Supply and Demand and Long-run Equilibrium Price
Part 1:
Suppose that the tin mining market is perfectly competitive. The market demand curve is given by D(P) = 300 – P, where D is measured in units per year, and P is measured in $ per units.
There are many potential entrants into this market, all of whom have identical cost curves. These cost curves are summarized in Table 1 below:
Table 1
Cost Curve
Formula
Maginal cost (in $ per unit)
MC = 30.
Fixed cost per year
FC = 100.
(Annualized) Capital charge
CC = 100.
Capacity (in units per year)
C = 20.
The Deliverables
Please complete each of the following tasks. While you do not need to show every graph and every step of algebra that you used to arrive at your answers, please show enough of your work so that I can figure out the logic that you used to arrive at your answer. Please keep your answer to Part 1 to three pages or less.
Task 1: Draw in a graph the short-run supply curve of a single firm. Express as a function of Q the ATC and FR-ATC curve and draw them in a separate graph. Compute the minimum level of the ATC and FR-ATC curves and represent them graphically.
Task 2: Suppose that the industry consists of 10 firms with cost curves given by those in Table 1. Find the short-run equilibrium price when the market consists of these 10 firms. (You should assume that these 10 firms act as price takers.)
Task 3: Assume that there is large number of potential entrants with cost curves given by those in Table 1. Given this, what is the long-run equilibrium price in this market? At this price, how much does a typical firm supply? How many new entrants come into the market? What is the profit of a firm of at this equilibrium (taking into account the initial investment)?
Task 4: As in Task 3, let’s suppose that there are the same 10 incumbents, and a large number of potential entrants into this industry. However --- and here is the twist! --- suppose that the cost curves of these potential entrants, rather than being described by Table 1 above, have cost
Suppose that the tin mining market is perfectly competitive. The market demand curve is given by D(P) = 300 – P, where D is measured in units per year, and P is measured in $ per units.
There are many potential entrants into this market, all of whom have identical cost curves. These cost curves are summarized in Table 1 below:
Table 1
Cost Curve
Formula
Maginal cost (in $ per unit)
MC = 30.
Fixed cost per year
FC = 100.
(Annualized) Capital charge
CC = 100.
Capacity (in units per year)
C = 20.
The Deliverables
Please complete each of the following tasks. While you do not need to show every graph and every step of algebra that you used to arrive at your answers, please show enough of your work so that I can figure out the logic that you used to arrive at your answer. Please keep your answer to Part 1 to three pages or less.
Task 1: Draw in a graph the short-run supply curve of a single firm. Express as a function of Q the ATC and FR-ATC curve and draw them in a separate graph. Compute the minimum level of the ATC and FR-ATC curves and represent them graphically.
Task 2: Suppose that the industry consists of 10 firms with cost curves given by those in Table 1. Find the short-run equilibrium price when the market consists of these 10 firms. (You should assume that these 10 firms act as price takers.)
Task 3: Assume that there is large number of potential entrants with cost curves given by those in Table 1. Given this, what is the long-run equilibrium price in this market? At this price, how much does a typical firm supply? How many new entrants come into the market? What is the profit of a firm of at this equilibrium (taking into account the initial investment)?
Task 4: As in Task 3, let’s suppose that there are the same 10 incumbents, and a large number of potential entrants into this industry. However --- and here is the twist! --- suppose that the cost curves of these potential entrants, rather than being described by Table 1 above, have cost