The market for apple pies in the city is competitive and has the following demand schedule:
Price Quantity Demanded
$1 1,200
2 1,100
3 1,000
4 900
5 800
6 700
etc...
13 0
Each producer in the market has fixed costs of $9 and the following marginal cost:
Quantity Marginal cost
1 pie $2
2 4
3 6
4 8
5 10
6 12
A) compute each producer's total cost and average total cost for 1 to 6 pies.
B) The price of a pie is now $11. How many pies are sold? How many pies does each producer make? How many producers are there? How much profit does each producer earn?
C) Is the situation described in bar (b) a long-run equilibrium? Why or why not?
D) Suppose that in the long run there is free entry and exit. How much profit does each producer earn in the long-run equilibrium? What is the market price and number of pies each producer makes? How many pies are sold? How many pie producers are operating?
I know this is a lot but I really could use the help! Thanks.
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A) To compute each producer's total cost and average total cost for 1 to 6 pies, we need to add the fixed costs to the respective marginal costs:
Quantity (Q) | Marginal cost (MC) | Fixed Cost (FC) | Total Cost (TC) | Average Total Cost (ATC)
1 | $2 | $9 | $11 | $11/1 = $11.00
2 | $4 | $9 | $13 | $13/2 = $6.50
3 | $6 | $9 | $15 | $15/3 = $5.00
4 | $8 | $9 | $17 | $17/4 = $4.25
5 | $10 | $9 | $19 | $19/5 = $3.80
6 | $12 | $9 | $21 | $21/6 = $3.50
B) When the price of a pie is $11, we need to determine the quantity demanded at this price by referring to the demand schedule:
Price | Quantity Demanded
$11 | ?
From the demand schedule, we can see that at a price of $11, the quantity demanded is 0. Therefore, no pies are sold at this price.
C) In the situation described in part (b), where no pies are sold at a price of $11, it is not a long-run equilibrium. This is because at this price level, there is excess supply in the market. In a long-run equilibrium, the quantity supplied would equal the quantity demanded.
D) In the long-run equilibrium with free entry and exit, the market will adjust to ensure that economic profit is zero for each producer. This means that each producer will only earn a normal profit, covering all costs including opportunity costs.
Since each producer has fixed costs of $9 and the market price is $11, the average total cost (ATC) for each producer will be $11.
To determine the number of pies each producer makes in the long-run equilibrium, we need to find the quantity where ATC equals the market price:
ATC = Market price
$11 = $3.50 (ATC when producing 6 pies)
Therefore, each producer will make 6 pies.
To find the total number of pies sold, we need to sum up the quantities produced by each producer:
6 pies * 1 producer = 6 pies in total
The number of pie producers operating in the long-run equilibrium will depend on the market conditions. If there are no barriers to entry or exit, the number of producers will adjust to ensure that there is no economic profit or loss.
The market price will also adjust to ensure that there is no economic profit or loss. In this case, the market price is $11, the same as the cost of producing 6 pies for each producer.
Therefore, each producer will earn zero economic profit in the long-run equilibrium.
A) To compute each producer's total cost and average total cost for 1 to 6 pies, we need to add the fixed costs to the respective marginal costs for each quantity.
For 1 pie:
Total cost = Fixed cost + Marginal cost
= $9 + $2
= $11
Average total cost = Total cost / Quantity
= $11 / 1
= $11
For 2 pies:
Total cost = Fixed cost + Marginal cost
= $9 + $4
= $13
Average total cost = Total cost / Quantity
= $13 / 2
= $6.50
Repeat the same process for 3 to 6 pies to compute the total cost and average total cost for each quantity.
B) When the price of a pie is $11, we need to find the quantity demanded and the quantity supplied to determine the number of pies sold. Let's cross-reference the quantity demanded and quantity supplied at that price point.
Given the demand schedule:
Price Quantity Demanded
$1 1,200
$2 1,100
$3 1,000
$4 900
$5 800
$6 700
...
$13 0
At a price of $11, the quantity demanded is not specified in the demand schedule. But we can assume that the quantity demanded will be less than or equal to 0 since it decreases as the price increases.
To find the quantity supplied, we need to determine which producer's marginal cost is equal to or less than the price of $11. Looking at the marginal cost table, we can see that the first producer has a marginal cost of $2 for 1 pie, and the second producer has a marginal cost of $4 for 2 pies. Therefore, the quantity supplied will be 2 pies.
Now, let's answer the specific questions:
How many pies are sold?
Quantity sold = Quantity supplied = 2 pies
How many pies does each producer make?
The first producer makes 1 pie, and the second producer makes 1 pie.
How many producers are there?
There are two producers.
How much profit does each producer earn?
To calculate the profit, we need to subtract the total cost from the revenue.
Revenue = Price * Quantity sold
= $11 * 2
= $22
Producer 1:
Profit = Revenue - Total Cost
= $22 - $11
= $11
Producer 2:
Profit = Revenue - Total Cost
= $22 - $13
= $9
C) The situation described in part (B) may not be a long-run equilibrium because there is still profit available for producers. In a long-run equilibrium, all profits should be competed away, and firms should earn zero economic profit. Since producers in part (B) are earning positive profit, other producers can enter the market.
D) In the long-run equilibrium with free entry and exit, economic profit should be zero for each producer. To determine this equilibrium, we need to find the market price and quantity supplied when economic profit is zero.
To achieve zero economic profit, the price should be equal to the average total cost (ATC). Let's find the quantity supplied at the point where price = ATC for each producer.
Producer 1 (ATC = $11):
Quantity supplied by Producer 1 = Quantity demanded at $11 (determined from the demand schedule) = 1,000 pies
Producer 2 (ATC = $6.50):
Quantity supplied by Producer 2 = Quantity demanded at $6.50 (determined from the demand schedule) = 1,200 pies
The market price will be determined by the quantity supplied at the lowest cost (Producer 2) because Producer 1's quantity supplied is less than Producer 2's quantity supplied.
Market price = Producer 2's ATC = $6.50
The number of pies each producer makes will be as follows:
Producer 1: 1,000 pies
Producer 2: 1,200 pies
The total quantity sold will be the sum of producer quantities:
Total pies sold = Producer 1's quantity + Producer 2's quantity
= 1,000 + 1,200
= 2,200 pies
The number of pie producers operating in the long-run equilibrium will depend on the market conditions. If more producers find it profitable to enter the market due to the existing positive profit opportunities, the number of producers may increase. Similarly, if existing producers face losses, some may exit the market, reducing the number of producers.
Note: The number of pie producers operating in the long-run equilibrium is not specified in the provided information.