You can sell 90 pet chias per week if they are marked at $1 each, but only 50 each week if they are marked at $2/chia. Your chia supplier is prepared to sell you 40 chias each week if they are marked at $1 per chia, and 100 each week if they are marked at $2 per chia.(a)Write down the associated linear demand and supply functions.demand function q(p) = supply function q(p) = (b)At what price (in dollars) should the chias be marked so that there is neither a surplus nor a shortage of chias?$
Question
You can sell 90 pet chias per week if they are marked at 2/chia. Your chia supplier is prepared to sell you 40 chias each week if they are marked at 2 per chia.(a)Write down the associated linear demand and supply functions.demand function q(p) = supply function q(p) = (b)At what price (in dollars) should the chias be marked so that there is neither a surplus nor a shortage of chias?$
Solution
(a) The demand and supply functions are linear and can be written in the form q(p) = mp + b, where m is the slope and b is the y-intercept.
For the demand function, we know that at 2, 50 chias are sold. So, we can find the slope (m) as (50-90)/(2-1) = -40. The y-intercept (b) is the quantity sold when the price is 1 increase in price, at $0, the quantity sold would be 90 + 40 = 130. So, the demand function is q(p) = -40p + 130.
For the supply function, we know that at 2, 100 chias are supplied. So, the slope (m) is (100-40)/(2-1) = 60. The y-intercept (b) is the quantity supplied when the price is 1 increase in price, at $0, the quantity supplied would be 40 - 60 = -20. So, the supply function is q(p) = 60p - 20.
(b) The price at which there is neither a surplus nor a shortage of chias is the price at which the quantity demanded equals the quantity supplied. So, we set the demand function equal to the supply function and solve for p:
-40p + 130 = 60p - 20 100p = 150 p = 150/100 = $1.50
So, the chias should be marked at $1.50 each to ensure there is neither a surplus nor a shortage.
Similar Questions
The total cost (in dollars) for a company to manufacture and sell 𝑥 items per week is 𝐶=50𝑥+2960, whereas the revenue brought in by selling all 𝑥 items is 𝑅=140𝑥-0.6𝑥2. How many items must be sold to obtain a weekly profit of $400?Hint: Profit = Revenue - Cost.They need to sell or items.
Complete the problem by using the accompanying figure, which shows a supply function and a demand function. (Assume price is measured in dollars.)Match the question with the correct answer. Is there a surplus or shortage when the price is $38? a. 56 units If the price is $38, what quantity is demanded? b. 4 units How many units is the surplus or shortage? c. 52 units If the price is $38 what quantity is supplied? d. surplus
Amy buys a new dog for $1500. She receives consumer surplus of $300 on her purchase. Her willingness to pay is: A. $300 B. $1500 C. $1800 D. $1200
The following table shows the revenue and costs of a Parrot farmer in a perfectly competitive industry. Table 1 Quantity of Parrots harvested: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Total Revenue ($): 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 Total Cost ($): 3, 5, 9, 15, 23, 33, 45, 59, 75, 94, 115 MR: MC: a) Fill in the values for MR and MC in Table 1 b) How much is total fixed cost for this Parrot farmer? Why? c) If the farmer chooses to maximise profit, what would marginal cost be equal to and what would be the ‘range’ for the appropriate output level? Why? d) What is the maximum profit available to this farmer’s firm? e) If the market price of Parrots fell below $10 in the market then what should the farmer do in the short run? What about the long run?
For a certain product, the demand function is 𝐷(𝑄) = 1000 − 25𝑄 and thesupply function is 𝑆(𝑄) = 100 + 𝑄2. Calculate:a) The market equilibrium price and quantityb) Compute the consumer and producer surplus.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.