Question

Consider again Worked-Out Problem 14.2. The daily demand for pizza is

          Qd=32,900−600P,Qd=32,900−600P,

where P is the price of a pizza. The daily costs for a pizza company include $845 in avoidable fixed costs and variable costs equal to

          VC=5Q+Q2/80,VC=5Q+Q2/80,

where Q is the number of pizzas produced each day. Marginal cost when producing Q pizzas is

          MC=5+Q/40.MC=5+Q/40.

Recall that the price is $11.50, and the total quantity demanded is 26,000 pizzas per day. In a long-run equilibrium, each active firm produces 260 pizzas per day, its efficient scale. That means there are 100 active firms in the initial long-run equilibrium. Suppose that starting at the initial long-run equilibrium with a price of $11.50 and 100 active firms, the government requires firms to pay a tax of $11.50 per pizza.

a. Complete the table below.

Instructions: Round quantities to the nearest whole number and prices to 2 decimal places.

	No tax	With a tax = $11.50
Short-run equilibrium price	11.50
Short-run equilibrium quantity	26,000
Consumer surplus	562,000
Producer surplus	84,500
Aggregate surplus	647,400
Government revenue	—
Deadweight loss	—

b. In the long run, the equilibrium price will be $ and the quantity will be .   

c. Relative to the short-run equilibrium, deadweight loss:

	decreases.
	stays the same.
	cannot be determined.
	increases.

Answer 1

a. The daily demand function of pizza is given as Qd=32,900-600P where Qd and P represent the quantity demanded and price of each pizza slice respectively. The inverse demand function of pizza would be: P=54.83-Qd/600. The marginal cost of pizza production by each firm is given as MC=5+Q/40 and in the long-run a tax of $11.50 is imposed on each firm for per pizza production. Therefore, the new marginal cost of pizza production faced by each firm after the tax imposition becomes: MC=11.50+(5+Q/40)=16.5+Q/40. Now, based on the profit-maximization condition or principle of any competitive firm, the output level of each competitive firm in any market corresponds to the quality between the marginal cost of production and the price of the concerned good or service.

Therefore based on the profit-maximizing condition of a competitive firm, it can be stated, in this case:-

P=MC

54.83-Qd/600=16.5+Q/40

-Q/40-Qd/600=-54.83+16.5

-0.0266Q=-38.33

Q=-38.33/-0.0266

Q*=1441 approximately

Hene, the equilibrium quantity of pizza in the market would be 1441 approximately.

Now, plugging the value of Q* into the inverse demand function, we can obtain:-

P=54.83-Qd/600

P=54.83-1441/600

P=54.83-2.40

P=52.43

Thus, the equilibrium price of pizza in the market after the tax imposition is $52.43.

Now, when Qd=0, the maximum willingness to pay of the pizza consumers would be:-

P=54.83-Qd/600

P=54.83-0/600

P=54.83

The maximum willingness to pay for the consumers would be $54.83. Therefore, the consumer surplus in the pizza market after the tax imposition=0.5*(54.83-52.43)*(1441-0)=0.5*2.4*1441=$1729.20

Now, when the Q=0 the minimum willingness to receive of the pizza sellers or producers would be:-

MC=16.5+Q/40

MC=16.5+0/40

MC=16.5

Hence, the minimum price that the pizza sellers or producers are willing to receive would be $16.5. Thus, the producer surplus in the pizza market after the tax imposition=0.5*(1441-0)*(52.43-16.5)=0.5*1441*35.93=$25,887.56

Therefore, the total or overall surplus in the pizza market after the tax imposition=($1729.20+$25,887.56)=$27,616.76

The total government revenue collected after the tax imposition in the market=($11.50*1441 pizzas)=$16,571.50

Now, plugging the value of Q* into the old or pre-tax marginal cost function of pizza production, we get:-

MC=5+Q/40

MC=5+1441/40

MC=5+36

MC=41

Thus, the price received by the pizza sellers or producers after the tax imposition on per pizza production is $41

The total or overall deadweight loss in the market due to the tax imposition=0.5*(26,000-1441)*(52.43-41)=0.5*24,559*11.43=$140,354.68

b. Hence, in the long-run the equilibrium quantity and price of apples would be $52.43 and 1441 apples as derived in part a. of the question.

c. Compared to the short-run scenario with the absence of any production tax on pizza, the deadweight loss is greater in the long-run compared to the short-run or in other words, it increases in the long-run as the producer surplus would decrease and the total or overall surplus would also decline. Therefore, the correct answer, in this case, would be increases or the last option given in the answer choices or options.