The cardboard box industry is composed of 100 identical firms, each having short
ID: 1117799 • Letter: T
Question
The cardboard box industry is composed of 100 identical firms, each having short-run total costs given by: STC = 0.5q^2 + 10q +5 Where q is the output of cardboard boxes per day.The market supply is given by: 100q = 100P -1000. And the market demand for cardboard box production is given by: Q = 1,100 – 50P
a. What will be the equilibrium in this marketplace? What will each firm’s short-run profits, and what is profit for the industry as a whole?
b.Compute the total producer surplus in this market.
c.Suppose the government poses a $3 tax on snuffboxes. How would this tax change the market equilibrium (i.e. demander price, supplier price, after tax quantity, and total tax revenue)?
d.How would the burden of this tax be shared between buyers and sellers?
e.Calculate the total loss of producer surplus as a result of the taxation of cardboard boxes?
What is the total loss in profits as a result of the taxatio
Explanation / Answer
Market demand for cardboard box industry: Q = 1,100 – 50P; Supply: 100Q = 100P – 1,000; STC = 0.5q^2 + 10q + 5.
• a. Demand equals supply at equilibrium.
1,100 – 50P = 100P – 1,000
150P = 2,100
P = $14.
Q = 1,100 – 50(14)
Q = 400.
Individual firm’s output = 400/100 = 4.
Individual firm’s profit = [14*4] – [0.5(4)^2 + 10(4) + 5]
Individual firm’s profit = 56 – 53 = $3.
Market’s total profit = 100 x 3 = $300.
• b. Producer surplus:
When Q is zero, P = $10.
Producer surplus = 1/2x(14–10)(400)
Producer surplus = $800.
• c. When tax of $3 is imposed, the supply equation changes to: 100Q = 100(P-3) – 1,000. Demand remains the same.
1,100 – 50P = 100P – 300 – 1,000
150P = 2,400
P = 2,400/150
Ps = $16.
Pd = $13.
Q = 300.
Total tax revenue = $3 x 300 = $900.
• d. Consumers pay: (16-14) x 300
Consumers pay = $600. Consumers pay $2.
Producers pay = (!14-13)x300
Producers pay = $300. Producers pay $1.
• e. Loss in producer surplus:
Loss in PS = 1/2x(300)(13-10) = $450.
Short-run profits:
Profits = [($13x300) – 100C
C = 0.5(3)^2 + 30 + 5 = 39.5
Profit = $3,900 + 3,950 = -$50.
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