Question

Question 1: The inverse demand for gasoline is given by P=100-Q, where Q is the price per gallon and Q is the quantity demanded. Assume that Shell is the only gas station in town and that other gas stations are too far to be considered substitutes. The marginal cost of gasoline is given by MC= 12Q.

a. How many gallons of gasoline will Shell sell? At what price?

To reduce emissions from cars the government imposes a $10/ gallon tax on Shell.

b. Find the equilibrium price and quantity after the tax. (Hint: The tax increases the cost to Shell )

c. How is the tax burden shared between buyers and sellers? (i.e. what is the price increase to consumers? By how much does the price received by shell drop? )

Question 2: There are two firms in the apples market that are Cournot competitors, firm A and firm B. The demand for apples is given by P=120-Q, the cost per unit is $20 and there are no fixed costs.

a. Assume firm B produces 20 units. Draw the demand curve facing firm A and label your axes.

b. Assume firm B produces 20 units. What is firm A’s marginal revenue equation?

c. Assume firm A does not know how much firm B produces. What is firm A’s marginal revenue? What is firm A’s best response function?

d. Firm A discovers a new fertilizer that allows its apples to ripen early. If firm A uses the fertilizer it can bring its apples to market before its competitor. Assume there is no cost to using the fertilizer. Does firm A want to use the fertilizer? Explain your answer.

Answer 1

ANS 1 A.FIRST OF ALL WE WILL TAKE

MC=12Q_____( i)

p=100-Q_______( ii)

WE KNOW AT EQU.

P=MC

i.e., 100-q=12q

i.e., 100=12q + q

i.e., 100=13 q

i.e.,q=100/13

putting value of q in equation (ii)

p= 100- 100/13

= (1300-100)/13

=$1200/13

1 b) Given tax = $10/gallon

value of tax= 10*100/13

=$1000/13

new equilibrium price= $1000/13+ $1200/13+ $2200/13

we know at equilibrium p=mc=12q

i.e., 2200/13=12q

i.e., q= 550/39 gallons

1 c) some information missing