Assume that there are two firms in the market described by the inverse demand function P(q1,q2)%3D186 - (2/2)(q1+q2). Firm 1 has marginal costs of 51 and decides on first. Firm 2 has marginal costs of 62 and moves second. Both firms decide on quanties once. How much does firm 1 produce in equilibrium?
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- The business venture involves the sale of decorative jewelry cases. It costs the startup $280 to produce 40 decorative jewelry cases a week while it costs $320 to produce 60 decorative cases per week as well. you and your partners are told that the demand, x, for your product is given as a linear function of price, p, where p(x)=15−0.02x Use the information above, to answer the following questions: 1. Given that the break even points are 16 and 634, If the intention is to make at most 800 jewellery cases a week, what range of quantity demanded can the startup ensure a profit is made. 2. Determine the Maximum Profit that can be made by this new business venture.Suppose the Boston to Philadelphia airline route is serviced by three airlines – US Airways (Firm A) and JetBlue (Firm B) and Continental (Firm C). The demand for airline travel between these two cities is Q = 150 – p. The cost function is C(Q) = 30Q. The cost function is the same for all three airlines. Assume that the three airlines are making investments in airline capacity. In other words, they are simultaneously choosing quantity. (Cournot Competition) Derive US Airways’ residual demand function given JetBlue’s output, qB, and Continental’s output, qC. What is the Marginal Revenue for US Airways? Derive US Airways reaction function Derive the market equilibrium quantity, Q*, price, p*, and Profit.Consider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.
- Suppose the outputs of beauty shops and pet-grooming salons are complementary, providing one-stop shopping for personal and pet maintenance. Betty Beehive is thinking about moving her beauty shop from an isolated location to a vacant building next to Peter’s pet grooming shop.In making her decision, she makes the following assumptions: If Betty moves, she will keep all her current customers (20 people per week) and attract 25% of Peter’s current customers. Peter currently has 60 customers per week. 3. Excluding rent, Betty’s profit per beauty treatment is $10. 4.The weekly rent at the new location is $200 higher than Betty’s current rent. Question = If Betty moves her beauty shop, will her profits increase or decrease? By how much? Question =Suppose that if Betty makes the move, 50 percent of her original customerswill switch from George’s grooming salon to Peter’s. If Peter’s profit pertreatment is $8, how much would he be willing to pay Betty to make themove? Will the…The supply function for a product is 2p - 4 - 10 = 0. while the demand function for the same product is (p + 10)(4 + 30) = 7200. Find the market equilibrium point.= Q.3 Two firms produce homogeneous products. The inverse demand function is given by: p(x₁, x₂) = 80x₁-x2, where x₁ is the quantity chosen by firm 1 and x₂ the quantity chosen simultaneously by firm 2. The cost function of firm 2 is C₂ (x₂) = 20x₂. The cost function of firm 1 is C₁ (x₁) = ₁x₁. Nature chooses C₁ = C₁ = 15 with probability 0.5 and c₁ = CH = 25 with probability 0.5. While firm 1 observes nature's choice, firm 2 cannot observe that choice. Identify the static Bayesian Nash equilibrium.
- A competitive firm produces a product using the function f(x1,x2)=8x1/21x1/22f(x1,x2)=8x11/2x21/2. The factor prices are p1=$2.50p1=$2.50 and p2=$4p2=$4 and the firm can purchase as much of either factor at the given prices. What is the firm's marginal cost? a. None of the above b. ≈$1.07 c. ≈$2.32 d. ≈$1.74Problem # 1 You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for Titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 - QA./600 and PG = 12 - QG./100, where annual quantities are in thousands of pounds and prices are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. a) What is the optimal price and quantity for the aircraft segment? b) What is the optimal price and quantity for the golf segment?An industrial firm makes two products, A and B. These products require water resources where they are very scarce. The products they make are unique, and hence they can set the unit price of each product at any value they want to. However, experience tells them that the higher the unit price for a product, the less amount of that product they will sell. The relationship between the unit price and quantity that can be sold is given by the following two demand functions: Assume for simplicity that the unit price for product A is (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).
- consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7A diner has no competition when it comes to it's famous reuben sandwich combo plate, for which the graph shows the diners demand (d), marginal cost (mc), and marginal revenue (mr), curves. The price of $20 is based on the mr = Mc rule for profit maximazation. The rectangular region shown represents the net revenue from sales of the sandwich (total revenue from reuben combo sales minus total variable costs associated with reuben combo sales). Now, suppose the diner decides to raise the price during the lunch hour, which accounts for 60% of reuben combo sales, knowing that it's lunch-hour patrons are the most loyal buyers of the reuben combo and also that they are locked into the lunchtime slot by their work schedules. The diner raises the price just enough not to lose any lunch-hour buyers. Use the area tool to outline the region representing the resulting additional net revenue from the price increases. Part 2: As a result of the revised price structure, the diners net revenue…Market Equilibrium) A successful advertising campaign by the California Milk Processor Board increases demand for milk. In the short-term, this moves the market demand curve to the right (i.e., increases demand at all price level). The new (short-term) market demand function becomes: Qd(P) = 10062 - 100P The advertising campaign does not affect the (short-term) market supply function which remains: Qs(P) = 3564 + 800P A. Calculate the new Equilibrium Price. B. Calculate the new Equilibrium Quantity. 2. (Profit Maximization in a perfectly competitive market). Using the new market price that you calculated in question 3 and assume that your farm’s weekly cost function is unchanged: TC(Q) = $1036.8 + $2Q + $0.0045Q^2 A. What is the new Profit Maximizing Output Level (Q*) for your farm? B. Where are the farm's Weekly Profits at the new Profit Maximizing Output Level? C. Is this market at its long-run equilibrium? If yes, explain why. If not, discuss what will need to…