Inst. N. hash
Exercises: Econ 407
In each of the following cases assume a purely competitive market.
1. Given the following market demand and supply functions:
qd= 200-5p, qs= 4p-70 where p, qd, qs > 0
a. Find the equilibrium price and quantity.
b. What would happen if government set a maximum price of
$20?
c. What would happen if government set a minimum price of $35?
2. Given the following market demand and supply functions:
qd= 40-1/2p and qs=75p-10 where p, qd, qs > 0
a. Find the equilibrium price and quantity.
b. What would happen if government set a maximum price of $5?
c. What would happen if government set a minimum price of $10?
3. Given the following market demand and supply functions;
qd=120-a*p and qs=c*p-20 where a, c, p, qd, qs > 0
a. Find the equilibrium price and quantity.
b. What values would have to be assigned to parameters c and a in order for the equilibrium price to be $20?
4. Given the following market demand and supply functions:
qd=b-3p qs=4p-d where b, d, p, qd, qs > 0
a. Find the equilibrium price and quantity.
b. What values would have to be assigned to b and d in order for the equilibrium price to be $6?
c. If values of b and d doubled, what effect would this have upon equilibrium price?
5. a) Assume that the demand of problem 1, changes to qd=407-5p. What is the new equilibrium price and quantity?
b) Assume that the demand of problem 1 remains unchanged, but that the supply changes to qs=4p-106. What is the new equilibrium price and quantity
c) Assume now that the demand changes to qd=407-5p and supply to qs=4p-106. What is the new equilibrium?
9. a) Given the demand and supply function of problem 1 what is the effect on equilibrium price and quantity of a specific tax of $9 imposed on the supplier? What proportion of the tax is borne by the consumer?
b) How much revenue will the government collect as a result of the tax?
Note: a specific tax is a tax that collects a fixed amount per unit of a product sold regardless of the actual selling price. As a result, the price received by the supplier is p-amount of the specific tax. To accommodate this a new supply function has to be defined with the price argument replaced by: price-specific tax. The imposition of a specific tax changes both the equilibrium price and quantity. See the following example
qd=100 -2p, and qs= 3p -50. Now suppose a specific tax of $5 is imposed upon the supplier. As a result, the supplier will receive p-$5. The new supply function is going to be:
qs = 3(p-5) -50, which after simplification gives: qs=3p -65. The new equilibrium price will be : $33 which compared to the old equilibrium price is $3 higher. Now the consumer pays $33 and the supplier receives 33; however net of the tax, the supplier receives $33-$5 =$27.