Question

Ayabonga designs and manufactures cycling products. The demand and supply functions for bikes are pd=600−1,5qd and ps=−30+6qs, respectively. Where p is the price, and q is the quantity. The equilibrium price and quantity are :

A. P=84;q=474.
B. p=474;q=84.
C. p=600;q=30.
D. p=30;q=600.

Answer 1

At a price of $210, the quantity demanded is 260 units and the quantity supplied is 40 units. The price at which the quantity supplied is equal to 48,000 is $287,970. The equilibrium price and quantity can be determined by graphing the demand and supply curves or by analyzing the table; the equilibrium price is $84 and the equilibrium quantity is 474 units.

Step-by-step explanation:

a. At a price of $210, the quantity demanded can be found by substituting the price into the demand function and solving for q:
pd = 600 - 1.5qd
$210 = 600 - 1.5q
1.5q = 600 - 210
q = (600 - 210) / 1.5 = 260 units

To find the quantity supplied, substitute the price into the supply function and solve for q:
ps = -30 + 6qs
$210 = -30 + 6q
6q = 210 + 30
q = (210 + 30) / 6 = 40 units

b. To find the price at which the quantity supplied is equal to 48,000, substitute 48,000 into the supply function and solve for p:
ps = -30 + 6qs
p = -30 + 6(48,000)
p = -30 + 288,000
p = 287,970

c. To graph the demand and supply curves, plot the price and quantity values from the given functions on a coordinate plane, with quantity on the y-axis and price on the x-axis. The equilibrium price and quantity can be determined by finding the point of intersection between the demand and supply curves. From the table, the equilibrium price is $84 and the equilibrium quantity is 474 units.