4. Consider a market where every firm and every potential entrant has the iden- tical cost function C(q) = 3q³-6q² +6q. (a) Find the firm's inverse supply function. (b) Suppose the market demand function is given by QP (P) = 20-2P. Find the long-run equilibrium price, quantity, and the number of firms. (c) Suppose the demand function suddenly becomes perfectly inelastic at quan- tity Q = 7. Find the long-run equilibrium price, quantity and the number of firms. (d) Suppose the demand becomes perfectly inelastic at quantity Q = 7, and the government decides to collect a per unit tax t = 4 from the producers for every unit of the good they sell. Find the long-run equilibrium price, quantity and the number of firms.
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- Consider a market where the inverse demand function is P = 400 – 20Q, where Q is the aggregate output. Assume there are three firms which compete à la Bertrand. a)What is the equilibrium price and the corresponding aggregate output if all firms have a constant marginal cost equal to 40? b)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 100? c)What is the equilibrium price and the corresponding aggregate output if one firm has a constant marginal cost equal to 40 and the other firms have a constant marginal cost equal to 260?5. Suppose that market demand is described by P = 100 – (Q+q), where P is the market price, Q is the output of the incumbent firm and q is the output of a potential entrant to the market. The incumbent firm’s total cost function is TC(Q) = 40Q, whereas the cost function of the entrant is C(q) = 100 + 40q, where 100 is a sunk cost incurred to enter the market. If the entrant observes the incumbent producing Q units of output and expects this output level to be maintained, write down the equation for the residual demand curve that the entrant firm faces. If the entrant firm maximize profit given the residual demand curve in a) what output qe will the entrant produce? [Write qe as a function of Q] How much output would the incumbent firm have to produce to just keep the entrant out of the market? [That is, solve for the limit output QL.] At what price will the incumbent sell the limit output?5. Suppose the demand for crude oil is given by the function: Q = -2000P + 70,000 where Q is quantity of oil in thousands of barrels and P is price per barrel of oil. Suppose there are 1000 identical small crude oil producers each with marginal cost MC = Q + 5 Where Q is the output of the typical firm: a) Derive the market supply curve and the equilibrium price and quantity b) Suppose a practically infinite supply of crude oil is discovered in North- Eastern Province (NEP) by a would-be price-leader and that the oil can be produced at constant average and marginal cost of Kshs.15 per barrel. If the supply behavior of the competitive firm described above is not changed by this discovery, how much should the price leader produce in order to maximize profits? c) What price and quantity will now prevail in the oil market? d) Graph (sketch) the results obtained above and show whether the consumer surplus increases as a result of the North-Eastern Province oil discovery? Indicate how the…
- Consider a market where every firm and every potential entrant has the identical cost functionC(q) = 3q3 − 6q2 + 6q.(a) Find the firm’s inverse supply function. b)SupposethemarketdemandfunctionisgivenbyQD(P)=20−2P.Find the long-run equilibrium price, quantity, and the number of firms. (c)Suppose the demand function suddenly becomes perfectly inelastic at quantity Q ̄ = 7. Find the long-run equilibrium price, quantity and the number of firms.(d) [5] Suppose the demand becomes perfectly inelastic at quantity Q ̄ = 7, and the government decides to collect a per unit tax of t = 4 from the producers for every unit of the good they sell. Find the long-run equilibrium price, quantity and the number of firms Please express final numerical answers in decimal format Equation attached belowJames mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…Please no written by hand and no emage Two firms compete in a homogeneous product market where the inverse demand function is P = 20 −5Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $1.6 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $10. The current market price is $15 and was set optimally last year when Firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market.Determine the current profits of the two firms. Firm 1's profits: $Firm 2's profits: $What would each firm’s current profits be if Firm 1 reduced its price to $10 while Firm 2 continued to charge $15?Firm 1's profits: $Firm 2's profits: $Suppose that, by cutting its price to $10, Firm 1 is able to drive Firm 2 completely out of the market. After Firm 2 exits the market, does Firm 1 have an…
- Suppose the profit maximizing firm sells the same good in two individual markets that it is able to keep separate. Since the price elasticity of demand is different in each market, the firm recognizes that rather than charge all customers the same price, it can increase profits by charging different prices in each of the two markets. The demand equations for each market are shown below: Market 1 P=25-2Q Demand The firm's Total Cost Function is: TC=5Q a) What is the optimal output in Market 1? b) What price will be charged in Market 1? Market 2 P=15-Q c) what is the optimal output in market d) what price will be charged in market e) what is the firm's total profit f ) illustrate your answerA. Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s chosen price as given (price taker) and chooses output so as to maximise its own profit. Write down the profit function of the follower. Calculate the profit maximising quantity that the follower selects given the leader’s chosen price p (i.e., calculate the follower’s supply curve S(p)). Interpret the solution to the profit maximising problem. B. The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) as defined in (c) above. Calculate the leader’s residual demand curve using the result in (b). Solve for p as a function of the leader’s output y1, i.e. the inverse demand function facing the leader. Write…If the demand function for a company is given by the equation p= -(16+4)q+(16+16000), and the supply is given by the equation q=(16+550)-p. Find the equilibrium point.
- 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.In a competitive market, the long-run demand is given by P = 20 - (0.01)*q Firms in the industry have as their cost structure the expression C = q3 - 5q2 + 10q. Determine: (a) equilibrium price b) Quantity produced-sold of the firm. c) What quantity is traded in the market? d) Over what time period does this market work? (short or long term?) e) What is the profit of the individual firm? f) What will be the behavior of the individual firm, will it exit or stay in the market?c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s chosen price as given (price taker) and chooses output so as to maximise its own profit. Write down the profit function of the follower. Calculate the profit maximising quantity that the follower selects given the leader’s chosen price p (i.e., calculate the follower’s supply curve S(p)). Interpret the solution to the profit maximising problem. d) The leader is facing the residual demand curve R(p)=D(p)-S(p) with D(p) and S(p) as defined in (c) Calculate the leader’s residual demand curve using the result in (c). Solve for p as a function of the leader’s output y1, i.e. the inverse…