopolist's optimal output and price, we need to equate marginal revenue (MR) with marginal cost (MC). Since the monopolist is a single seller, MR is the same as the demand curve.
MR1 = p1 = 15 - q1
MC1 = d(Tc)/dq1 = 3
Setting MR1 = MC1:
15 - q1 = 3
q1 = 12
Substituting q1 into the demand equation, we can find the price:
p1 = 15 - 12
p1 = 3
Therefore, in Market 1 with price discrimination, the output (q1) is 12 and the price (p1) is 3.
For Market 2:
Demand: p2 = 25 - 2q2
Total Cost: Tc = 5 + 3q2
MR2 = p2 = 25 - 2q2
MC2 = d(Tc)/dq2 = 3
Setting MR2 = MC2:
25 - 2q2 = 3
2q2 = 22
q2 = 11
Substituting q2 into the demand equation, we can find the price:
p2 = 25 - 2(11)
p2 = 3
Therefore, in Market 2 with price discrimination, the output (q2) is 11, and the price (p2) is 3.
b) Law Forbids Different Prices in Two Regions:
If the law prohibits charging different prices in the two regions, the monopolist must set the same price for both markets.
To find the output and price under this condition, we consider the combined demand for both markets:
Total Demand: p = p1 = p2
Combined Demand: p = 15 - q1 = 25 - 2q2
Now, we can solve for the equilibrium price and output when the monopolist cannot discriminate prices:
p = 15 - q1 = 25 - 2q2
Rearranging the equation:
q1 = 10 - q2
Substituting this equation into either the first or second demand equation, we can solve for q2:
15 - (10 - q2) = q2
5 + q2 = q2
5 = 0 (No solution)
Since there is no solution, it means that the monopolist cannot operate profitably under the condition where different prices are prohibited in the two regions.
Therefore, the monopolist cannot find an optimal output and price when prohibited from charging different prices in the two markets.