Question

Consider a city that has a number of hot dog stands operating throughout the downtown area. Suppose that each vendor has a marginal cost of $1.50 per hot dog sold and no fixed cost. Suppose the maximum number of hot dogs that any one vendor can sell is 100 per day.(a) If the price of a hot dog is $2, how many hot dogs does each vendor want to sell?(b) If the industry is perfectly competitive, will the price remain at $2 for a hot dog in the long run? If not, what will the price be?(c) At the price in part (b), if each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the city is Q = 4400 – 1200P, how many vendors are there?(d) Suppose the city decides to regulate hot dog vendors by issuing permits. If the city issues only 20 permits and if each vendor continues to sell 100 hot dogs a day, what price will a hot dog sell for?(e) Suppose the city decides to sell the permits. What is the highest price that a vendor would pay for a permit?

Answer 1

The total, marginal revenue, and costs for Doggies Paradise Inc. have been calculated, with the intention of realizing the profit-maximizing quantity where marginal revenue equals marginal cost. Revenue, cost, and marginal curves were discussed to graphically illustrate the profit maximization point.

Step-by-step explanation:

To calculate the total revenue, marginal revenue, total cost, and marginal cost for Doggies Paradise Inc., we first organize the provided data into a table. The firm sells dog coats at $72 each, with fixed costs of $100, and varying total variable costs for different output levels.

To find the total cost at each output level, we add the fixed costs to the respective variable costs. Marginal cost is calculated as the change in total cost when an additional unit is produced (compared to the previous one). To derive marginal revenue, we consider that in a perfectly competitive market, marginal revenue is equal to the price of the product ($72) since the firm can sell additional units at market price without reducing the price.

The profit-maximizing quantity is where marginal revenue equals marginal cost (MR=MC). Firms in perfectly competitive markets take the market price as given; hence, their marginal revenue is constant. The quantity where MR intersects MC upwardly is the profit-maximizing output because producing more would add more to cost than to revenue.

Graphically, the total revenue curve is a straight line starting from the origin (since revenue is zero when quantity is zero) and has a constant slope equal to the price. The total cost curve starts at the fixed cost and becomes steeper as quantity increases due to rising variable costs. The marginal cost curve instead, will intersect the marginal revenue curve at the firm's profit-maximizing output.

Answer 2

Check the following explanation

Step-by-step explanation:

(a) Since the marginal cost is constant at $1.50 and not increasing, the amount of hot dogs suppliers would want to supply is infinite as $1.50 will always be less than $2 and the more they supply, the more they earn.

(b) No, it would not remain at $2 for a long time. In a perfectly competitive industry, firms can easily enter or leave the industry, therefore, any supernormal profits will attract new firms to enter the industry and increase the overall supply of hot dogs, bringing the price back down to $1.50, where P = MC.

(c) When P = 1.50, Quantity demanded = 4400 - 1200(1.50) = 2600.

Number of firms = 2600/100 = 26 firms.

(d) Quantity supplied = 20(100) = 2000

When demand = supply, 2000 = 4400 - 1200P

P = 2

(e) Supernormal profits per day = (2-1.50)(100) = $50

Therefore, firms will pay a maximum of $50 a day, which is equals to the amount of supernormal profits earned.