Question

In: Economics

Suppose there are two suppliers of distilled water, labeled firm A and firm B. Distilled water...

Suppose there are two suppliers of distilled water, labeled firm A and firm B. Distilled water is considered to be a homogenous good (well, all water tastes the same, anyway). Let p denote the price per gallon, qA quantity sold by firm A, and qB the quantity sold by firm B. Firm A is located nearby a spring and therefore bears a production cost of cA = $1 per one gallon of water. Firm B is not located near a spring, and thus bears a cost of cB = $2 per gallon. The inverse demand function for distilled water is given by p = 120 – 0.5 Q = 120 – 0.5 (qA + qB) ; where Q = qA +qB denotes the aggregate industry supply of distilled water.

Solve the following problems:

(i) Formulate the profit-maximization problem of firm A.

(ii) Solve for firm A's best-response function, qA = RA (qB).

(iii) Formulate the profit-maximization problem of firm B.

(iv) Solve for firm B's best-response function, qB = RB(qA).

(v) Draw the two best-response functions. Denote the vertical axis by qA, and the horizontal axis by qB.

(vi) Solve for the Cournot equilibrium output levels ???? ?? and ???? ?? . State which firm sells more water and why.

(vii) Solve for the aggregate industry supply and the equilibrium price of distilled water.

(viii) Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why?

Solutions

Expert Solution

(i) Formulate the profit-maximization problem of firm A.

?A = Revenue - cost

= (120 – 0.5 (qA + qB)qA - qA

Maximize ?A = 119qA - 0.5qA^2 - 0.5qAqB

(ii) Solve for firm A's best-response function, qA = RA (qB).

119 - qA - 0.5qB = 0

qA = 119 - 0.5qB

(iii) Formulate the profit-maximization problem of firm B.

?B = Revenue - cost

= (120 – 0.5 (qA + qB)qB - 2qB

Maximize ?B = 118qB - 0.5qB^2 - 0.5qAqB

(iv) Solve for firm B's best-response function, qB = RB(qA).

118 - qB - 0.5qA = 0

qB = 118 - 0.5qA

(v) Draw the two best-response functions. Denote the vertical axis by qA, and the horizontal axis by qB.

(vi) Solve for the Cournot equilibrium output levels ???? ?? and ???? ?? . State which firm sells more water and why.

qB = 118 - 0.5qA

qB = 118 - 0.5*(119 - 0.5qB)

= 118 - 59.5 + 0.25qB

qB = 78 and qA = 80.

Firm A sells more water

(vii) Solve for the aggregate industry supply and the equilibrium price of distilled water.

qA + qB = Q = 78 + 80 = 158. Price = 120 - 0.5*158 = 41

(viii) Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why?

?A = 119*80 - 0.5*(80^2) - 0.5*80*78 = 3200

?B = 118*78 - 0.5*(78^2) - 0.5*80*78 = 3042

Aggregate profit = 6242. Firm A earns a higher profit because

  • it produces more
  • it has lower cost

Related Solutions

(3) Suppose there are two suppliers of distilled water, labeled firm A and firm B. Distilled...
(3) Suppose there are two suppliers of distilled water, labeled firm A and firm B. Distilled water is considered to be a homogenous good (well, all water tastes the same, anyway). Let p denote the price per gallon, qA quantity sold by firm A, and qB the quantity sold by firm B. Firm A is located nearby a spring and therefore bears a production cost of cA = $1 per one gallon of water. Firm B is not located near...
Given four beakers labeled A, B, C, and D. Add 40 mL of distilled water to...
Given four beakers labeled A, B, C, and D. Add 40 mL of distilled water to beakers A and C. Add 40 mL of the prepared sodium acetate/acetic acid buffer solution to both beakers B and D. Pipette 1.0 mL of 6 M HCl, hydrochloric acid solution into beakers A and B. Pipette 1.0 mL of 6 M NaOH, sodium hydroxide solution into beakers C and D. If the concentration of CH3CO2Na after dilution is 0.62M and the concentration of...
In step 4 of part A where you add distilled water to the acid KHP, suppose...
In step 4 of part A where you add distilled water to the acid KHP, suppose you add 40 mL DI h2o instead of 30mL to the flask to dissolve the KHP. Why would this affect the overall outcome of your data? Why/why not? Hint: try to determine whether or not your calculations are affected by this change.   this was a titration performed between KHP and NaOH solution
Suppose there are two firms, Firm A and Firm B that produce identical products in a...
Suppose there are two firms, Firm A and Firm B that produce identical products in a duopoly. Firm A has a constant marginal cost of production, MCA = 10 and Firm B has a constant marginal cost, MCB = 14. The market demand curve for the the product is given by P = 42 − 0.004Q where Q = (QA + QB). (a) Suppose that Firm A has a first-mover advantage. That is, Firm A is able to choose output...
Suppose firm A and firm B are the only two firms in an industry. Each firm’s...
Suppose firm A and firm B are the only two firms in an industry. Each firm’s Marginal Abatement cost functions is given by: MACa = 200-Ea MACb = 200-2Eb Also, there are four people, each with marginal damage function: MDi = 1/3Et , Where Et = Ea+Eb a) What is the uncontrolled emission levels of each firm? b) Find the aggregate MAC function c) Find the aggregate MD function d) Determine the socially optimal level of emissions ?t ∗ and...
Suppose there are two firms: Firm A and Firm B. These firms are each emitting 75...
Suppose there are two firms: Firm A and Firm B. These firms are each emitting 75 tons of pollution. Firm A faces marginal abatement cost MACA = 3A and Firm B faces marginal abatement cost MACB = 9A where A is tons of pollution abatement. The government’s control authority wishes the firms to reduce their total emissions by 60 tons using a Cap and Trade system and will initially auction off the permits 1a How many allowances will the control...
What are the similarities and differences between water that has been distilled and water that has...
What are the similarities and differences between water that has been distilled and water that has been deionized using a RO device?
Suppose that Firm A and Firm B are two of the largest producers of a special pool-cleaning robot.
Suppose that Firm A and Firm B are two of the largest producers of a special pool-cleaning robot. Suppose that the marginal cost of making such a robot is constant at $1,000 per unit, and there is no start-up cost. The demand for the robot is described by the following schedule.Price(in 000s)Quantity(in 000s)TR(in 000s)MR(in 000s)TC(in 000s)MC(in 000s)Profit(in 000s)86776859410311212113a.         Complete the columns for total revenue, marginal revenue, total cost, marginal cost, and profit.b.         If the market for the robots was perfectly...
Compare distilled water to tap water. Can you call these solutions? Are these electrolytes or nonelectrolytes?...
Compare distilled water to tap water. Can you call these solutions? Are these electrolytes or nonelectrolytes? Why? What other solutions can you think that are examples of electrolyte and nonelectrolyte solutions? please use more than 150 words.
What is the osmolarity of distilled water? what is the osmolarity of 40mM CaCl2? Is it...
What is the osmolarity of distilled water? what is the osmolarity of 40mM CaCl2? Is it hypertonic, isotonic or hypotonic?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT