Question

A group of retailers will buy 108 televisions from a wholesaler if the price is $500 and 148 if the price is $450. The wholesaler is willing to supply 88 if the price is $430 and 168 if the price is $520. Assuming that the resulting supply and demand functions are linear, find the equilibrium point for the market.

a) Price: $470, Quantity: 128
b) Price: $480, Quantity: 138
c) Price: $490, Quantity: 148
d) Price: $500, Quantity: 158

Answer 1

To find the equilibrium point, one must determine the linear demand and supply functions from the provided data points and solve for the price and quantity where quantity demanded equals quantity supplied. The options given (a through d) do not offer enough data to calculate the market equilibrium.

Step-by-step explanation:

To find the equilibrium point for the market, we need to determine the price and quantity at which the supply and demand curves intersect. We have two points for the demand curve: (108, $500) and (148, $450), and two points for the supply curve: (88, $430) and (168, $520). By finding the equations for the demand and supply functions, which are linear, we can solve for the point at which they are equal, i.e., where quantity demanded equals quantity supplied.

Let's denote the demand function as Qd = a - bP and the supply function as Qs = c + dP. Using the given points, we can formulate two systems of linear equations to determine the coefficients a, b, c, and d. By then solving these equations, we find the values at which Qd = Qs. This intersection represents the equilibrium of the market. Unfortunately, we cannot determine the correct equilibrium point from the options provided (a through d) without calculating these functions, as none of them include sufficient context or data to solve the problem.