An industry currently has 100 firms, each of which has fixed cost of $16 and average
variable cost as follows:
Quantity Average Variable Cost
1 $1
2 2
3 3
4 4
5 5
6 6
a. Compute a firm’s marginal cost and average total cost for each quantity from 1 to 6.
b. The equilibrium price is currently $10. How much does each firm produce? What is
the total quantity supplied in the market?
c. In the long run, firms can enter and exit the market, and all entrants have the same
costs as above. As this market makes the transition to its long-run equilibrium, will the
price rise or fall? Will the quantity demanded rise or fall? Will the quantity supplied by
each firm rise or fall? Explain your answers.
d. Graph the long-run supply curve for this market, with specific numbers on the axes
as relevant.
a. To compute a firm's marginal cost for each quantity, we can use the following formula:
Marginal Cost = Change in Total Cost / Change in Quantity
For the first quantity (Q = 1), the average variable cost is $1. Since there is no change in the quantity, the marginal cost will be the same as the average variable cost, which is $1.
For the second quantity (Q = 2), the average variable cost is $2. The change in total cost from Q = 1 to Q = 2 is $2 - $1 = $1. Therefore, the marginal cost is $1.
Following the same process, we can calculate the marginal cost for each quantity:
Q = 1: Marginal Cost = $1
Q = 2: Marginal Cost = $1
Q = 3: Marginal Cost = $1
Q = 4: Marginal Cost = $1
Q = 5: Marginal Cost = $1
Q = 6: Marginal Cost = $1
To compute average total cost, we need to add the fixed cost to the average variable cost:
Average Total Cost = Average Variable Cost + Fixed Cost
For each quantity, we calculate:
Q = 1: Average Total Cost = $1 + $16 = $17
Q = 2: Average Total Cost = $2 + $16 = $18
Q = 3: Average Total Cost = $3 + $16 = $19
Q = 4: Average Total Cost = $4 + $16 = $20
Q = 5: Average Total Cost = $5 + $16 = $21
Q = 6: Average Total Cost = $6 + $16 = $22
b. If the equilibrium price is $10, we need to find the quantity at which the market supply equals market demand. Since each firm has the same cost structure, the market supply is the sum of each firm's quantity produced.
The total quantity supplied in the market will be the sum of the quantities produced by each firm. To compute this, we sum up the quantities for each firm:
Q = 1: 100 * 1 = 100
Q = 2: 100 * 2 = 200
Q = 3: 100 * 3 = 300
Q = 4: 100 * 4 = 400
Q = 5: 100 * 5 = 500
Q = 6: 100 * 6 = 600
Thus, each firm will produce 100 units, and the total quantity supplied in the market will be 600 units.
c. In the long run, firms can enter and exit the market. If the market is making a transition to its long-run equilibrium, we need to consider the impact on price, quantity demanded, and quantity supplied by each firm.
As new firms enter the market, the overall supply will increase, leading to a surplus of goods. This surplus will put downward pressure on prices. Therefore, in the long run, the price is likely to fall.
The quantity demanded is determined by consumer preferences and the price. Assuming the consumer preferences remain unchanged, the quantity demanded is not expected to change significantly.
As more firms enter the market, the quantity supplied by each firm will decrease since the total quantity supplied in the market remains constant. This is because the same total quantity is now being produced by a larger number of firms.
d. To graph the long-run supply curve, we need to plot the quantity supplied on the vertical axis and the price on the horizontal axis. The long-run supply curve represents the relationship between the price and the total quantity supplied in the market when all firms are able to adjust their inputs and costs.
In this case, since the market has 100 firms and each firm produces 100 units, the long-run supply curve will be a horizontal line at a quantity of 10,000 units (100 firms * 100 units per firm), regardless of the price. This indicates that in the long run, the market can supply any quantity of goods at a constant price.