Answer to Question #71650 in Microeconomics for john johnson

Question

The cardboard box industry is composed of 100 identical firms, each having short-run total costs given by: STC = 0.5q2 + 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 taxation?

Answer 1

100 firms, STC = 0.5q2 + 10q +5, 100qs = Qs = 100P - 1,000, Qd = 1,100 – 50P.
a. The equilibrium in this marketplace is:
Qd = Qs,
1,100 - 50P = 100P - 1,000,
150P = 2,100,
P = $14.
Q = 100*14 - 1,000 = 400 units.
q = Q/100 = 400/100 = 4 units.
Firm TP = P*Q - STC = 14*4 - (0.5*4^2 + 10*4 + 5) = $3.
Industry TP = $3*100 = $300.
b. The total producer surplus in this market is:
PS = 0.5*14*400 = $2,800.
c. If a $3 tax on snuffboxes is imposed, then the market equilibrium is:
1,100 - 50P = 100(P - 3) - 1,000,
150P = 2,400,
P2 = $16.
Q2 = 1,100 - 50*16 = 300 units.
Total tax revenue is 3*300 = $900.
d. The burden of this tax will be shared between buyers and sellers, but buyers will pay more.
e. PS2 = 0.5*16*300 = $2,400.
The total loss of producer surplus as a result of the taxation of cardboard boxes is:
PS - PS2 = 2,800 - 2,400 = $400.
TP2 = 100*(16*3 - (0.5*3^2 + 10*3 + 5)) = $8.5.
The total loss in profits as a result of the taxation is:
8.5 - 3 = $5.5.