2. Digital pedometers are produced and sold in a perfectly competitive market, w
ID: 1146983 • Letter: 2
Question
2. Digital pedometers are produced and sold in a perfectly competitive market, where demand is given by MWTP(Q) = 18-0.2502 (a) Initially, firms can produce pedoneters at a total cost: TC(q) = 12+e+ h. The market is in long-run equilibrium. What is the prevailing market price for pedometers, and how many pedometers does a typical firm make? How many firms are there overall? (b) Somebody has written an open-source program that manufacturers of pedometers can use to lower their costs of making pedometers. Specifically, in the short-run, existing firms can now use the new technology to produce at a cost TC(q) = 12 + , but new firms cannot enter. what is the short-run supply curve of the existing firms using this new technology? What is the new market price, total quantity, and quantity produced by each firm? (c) In the long-run, new firms can enter and use the new production technology. What is the new long run eqim price, total quantity, number of firms, and output per firm?Explanation / Answer
a). Solution :- TC(q) = 12 + q + q2 / 12
MC(q) = 1 + q / 6 (Marginal cost i.e., MC is the first derivative of total cost function)
P = 18 - 0.25q (Demand function)
Equating P and MC in the given question,
18 - 0.25q = 1 + q / 6
18 - 1 = q / 6 + q / 4 (0.25 q can be also written as q / 4)
17 = (2q + 3q) / 12
17 * 12 = 5q
204 = 5q
q = 204 / 5
q = 40.8 units.
P = 18 - 0.25 * 40.8 (Put the value of q = 40.8 in demand function)
P = 18 - 10.20
P = $ 7.80
Conclusion :- Market price per pedometer = $ 7.80 and Number of pedometers made by a firm = 40.8
b). Solution :- TC(q) = 12 + q / 2 + q2 / 12
MC(q) = 1 / 2 + q / 6 (Marginal cost i.e., MC is the first derivative of total cost function)
MC(q) = 0.50 + q/6 (1 / 2 can also be written as 0.50)
Short run supply curve equation = 0.50 + q/6 (Marginal cost represents short run supply curve of firms in perfectly competitive market).
Equating P and MC in the given question,
18 - 0.25q = 0.50 + q / 6
18 - 0.50 = q / 6 + q / 4 (0.25 q can be also written as q / 4)
17.50 = (2q + 3q) / 12
17.50 * 12 = 5q
210 = 5q
q = 210 / 5
q = 42 units.
P = 18 - 0.25 * 42 (Put the value of q = 40.8 in demand function)
P = 18 - 10.50
P = $ 7.50
Conclusion :- Short run supply curve equation = 0.50 + q/6
Market price per pedometer = $ 7.50 and Number of pedometers made by each firm = 42.
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