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Asked by ashley alvarez on May 14, 2024

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In the town of Battle Springs, the market for fast food is dominated by Mr. Berger. The other companies tend to follow Mr. Berger's lead in setting price and style of burger. The total demand for cheeseburgers in Battle Springs is:
P = $1.50 - $0.00015Q.
The marginal cost of producing and serving burgers at Mr. Berger is:
MCL = 0.25 + 0.0000417Q.
The competitive supply curve of burgers by all the other (competitor) firms is:
Pf = 0.50 + 0.000285Qf.
Compute the price that will be set in the market when Mr. Berger behaves as a dominant firm and maximizes profit for itself. Also, compute the production rate by Mr. Berger and the competitor firms.

Marginal Cost

The escalation in cumulative costs incurred from creating an additional unit of a good or service.

Competitive Supply Curve

A graphical representation showing the quantities of a good or service that a firm is willing to supply at different prices in a competitive market.

Dominant Firm

A firm that has a large share of the total sales in a particular market, giving it significant control over the market.

  • Recognize various market frameworks, such as the leading firm model and the model of kinked demand curve.
  • Compute the optimal pricing and production quantities for maximal earnings given diverse cost and demand conditions.
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hafizuddin RichaamiinMay 16, 2024
Final Answer :
The price will be determined along Mr. Berger's demand curve, where The price will be determined along Mr. Berger's demand curve, where First, we find D<sub>L</sub>, which is the difference in quantity that will be forthcoming from the followers (QS) and the dominant firm Q<sub>L</sub> at various prices below the intersection of S<sub>f</sub> and D. This difference at various prices represents the locus of points tracing of D<sub>L</sub>. Total demand: P = 1.50 - 0.00015Q, which can be expressed as Q = 10,000 - 6,666.67P Competitor supply: P = S<sub>f</sub> = 0.50 + 0.000285Q<sub>f</sub>, which can be expressed as Q<sub>f</sub> = -1,754.40 + 3,508.77P. (S<sub>f</sub> = P) Take the difference and the result is the dominant firm's demand curve: Q<sub>L</sub> = 10,000 - 6,666.67P + 1,754.40 - 3,508.77P Q<sub>L</sub> = 11,754.40 - 10,175.44P or P = 1.155 - 0.0000983Q Now find MR for the dominant firm, Mr. Berger. R<sub>L</sub> = P ∙ Q<sub>L</sub> = 1.155Q<sub>L</sub> - 0.0000983Q<sub>L</sub><sup>2 </sup> MR<sub>L</sub> = 1.155 - 0.000197Q<sub>L </sub> Equate MR<sub>L</sub> to MC<sub>L</sub> to find Mr. Berger's production rate.1.155 - 0.000197Q<sub>L</sub> = 0.25 + 0.0000417Q<sub>L </sub> 0.905 = 0.0002387Q<sub>L </sub> Q<sub>L</sub> = 3,791 At this production rate, the dominant firm would set the price at: P<sub>L</sub> = 1.155 - 0.0000983(3,791) P<sub>L</sub> = 0.78 per unit. Under these conditions, the competitor firms will produce along their collective supply curve at Q<sub>f</sub> = -1,754.40 + 3,508.79(0.78) = 982.46 First, we find DL, which is the difference in quantity that will be forthcoming from the followers (QS) and the dominant firm QL at various prices below the intersection of Sf and D. This difference at various prices represents the locus of points tracing of DL.
Total demand:
P = 1.50 - 0.00015Q, which can be expressed as
Q = 10,000 - 6,666.67P
Competitor supply:
P = Sf = 0.50 + 0.000285Qf, which can be expressed as
Qf = -1,754.40 + 3,508.77P. (Sf = P)
Take the difference and the result is the dominant firm's demand curve:
QL = 10,000 - 6,666.67P + 1,754.40 - 3,508.77P
QL = 11,754.40 - 10,175.44P or
P = 1.155 - 0.0000983Q
Now find MR for the dominant firm, Mr. Berger.
RL = P ∙ QL = 1.155QL - 0.0000983QL2
MRL = 1.155 - 0.000197QL
Equate MRL to MCL to find Mr. Berger's production rate.1.155 - 0.000197QL = 0.25 + 0.0000417QL
0.905 = 0.0002387QL
QL = 3,791
At this production rate, the dominant firm would set the price at:
PL = 1.155 - 0.0000983(3,791)
PL = 0.78 per unit.
Under these conditions, the competitor firms will produce along their collective supply curve at The price will be determined along Mr. Berger's demand curve, where First, we find D<sub>L</sub>, which is the difference in quantity that will be forthcoming from the followers (QS) and the dominant firm Q<sub>L</sub> at various prices below the intersection of S<sub>f</sub> and D. This difference at various prices represents the locus of points tracing of D<sub>L</sub>. Total demand: P = 1.50 - 0.00015Q, which can be expressed as Q = 10,000 - 6,666.67P Competitor supply: P = S<sub>f</sub> = 0.50 + 0.000285Q<sub>f</sub>, which can be expressed as Q<sub>f</sub> = -1,754.40 + 3,508.77P. (S<sub>f</sub> = P) Take the difference and the result is the dominant firm's demand curve: Q<sub>L</sub> = 10,000 - 6,666.67P + 1,754.40 - 3,508.77P Q<sub>L</sub> = 11,754.40 - 10,175.44P or P = 1.155 - 0.0000983Q Now find MR for the dominant firm, Mr. Berger. R<sub>L</sub> = P ∙ Q<sub>L</sub> = 1.155Q<sub>L</sub> - 0.0000983Q<sub>L</sub><sup>2 </sup> MR<sub>L</sub> = 1.155 - 0.000197Q<sub>L </sub> Equate MR<sub>L</sub> to MC<sub>L</sub> to find Mr. Berger's production rate.1.155 - 0.000197Q<sub>L</sub> = 0.25 + 0.0000417Q<sub>L </sub> 0.905 = 0.0002387Q<sub>L </sub> Q<sub>L</sub> = 3,791 At this production rate, the dominant firm would set the price at: P<sub>L</sub> = 1.155 - 0.0000983(3,791) P<sub>L</sub> = 0.78 per unit. Under these conditions, the competitor firms will produce along their collective supply curve at Q<sub>f</sub> = -1,754.40 + 3,508.79(0.78) = 982.46 Qf = -1,754.40 + 3,508.79(0.78) = 982.46

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