11. Two clinics want to merge. The price elasticity of demand is -0.20, and each
ID: 1197496 • Letter: 1
Question
11. Two clinics want to merge. The price elasticity of demand is -0.20, and each clinic has fixed costs of $60,000. One clinic has a volume of 7,200, marginal costs of $60, and a market share of 2 percent. The other clinic has a volume of 10,800, marginal costs of $60, and a market share of 4 percent. The merged firm would have a volume of 18,000, fixed costs of $80,000, marginal costs of $60, and a market share of 6 percent. (5 pts)
What are the total costs, revenues, and profits for each clinic and the merged firm? . How does the merger affect markups and profits?
Explanation / Answer
Working Note:
(1) Price (P) = [e / (1 + e)] x MC where e: Price elasticity of demand
Clinic one, P = [- 2 / (- 2 + 1)] x $60 = (-2 / - 1) x $60 = $120
Cline two, P = [- 2 / (- 2 + 1)] x $60 = $120
Since merged clinic has same MC, P = $120
(2) Revenue, TR = P x Q (Volume)
(3) TC = FC + [Q x MC]
(4) Profit = TR - TC
(5) Mark-up = (P - MC) / P
For clinic one, clinic two & merged clinic,
Mark-up = $(120 - 60) / $120 = $60 / $120 = 50%
Therefore:
Clinic One
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
7,200
120
8,64,000
60,000
60
4,92,000
3,72,000
50
Clinic Two
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
10,800
120
12,96,000
60,000
60
7,08,000
5,88,000
50
Merged Clinic
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
18,000
120
21,60,000
80,000
60
11,60,000
10,00,000
50
As is seen, ost-merger profit is higher than the sum of pre-merger individual profits. But mark-up remains the same before & after the merger because marginal costs & prices are unchanged.
Clinic One
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
7,200
120
8,64,000
60,000
60
4,92,000
3,72,000
50
Clinic Two
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
10,800
120
12,96,000
60,000
60
7,08,000
5,88,000
50
Merged Clinic
Q
P($)
TR ($)
FC ($)
MC ($)
TC ($)
Profit ($)
Mark-Up (%)
18,000
120
21,60,000
80,000
60
11,60,000
10,00,000
50
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