Answer to Question #273282 in Microeconomics for shasha

Question

The world producer price for baseball is $24 per dozen, and almost all of them are produced

outside the United States. Suppose the U.S. demand curve and supply curves are:

QD = 100 000 – 2 000 P

QS = - 10 000 + 1 000 P

P : price per dozen

Q: dozens

1) Before a tariff is imposed, what is the U.S. equilibrium price? Domestic consumption?

Domestic production? imports?

2) Congress has decided to help the baseballmanufacturing industry by imposing a tariff of $ 6 per dozen. What are the new equilibrium price, domestic consumption, domestic production, and imports?

3) What are the losses to U.S. consumers, gains to U.S. producers, and deadweight loss? (Hint: The area of a trapezoid is [height] [ base 1 + base 2 ] / 2 where base 1 and base 2 are the parallel sides of the trapezoid.)

Answer 1

Task #273282

(1). Before a tariff is imposed, what is the U.S. equilibrium price? Domestic consumption? Domestic production? imports?

Solution:

The domestic consumption equilibrium is:

$QD = 100 000 – 2 000 P$

$P =\$24$

$QD = 100 000 – 2 000 (24)= 52,000$

The domestic production equilibrium is : 

$QS = - 10 000 + 1 000 P$

$P=\$24$

$QS = - 10 000 + 1 000 (24)= 14,000$

Imports :

$I= 52,000-14,000=38,000$  

$I=38,000$  

(2) . Congress has decided to help the baseball manufacturing industry by imposing a tariff of $ 6 per dozen. What are the new equilibrium price, domestic consumption, domestic production, and imports?

Solution;

The new equilibrium price after the tariff is:

$P= 24 + 6=\$ 30$  

The domestic consumption equilibrium is:

$QD = 100 000 – 2 000 P$

$P=\$30$

$QD = 100 000 – 2 000 (30)= 40,000$

The domestic production equilibrium is :

$QS = - 10 000 + 1 000 P$

$P=\$30$

$QS = - 10 000 + 1 000 (30) = 20,000$

Imports fall from:

$I= 40,000-20,000= 20,000$  

$I= 20,000$

(3). What are the losses to U.S. consumers, gains to U.S. producers, and dead weight loss? (Hint: The area of a trapezoid is [height] [ base 1 + base 2 ] / 2 where base 1 and base 2 are the parallel sides of the trapezoid.)

Solution:

The loss in consumer surplus is the area of the trapezoid:

$\$6(\frac {40,000+52,000}{2}) =\$276,000$

The gain in producer surplus is the are of the trapezoid:

$\$6(\frac{20,000+14000}{2})= \$102,000$

Revenue earned by the government form the tariff:

$\$6(40,000-20000)=\$120,000$

Dead weight loss:

$\$276,000-\$102,000-\$120,000= \$54,000$