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safari File Edit View History Bookmarks window Help M smartsite.ucdavis.edu a secure search McAfee Chegg Study I Guided Solutions and https://smartsite.ucdavis.edu/access/... SmartSite@UCDavis ARE 100B A01-A Suppose Callaway prices the C-Tec high 2. Figure 9.12 Price 20 18 16 14 12 10 8 Quantity Reference: Ref 9-14 (Figure 9.12) Suppose the firm's demand curve for its product increases from D1 to D2. The firm's marginal cost is given by MC-50 a. Solve for the change in the profit-maximizing quantity resulting from the increase in demand. b. Solve for the change in the profit-maximizing price resulting from the increase in demand.Explanation / Answer
a) When the firm's demand curve is at D1 , the firms revenue will be = Price X quantity demanded
Revenue at D1 = $ 10 X 4 units
Revenue at D1 = $ 40
When the firm's demand curve is at D2 , the firms revenue will be = $ 15 X 6
Revenue at D2 = $ 90
The marginal revenue when the demand curve shifts from D1 to D2 = $ 90 - $ 40
Marginal revenue of the firm = $ 50
Equating marginal revenue = marginal cost
MR = MC
$ 50 = 5Q
Q = 10 units ( The profit maximizing quantity resulting from the increase in demand )
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b) The profit maximizing price is when marginal revenue = marginal cost
Marginal revenue = P { ( 1+ (1/ep ) }
ep = price elasticity of demand
ep = % change in quantity demanded / % change in price
from Demand curve D1 to D2 , the % change in quantity demanded = 50%
% change in price from Demand curve D1 to D2 = 50 %
ep = 50% / 50%
ep = 1 ( unitary elastic)
P { ( 1+ (1/ep ) } = 5Q
The profit maximizing quantity = 10 units ; Marginal cost = 5Q
Marginal cost = 5 X 10
Marginal cost = $ 50
P ( 1 + 1/1 ) = 5 X 10
P ( 2) = 50
P = $ 25
The profit maximizing price resulting from the increase in demand = $ 25 .
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