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p(q) = 38−4q

c(q) = 10 + 8q + q^2

find the total surplus. After setting p=MC, the efficient price is 18 and the efficient quantity is 5. The answer for the total surplus is 65, but I keep getting 75. what am I doing wrong? 38-8=30 which is the height. (30x5)/2=75?

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4 May 2023
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Related questions

I understand the first half but get stuck with the budget nuetral subsidy (6-10)

Consider a market where demand is: P = 70 – Q and supply is S: P = Q.

1. Equilibrium quantity Qe is a. 35 b. 36 c. 45 d. 56

2. Equilibrium price Pe is a. $34 b. $35 c. $36 d. $37

3. Consumer surplus CS is a. $610 b. $612.5 c. $615 d. $648

4. Producer surplus PS is a. $610 b. $612.5 c. $615 d. $648

5. Total surplus TS is a. $1,222 b. $1,223 c. $1,224 d. $1,225

Construct a budget neutral subsidy in the above market.

6. Post-subsidy quantity Q’ is a. 35 b. 36 c. 45 d. 56

7. Post-subsidy price P’ is a. $34 b. $35 c. $36 d. $37

8. Consumer surplus CS’ is a. $610 b. $612.5 c. $615 d. $648

9. Producer surplus PS’ is a. $610 b. $612.5 c. $615 d. $648

10. Total surplus TS is (do not forget to account for the subsidy expenditure SE) a. $1,222 b. $1,223 c. $1,224 d. $1,225

In working the following problem, I solved for P to derive: P=60.65-.5Q. From there I calculated TR and MR. I set up excel with Q ranging up to 60 and used P as a function of Q with the P equation. TR=60.65Q-.5Q^2 MR=60.65-1Q I set MC = to the .65 (constant cost but I am not sure that this was correct.) I was able to solve for Q=60 and plug in to Price equation to get profit but I am not sure that this is correct. Please help!

Games to Get, LLC currently enjoys a patent on gaming software that predicts usage for clients involved in civil lawsuits. Demand for this software is

QD = 121.3 – 2P. Software creation and development was $2,350. G2G can generate each copy for a (constant cost) of $0.65).

a. How many copies of the software should G2G attempt to sell? At what price? How much profit would be generated?

b. G2G’s patent expires in 12 months, and soon other gaming companies will produce competing software. What quantity and price will result once competing software emerges? How much consumer surplus will my clients gain once the competitors enter? (For measuring consumer surplus, recall that area of a triangle = ½ * base * height.) My calculation suggests that while in monopoly status, a price of 30.65 can be charged, whereas in competition, P rises. :(

c. How much deadweight loss is created by G2G’s patent and monopoly on this software?

Suppose that there are two firms competing in the market for taxi services. Big Ben Taxis has the marginal cost MCB = $9 per trip, and the fixed cost FCB = $3,000,000. While Whitehall Taxis has the marginal cost MCW = $15 per trip, and the fixed cost FCW = $1,000,000. Inverse demand for taxi trips in the market is given by the function, P = 75 − Q/10,000 . In this equation, P is the price of a taxi trip, and Q is the total quantity of taxi trips supplied by the two taxi companies.

Question 1: Find the equilibrium price and quantities for the case in which the two taxi companies engage in Cournot (quantity) competition. What profits will Big Ben Taxis and Whitehall Taxis earn. (11 Marks)

Question 2: Using your answers to question 1, determine which firm has the greater market power. (4 Marks)

Question 3: Now suppose that a firm can only supply taxi services if it purchases a licence from the government. What is the highest fee that the government can charge for a license, if the government wants both Big Ben Taxis and Whitehall Taxis to purchase a license? (Note: A licence does not place a limit on the number of taxi trips a company can supply. You should assume that both firms are charged the same fee.) (2 Marks)

Question 4: If, instead, the government wants to maximise the revenue it receives from taxi license fees, how many licenses should it sell, and what fee should it charge? (8 Marks)

Q1 and Q2 answered, can anyone help with Q3 and Q4?

Q1

)P = 75 - (Q / 10,000) = 75 - [(QB + QW) / 10,000] (

QB, QW: Quantity of Big Ben & Whitehall respectively)

Total revenue, Big Ben, TRB = P x QB = 75QB - [(QB2 + QW.QB) / 10,000]

Marginal revenue, Big Ben, MRB = dTRB / dQB = 75 - [(2QB + QW) / 10,000]

Equating MRB with MCB, 75 - [(2QB + QW) / 10,000] = 9 750,000 - 2QB - QW = 90,000 2QB + QW = 660,000 .......(1) [Reaction function of Big Ben]

Total revenue, Whitewall, TRW = P x QW = 75QW - [(QW.QB + QW2) / 10,000]

Marginal revenue, Whitehall, MRW = dTRW / dQW = 75 - [(QB + 2QW) / 10,000]

Equating with MCW, 75 - [(QB + 2QW) / 10,000] = 15 750,000 - QB - 2QW = 150,000 QB + 2QW = 600,000 .....(2) [Reaction function of Whitehall]

Cournot equilibrium is obtained by solving (1) and (2).

2QB + QW = 660,000 .......(1) (2) x 2 results: 2QB + 4QW = 1,200,000 ...(3)

(3) - (1) yields:

3QW = 540,000 QW = 180,000 QB = 600,000 - 2QW = 600,000 - (2 x 180,000) = 600,000 - 360,000 = 240,000

Q = QW + QB = 180,000 + 240,000 = 420,000 P = 75 - (420,000 / 10,000) = 75 - 42 = 33

Profit = Total revenue - Total cost = (P x Q) - [FC + (MC x Q)] = Q x (P - MC) - FC [FC: Fixed cost]

Profit, Big Ben = [240,000 x (33 - 9)] - 3,000,000 = (240,000 x 24) - 3,000,000 = 5,760,000 - 3,000,000 = 2,760,000

Profit, Whitehall = [180,000 x (33 - 15) - 1,000,000 = (180,000 x 18) - 1,000,000 = 3,240,000 - 1,000,000 = 2,240,000 (3)

The fixed fee charged by government is equal to consumer surplus (CS) for each company, where CS is the area between demand curve and market price.

From demand curve, When Q = 0, P = 75 [Reservation price] For Big Ben, CS = (1/2) x $(75 - 33) x 240,000 = (1/2) x $42 x 240,000 = $5,040,000

This is the maximum license fee for Big Ben. For Whitehall, CS= (1/2) x $(75 - 33) x 180,000 = (1/2) x $42 x 180,000 = $3,780,000

This is the maximum license fee for Whitehall. (4) Revenue is maximized when marginal revenue is zero.

Marginal revenue, Big Ben, MRB = dTRB / dQB = 75 - [(2QB + QW) / 10,000] So, 75 - [(2QB + QW) / 10,000] = 0 750,000 - 2QB - QW = 0 2QB + QW = 750,000 ......(4)

Marginal revenue, Whitehall, MRW = dTRW / dQW = 75 - [(QB + 2QW) / 10,000] So, 75 - [(QB + 2QW) / 10,000] = 0 750,000 - QB - 2QW = 0 QB + 2QW = 750,000 ....(5) Multiplying (5) by 2, 2QB + 4QW = 1,500,000 ......(6) 2QB + QW = 750,000 ...... (4) (6) - (4) gives: 3QW = 750,000 QW = 250,000 QB = 750,000 - (2 x 250,000) = 750,000 - 500,000 = 250,000 Q = QB + QW = 250,000 + 250,000 = 500,000 P = 75 - (500,000 / 10,000) = 75 - 50 = $25

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