Question

Imagine that the cell-phone market is made up of one large firm that leads the industry and sets its own price first, while smaller firms in the industry follow. There are 20 such smaller firms, each with a supply function of qi=22.50+ p/5 for i=1,2,…,20 firms, while p is the per-unit price. Total market demand for cell phones is given by the function Q=4,900.00−p. If the cost function for the leading firm is cL(qL )=10ᵩₗ, calculate the following values: Leading firm's production: qL =______ (Round to two decimals if necessary.) Total follower firm production: qF =______(Round to two decimals if necessary.) Equilibrium price: p=______ (Round to two decimals if necessary.)

Answer 1

To calculate the leading firm's production, total follower firm production, and the equilibrium price, one must solve the system of equations derived from the given supply function of follower firms, the cost function of the leading firm, and the total market demand.

Step-by-step explanation:

The student's question involves analyzing market supply and demand functions to determine the leading firm's production (qL), total follower firm production (qF), and the equilibrium price (p) in a hypothetical cell-phone market model. Each of the 20 follower firms has a supply function qi = 22.50 + p/5, where qi is the quantity supplied by firm i and p is the price. The total market demand is given by Q = 4,900.00 - p. For the leading firm with cost function cL(qL) = 10qL, we need to solve for the equilibrium where total quantity supplied equals total quantity demanded. Suppose the leading firm quantities its supply as qL. Then, total supply from follower firms is qF = 20(22.50 + p/5). The market is in equilibrium when qL + qF = Q. To solve for the main answer values, we set up the equation qL + 20(22.50 + p/5) = 4,900.00 - p and solve for p. Once we have p, we can find qL and qF.The calculation of each value involves algebra to manipulate the equations accordingly. For accuracy, rounding each result to two decimals is also essentia when necessary. This method of determining equilibrium embodies the basic principles of supply and demand dynamics within a market under the assumption that the leading firm sets the price which follower firms then adhere to.