The handmade snuffbox industry is composed of 100 identical firms, each having s
ID: 1203209 • Letter: T
Question
The handmade snuffbox industry is composed of 100 identical firms, each having short- run total costs given by STC = 0.5q^2 + 10q + 5. The short-run marginal costs are given by SMC = q -1-10 where q is the output of snuffboxes per day. What is the short-run supply curve for each snuffbox maker? What is the short-run supply curve for the market as a whole? Suppose the demand for total snuffbox production is given by Q^d = 1100 - 50P. What is the equilibrium in this marketplace? What is each firm's total short-run profit? Graph the market equilibrium and compute total producer surplus in this case. Suppose now the government imposed a $3 tax on snuffbox. How would this tax change the market equilibrium? How would the burden of this tax be shared between snuffbox buyers and sellers? Calculate the total loss of producer surplus as a result of taxation of snuffbox. Calculate the deadweight loss if $3 tax is imposed.Explanation / Answer
a.
Short-run marginal cost curve (SMC) is the short-run supply curve for each firm.
SMC = P = q + 10
q = P – 10 (Answer)
The short-run supply curve for the market is SMC × 100, since there are 100 firms.
SMC × 100 = 100P = (q + 10) × 100
= 100q + 1,000
100P = 100q + 1,000
Q = 100P – 1,000 [Since 100q = Q]
b.
The equilibrium condition is Demand = Supply
1100 – 50P = 100P – 1,000
150P = 2,100
P = 2,100 / 150
P = 14
Putting P = 14 in either the demand function or supply function,
Q = 1100 – 50P = 1100 – 50 × 14 = 400
Answer: The equilibrium price is 14 and quantity is 400 units in the market place.
Each firm’s short-run profit:
Since there are 100 firms, each firm should produce 400/100 = 4 units
TR = q × P = 4 × 14 = 56
Putting q = 4 in STC,
STC = 0.5q^2 + 10q + 5 = 0.5 × 4^2 + 10 × 4 + 5 = 53
Each firm’s short-run profit = TR – TC = 56 – 53 = 3 (Answer)
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