6: About 49 million gallons of milk were purchased annually in the United States

Question

6: About 49 million gallons of milk were purchased annually in the United States. Consumer prices for milk fluctuate a great deal over time and vary by region, but the average price consumers was about $3.30 per gallon. Taxes on milk are often imposed at 30 cents per gallon. Studies have shown that in the intermediate run (say, two to five years) the own-price elasticities of demand and supply are about Qd,P = 0.7 and Qs,P = 0.3. (Please round two digits and round up quantity) a). What quantities and prices would we anticipate if the taxes were removed? b). Graph the market equilibrium with and without a tax and deadweight loss. What is tax paid by the consumer and producer and what is the deadweight loss of the tax ?

Explanation / Answer

a).

“Own” price elasticity of demand - this is a measure of the percentage change in the quantity demanded “caused” by a percentage change in price. Because the demand function is an inverse relationship between price and quantity the coefficient of price elasticity will always be negative:

Price elasticity of demand = % change in quantity demand / % change in price

Let the demand curve be of the general linear form Q = a - bP and the supply curve be Q = c + dP, where a, b, c, and d are positive constants that we have to find from the information given above. To begin, recall the formula for the price elasticity of demand,

Qd,P = (P/Q)*(change in Q/change in P)

We know the values of the elasticity, P, and Q, which means we can solve for the slope, which is -b in the above formula for the demand curve

-0.7 = (3.3/49)*(-b)

b= 0.7*(49/3.) so, b = 10.39

To find the constant a, substitute for Q, P, and b in the demand curve formula: 49 = a - 10.39(3.30). Solving yields a = 83.3. The equation for demand is therefore Q = 83.3 - 10.39P. To find the supply curve, recall the formula for the elasticity of supply and follow the same method as above:

Qs,P = (P/Q)*(change in Q/change in P)

0.3 = (3.3/49)*d

d= 4.45

To find the constant c, substitute for Q, P, and d in the supply formula, which yields 49 = c + 4.45(3.3). Therefore c =34.15 and the equation for the supply curve is Q = 34.15 + 4.45P.

At equilibrium, Qs =Qd,

34.15 + 4.45Ps = 83.3 - 10.39Pb

Sinnce before tax, there Pb=Ps, solve for Ps=Pb=P

So, 49.15 = 14.84P and therefore P = $3.3

And Q = 49.01

b) The fraction of the tax borne by consumers is given in Qs,P/ (Qs,P –Qd,P) where ES is the own-price elasticity of supply and ED is the own-price elasticity of demand. Substituting for ES and ED, the pass-through fraction is

0.3/ (0.3- (-0.7) = 0.3

Therefore, consumers will pay 30% of the $0.30 tax, which is 09 cents, and suppliers will pay the remaining .21 cents.

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.