Determining supply curves
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Stanford Plastics, Inc. and Cal-Tech Associates, Inc. supply a generic phone jack that connects telephone cords to phone outlets. Proprietary cost and output information for each company reveal the following relations between marginal cost and output:
MCS=dTCS/dQ=$1+$0.00002QS (Stanford)
MCC=dTCC/dQ=$1.50+$0.000005QC (Cal-Tech)
The wholesale market for modular phone jacks is vigorously price-competitive, and neither firm is able to charge a premium for its products. Thus, P = MR in this market.
A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)
B. Calculate the quantity supplied by each firm at prices of $1, $1.50, and $2. What is the minimum price necessary for each individual firm to supply output?
C. Determine the industry supply curve when P < $1.50.
D. Determine the industry supply curve when P > $1.50. To check your answer, calculate quantity at an industry price of $2 and compare your answer with part B.
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Solution Summary
Solution describes the steps to determine supply curve for the given firms. It also determines the industry supply curves for the given price ranges.
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A. Determine the supply curve for each firm. Express price as a function of quantity and quantity as a function of price. (Hint: Set P = MR = MC to find each firm's supply curve.)
For Standard Associates, Marginal cost function is given by
MCS=1+0.00002Qs
Every firm sets its output level such that MR=MC to maximize its profits. In the price competitive industry P=MR.
So, Put P=MC
P=1+0.00002Qs
0.00002Qs=-1+P
Qs=-50000+50000P
For Cal-Tech, Marginal cost function is given by
MCC=1.50 ...
Education
- BEng (Hons) , Birla Institute of Technology and Science, India
- MSc (Hons) , Birla Institute of Technology and Science, India
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