In: Economics
Suppose you are given the following supply and demand functions for Zazzy Products: Q^D = 10,000 – 5P + 2P_y - 3P_b + 3M + 6A Q^S = 2,000 + 3P - 10P_w where: Q^D = quantity demanded of Zazzy Products Q^S = quantity supplied of Zazzy Products P = price per unit of Zazzy Products P_y = price per unit of Good Y P_b = price per unit of Good B M = consumer income A = number of advertisements for Zazzy Products P_w = price of input W, used to make Zazzy Products
a) With respect to buyer behavior for Zazzy Products, how is Good Y related to Zazzy Products? How do you know? (3 points)
b) With respect to buyer behavior for Zazzy Products, how is Good B related to Zazzy Products? How do you know? (3 points)
c) With respect to buyer behavior for Zazzy Products, what type of good is Zazzy Products when it comes to income changes? How do you know? (3 points)
d) With respect to seller behavior for Zazzy Products, what would happen to its production level if the price of the input, Good W, were to increase? How do you know? (3 points)
e) Assume the following figures: Price per unit of Good B = $4 Price per unit of Good Y = $2 Consumer Income = $30,000 Number of Advertisements for Zazzy = 15,000 Price per unit of Input W = $30 With this information, calculate the equilibrium price and quantity for Zazzy Products. You must show all your work. (8 points)
a) Good Y is a substitute to Zazzy products because . This means as Py increases by 1 unit, QD increases by 2 units. So, increase in price of y leads to increase in demand for Zazzy products. Thus, y is a substitute to Zazzy products because increase in price of Y, decreases the demand for Y and increases the demand for its substitutes.
b) Good B is a complemet to Zazzy products because . This means as Pb increases by 1 unit, QD decreases by 3 units. So, increase in price of b leads to decrease in demand for Zazzy products. Thus, b is a complement to Zazzy products because increase in price of b, decreases the demand for b and also decreases the demand for its complements.
c) Zazzy products are normal goods because . This means that as income increases, demand for zazzy products also increases. So, they are a normal good.
d) If price of input were to increase then supply would decrease because . So, as Pw increases by 1 unit, supply decreases by 10 units.
e) Q^D = 10,000 – 5P + 2P_y - 3P_b + 3M + 6A = 10,000 - 5P +
2(2) - 3(4) + 3(30,000) + 6(15,000) = 10,000 - 5P + 4 - 12 + 90,000
+ 90,000 = 189,992 - 5P
Q^S = 2,000 + 3P - 10P_w = 2,000 + 3P - 10(30) = 2000 + 3P - 300 =
1700 + 3P
At equilibrium, QD = QS. So,
189,992 - 5P = 1700 + 3P
So, 3P + 5P = 189,992 - 1700
So, 8P = 188,292
So, P = 188,292/8 = 23,536.5
Q = 1700 + 3P = 1700 + 3(23,536.5) = 1700 + 70,609.5 = 72,309.5
Price = $23,536.5
Quantity = 72,309.5