Consider a competitive firm with a total cost function given by TC (q) = 1000- Suppose that, in order to incentivize higher production, the government decides to refund firms for their cost of producing the FIRST q units produced, up to 1000 of them. QUESTION: What is the LARGEST market price at which the policy actually has an impact on the amount supplied by the firm (in comparison to the free- trade situation in which no such refund is present)?
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- Signaling. There are two firms, A and B. There are two time periods, 1 and2. There is one commodity, that can be produced by both firms, at linear cost. So,if firm i has marginal cost i, then the cost of producing q units of the commodity is ciq. The inverse demand for the commodity, at any given moment, is 100 − 4Q,where Q is the aggregate supply at that moment.In period 1, firm A is alone in the market. Firm A’s marginal cost is determinedby Nature, either it is 10 or it is 2, each with probability 1/2. A knows it’s cost.Firm A produces some quantity in period 1 and firm B observes this. Betweenperiods 1 and 2, firm B decides to enter the market or not. After making thisdecision, B is told firm A’s cost. It is too late at this point for B to change itsaction.In period 2, if B is in the market, then A and B compete on quantity.(1) In words, what are the steps to solving this problem?(2) There are two possible quantity-competition games that happen in this game.Solve them both.(3) Now…Suppose we allocate a fixed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P = 8 - 0.34q while the marginal cost is constant at $2 per unit. The total supply is 20 units and the discount rate is 1%. What is the marginal user cost during the first period?3.(9N10.8) Suppose that the long-run total cost function for the typical mushroom producer is given by: ( , ) 2 cqw wq q =-+ 10 100 where q is the output of the typica1 firm and w represents the hourly wage rate of mushroom pickers. Suppose also that the demand for mushrooms is given by Q = -1,000P+ 40,000 where Q js total quantity demanded and P is the market price of mushrooms. A. If the wage rate for mushroom pickers is $1, what will be the long-run equilibrium output for the typical mushroom picker? B. Assuming that the mushroom industry exhibits constant costs and that all firms are identical, what will be the long-run equilibrium price of mushrooms, and how many mushroom firms will there be? ( , ) 2 C. Suppose the government imposed a tax of $3 for each mushroom picker hired (raising total wage costs, w, to $4). Assuming that the typical firm continues to have costs given by: cqw wq q =-+ 10 100 how will your answers to parts (a) and (b) change with this new, higher wage rate?
- Suppose marginal cost and thus market supply, for an industry is given by the equation P = 4QS + 20. Also suppose the market demand curve is given by the equation QD = 40 – 0.5P Determine the equilibrium price and quantity for this industry assuming it is competitive market. Assuming government considers the current equilibrium price too high for the market and decides to set the new equilibrium price at 45, describe what the state of the market will look like The short run production assumes there is at least one fixed factor input.The production function relates the quantity of factor inputs used by a business to the amount of output that result. Using an appropriate diagram explain the short run production and stages of production.A firm’s profit is given by the following function, which maps output q ≥ 0 onto profit (revenue minus cost). π(q) = 11q − (q 2 + 2q + 10) = −q 2 + 9q − 10, The firm is constrained by a quota such that output q cannot be greater than a value Q. (a) What is the domain of this profit function? 1 of 2 ECON10071/20071 - 2020/21 (b) Given this, what is (global) profit maximising output when (i) Q = 6, and when (ii) Q = 2.The marginal and average total cost curves for barbers in an area are cosntant at $12.00/haircut. The daily demand curve for haircuts in the area is given by: P = 22 - 0.001Qd where P is the price in dollars per haircut and Qd is the daily quantity demanded in number of haircuts. Haircuts are provided in a perfectly competitive market and each barber can provide exactly 25 haircuts daily. Suppose that the government decides to limit the number of barbers to 320. Each year, barbers must obtain a government-issued license to cut hair. Based upon the previous information: a. What will be the long-run equilibrium price for a haircut given there are only 320 licensed barbers?b. How much economic profit will each licensed barber earn daily?
- The inverse demand function for a depletable resources is P=8-0.4q and the marginal cost of supplying it is $2 If 20 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to the first period and how much to the second period when the discount rate is 5% and 10% (Hint Demand Function is the same in both periods) Given the discount rate what would be the efficient price in the two periods? What would be the marginal user cost in each period? Assume a discount rate of 0% determine the efficient allocation amount between the two period Prepare a schedule of the discount rate and the efficient allocation for the two period and graph the relationship. What can you say about the discount rate and the allocation between the two periods?Consider an imperfectly competitive service provider, Muscat Automotive Repair Services (MARS), whose total cost of production is C = 30Q +0. 165Q2. Also, MARS faces two different market segments, A and B, whose demands can be linearly expressed as QA = 240 − PA and QB = 120 − 0.5PB . (Hint: the marginal cost is the slope of the total cost function). 4. If MARS decides to segment the market in accordance with the demands of groups A and B, find the profit-maximizing prices and quantities (PA, QA) and (PB, QB).5. What is the value of the consumer surplus for each group A and B, under this segmentation strategy?6. Draw the situation described in (4) and (5) above, clearly showing each group’s profitmaximizing price and quantity, and the areas that correspond to their consumer surpluses.7. Verify the inverse elasticity rule under each of the scenarios described (1) and (4) above.Which returns to scale will an efficient firm choose? What market structure has no loss in long run? What production function shows the maximum quantity of goods or services that can be produced with a set of inputs assuming one of the inputs used remains unchanged? Capacity planning refers to adjustment in production considering the what? What can destroy monopoly position?
- The inverse demand function for a depletable resource is P=8-0.4q and the marginal cost of supplying it is $2 If 20 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to the first period and how much to the second period when the discount rate is 5% and 10% (Hint Demand Function is the same in both periods) Given the discount rate, what would be the efficient price in the two periods? What would be the marginal user cost in each period? Assume a discount rate of 0% determine the efficient allocation amount between the two period Prepare a schedule of the discount rate and the efficient allocation for the two-period and graph the relationship. What can you say about the discount rate and the allocation between the two periods?Suppose marginal cost and thus market supply, for an industry is given by the equation P = 4Q S + 20. Also suppose the market demand curve is given by the equation Q D = 40 – 0.5P i. Determine the equilibrium price and quantity for this industry assuming it is competitive market. ii. Assuming government considers the current equilibrium price too high for the market and decides to set the new equilibrium price at 45, describe what the state of the market will look like CR, c) The short run production assumes there is at least one fixed factor input. The production function relates the quantity of factor inputs used by a business to the amount of output that result. Using an appropriate diagram explain the short run production and stages of production.Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural resource. a. How should the analysis of the maximization of the discounted profits from selling this resource (Equation 17.63 be modified to take this fact into account? b. Suppose that the demand for the resource in question had a constant elasticity form q(t)=a[p(t)]b . How would this change the price dynamics shown in Equation 17.67? c. How would the answer to Problem 17.7 be changed if the entire crude oil supply were owned by a single firm?