1. Your roommate's long hours in chem lab finally paid off--she discovered a secret formula that lets people do an hour's worth of studying in 5 minutes. So far, she's sold 200 doses and faces the following average-total-cost schedule:
Q = 199 & ATC = $199
Q = 200 & ATC = 200
Q = 201 & ATC = 201
If a new customer offers to pay your roommate $300 for one dose, should she make one more? Explain.
Would the answer be yes because to produce one more would cost $202 which is less than the $300 the customer is willing to pay.
3. You go out to the best restaurant in town and order a lobster, you realize that you are quite full. Your date wants you to finish your dinner because you can't take it home and because "you've already paid for it" What should you do?
Isn't because I am full that the remaining amount of lobster is a sunk cost. So it is best to let it go and not eat it.
10. An industry currently has 100 firms, all of which have fixed cost of $16 and average variable cost as follows:
Quantity / Average variable cost: (1/$1),(2,$2), (3,$3), (4,$4), (5,$5), and (6,$6)
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?
1) She should produce whenever Marginal Revenue > Marginal cost. MR=300. What is Marginal Cost?
if Q=199 and ATC=199 then Total Cost TC = 199*199=39601.
When Q=200,ATC=200 then TC = 40000, Thus MC=40000-39601 = 399.
When Q=201,ATC=201 then TC=40401. Thus MC=401.
Now, what do you think the roomate should do?
3) I agree with your answer.
10) Good problem. First construct a marginal cost curve for a firm. (Same procedure as in 1 above).
Next, determine the break-even point for your firm. That is, at what price will the firm have zero net profits.
By my calculations, firms break even at P=$8. At P=8, each of the firms will produce 4 units. So, total revenue = 4*8=32. AVC=4*4=16 and fixed costs=16.
Your question says nothing about the current (short-run) price. So, lets assume. If Price < $8, then firms will be in a loss situation. Some will drop out, shifting the supply curve inward. Quantity demanded will fall, price will rise (to $8).
If Price > $8 then firms will enjoy an economic profit. More firms will enter (assuming they have the same cost structures). Supply shifts out, Price goes down, quantity demanded goes up, each firm's output will either fall are stay the same.
2. A company is considering building a bridge across a river. The bridge would cost $2 million to build and nothing to maintain. The following table shows the company¡¯s anticipated demand over the lifetime of the bridge:
Price per crossing ($) 8 7 6 5 4 3 2 1 0
Number of crossings (¡®000) 0 100 200 300 400 500 600 700 800
a. If the company were to build the bridge, what would be its profit-maximizing price? Would that be the efficient level of output? Why or why not?
b. If the company is interested in maximizing profit, should it build the bridge? What would be its profit or loss?
c. If the government were to build the bridge, what price should it charge?
d. Should the government build the bridge? Explain your answer.
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1. To determine whether the roommate should make one more dose of the secret formula, we need to compare the marginal cost to the marginal revenue. The marginal cost is the additional cost of producing one more dose, while the marginal revenue is the additional revenue earned from selling one more dose.
In this case, the marginal cost can be calculated by finding the difference in total cost between producing Q=201 and Q=200. From the given average total cost (ATC) schedule, we see that when Q=200, ATC=200, which means the total cost (TC) is 200*200 = $40,000. When Q=201, ATC=201, so the TC is 201*201 = $40,401. Therefore, the marginal cost is TC(Q=201) - TC(Q=200) = $40,401 - $40,000 = $401.
The marginal revenue is the revenue gained by selling one more dose, which in this case is the price offered by the new customer, $300.
If the marginal revenue is greater than the marginal cost (MR > MC), then it is profitable for the roommate to produce one more dose. In this case, the marginal revenue ($300) is greater than the marginal cost ($401), so the roommate should go ahead and produce one more dose to take advantage of the higher price.
3. You are correct in your analysis. When considering whether to eat the remaining lobster, it is important to focus on the present scenario and your current level of fullness. The cost of the lobster that you've already paid for is a sunk cost, meaning it has been incurred and cannot be recovered. Therefore, you should make the decision based on your current satisfaction and well-being. If you are already full, it is best to let go of the remaining lobster and not force yourself to eat it, as it will not provide any additional benefit and may make you uncomfortable.
10. In this scenario, where the industry currently has 100 firms with fixed costs of $16 and average variable costs that increase with quantity, we need to analyze the long-run equilibrium.
To determine the price, quantity demanded, and quantity supplied in the long-run equilibrium, we need to consider the break-even point for each firm and the market dynamics.
First, calculate the break-even point for the firms. In this case, the break-even point occurs when the price (P) is equal to the average variable cost (AVC). As given, the AVC increases with quantity, so we need to find the quantity at which AVC becomes equal to the fixed cost (FC).
From the given information, the AVC is equal to the quantity itself. For example, when Q=1, AVC=1, when Q=2, AVC=2, and so on. We also know that the FC is $16 for each firm.
The break-even point occurs when AVC = FC, so we can set the equation Q = FC and solve for Q:
Q = $16
Q = 16
Therefore, when the price is equal to $16, each firm in the industry will produce 16 units.
Now, let's analyze the market dynamics. If the price in the market (P) is less than $16, firms will be in a loss situation because the price is lower than the break-even point. Some firms may choose to exit the market, reducing the supply of the product. This decrease in supply will lead to a decrease in quantity demanded and a rise in price.
On the other hand, if the price in the market (P) is greater than $16, firms will earn an economic profit and attract new firms to enter the market. This increase in supply will lead to a decrease in price and an increase in quantity demanded.
Overall, whether the price rises or falls, and whether the quantity demanded and supplied rise or fall, depends on the relationship between the market price (P) and the break-even point for each firm.