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Determine the profit-maximizingLOADING... prices when a firm faces two markets where the inverse demand curves are Market​ A: p Subscript Upper Aequals80minus2Upper Q Subscript Upper A​, where demand is less​ elastic, and Market​ B: p Subscript Upper Bequals60minus1Upper Q Subscript Upper B​, where demand is more​ elastic, and Marginal Costequalsmequals20 for both markets.

Respuesta :

Answer:

Market A: [tex]P_{A} = 20.00[/tex]

Market B: [tex]P_{B} = 20.00[/tex]

Explanation:

Market A: [tex]P_{A} = 80 - 2Q_{A}[/tex] ........................ (1)

Market B: [tex]P_{B} = 60 - 1Q_{B}[/tex] ........................ (2)

MC = m = 20 ............................................... (3) for both markets

For Market A:

Profit maximizing price can be obtained when  [tex]P_{A} = m[/tex]

Therefore, we have:

[tex]80 - 2Q_{A} = 20[/tex]

[tex]80 - 20 = 2Q_{A}[/tex]

[tex]60 = 2Q_{A}[/tex]

[tex]Q_{A} = \frac{60}{2}[/tex]

[tex]Q_{A} = 30[/tex]

Substituting 50 for [tex]Q_{A}[/tex] in equation (1), we have:

[tex]P_{A} = 80 - 2(30)[/tex]

[tex]P_{A} = 80 - 60[/tex]

[tex]P_{A} = 20.00[/tex]

For Market B:

Profit maximizing price can be obtained when  [tex]P_{B} = m[/tex]

Therefore, we have:

[tex]60 - 1Q_{B} = 20[/tex]

[tex]60 - 20 = 1Q_{B}[/tex]

[tex]40 = 1Q_{B}[/tex]

[tex]Q_{B} = 40[/tex]

Substituting 80 for [tex]Q_{B}[/tex] in equation (2), we have:

[tex]P_{B} = 60 - 1(40)[/tex]

[tex]P_{B} = 20.00[/tex]