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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