2. Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2 and f(x1, x2) = min{2x1, x2}, holding x2 at 2, and taking real factor prices w₁ and w2 as given.
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- true or false? The sufficient condition for profit maximization must be satisfied that MC cuts MR curve from below1. Estimated Demand. You are the manager of a firm that sells packs of coffee pods for coffee makers. You typically sell the packs for $24 and sell an average of 2,470 packs per month. You decide to raise the price to $28 per pack. When you do this your monthly sales fall to 1,482 packs per month. a. Assuming that your firm’s demand function is linear (i.e., takes the form QP=a-bP), calculate the linear demand function for the packs 2. Markups and elasticities. The marginal cost (MC) of producing your product is $16 a. Using the estimated demand curve from the previous question, calculate the point price elasticities of demand at the two price from question 1 b. Use the markups and elasticities and indicate whether the two prices are higher or lower than the profit maximizing price. NOTE: YOU DO NOT NEED TO CALCULATE THE PROFIT MAXIMIZING PRICE YET.A major software developer has estimated the demand for its new personal finance software package to be Q=1,000,000P-2 while the total cost of the package is C = 10,000+ 25Q. If this firm wishes to maximize profit, what percentage markup should it place on this product where percentage markup is defined as 100*(sale price - marginal cost)/marginal cost? 4. a. b. C. d. e. ANS: 90% 100% 20% 40% 250%
- If demand function is given by P = 40 - 2Q then what is the procedure to get marginal revnue ?The figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves of the car manufacturer. The quantity and price at polnt E are (Q*. P*) - (30, 5,500). Suppose now that the firm Increases the price to 5,550 and chooses the corresponding level of output from the demand function at the new price. Based on this Information, whlch of the following Is correct? 8,000 Demand curve 100 Quantity of cars, O O The firm will sell 30 cars at the higher price. O The firm's profit remains the same. O The quantity of cars produced reduced. O Tho firm's profit is now incroasod Price, Marginal cost ($)Suppose we are studying the long-run competitive market for robots, the market demand for robots isgiven byD(p)=24p. All the firms are identical with the following cost curveC(y)=y22+8. a)What is the long-run competitive market equilibrium? Rick is a single consumer in the market; his consumption of robots is given byDi(p)=Mp, whereMis his fixed income. Rick is also a government regulator for the robot market; he decides if themarket is competitive or a monopoly.Morty is a firm in the market (he faces the same cost curve as everyone else:C(y)=y22+8). Mortywould like to operate as a monopolist (instead of a firm in a competitive market). b)How much would Morty have to pay/compensate Rick in order for Rick to allow Morty to operateas a monopolist (The market demand curve is the same as part a))? c)Suppose instead this was an oligopoly market with 2 firms engaged in Bertrand competition; bothfirms face the same cost curve and demand curve as part a). How much…
- Suppose the lease for cubicles is under a long-term contract and the firm already chose how many cubicles to lease. Suppose specifically that the firm is leasing 5 cubicles. The firm, however, must decide how many employees to hire for its projects. Let P stand for the price of output produced by the firm and let w₁ stand for the cost per employee. Which of the following functions represents the firm's demand function for employees? Choose one: О А. 1.14 = P w1x-2.94 O B. x = (z WI Px-2.94 1.14 -2.94 P = w₁x1.14 O D. D. = (Px1.14) O E. 3 الف x= Px1.14. -2.94 -2.94In the market for Fante Kenley, the supply and demand functions respectively are Q° = 0.25P+ 10 and Q° =-0.5P+100 When there is excess demand, price adjusts according to the equation -0.5(Q" -0) dt a) Find the long run equilibrium price, P* (that is, the price at which there is no excess demand or supply). b) Formulate and solve he first order differential equation giving Pas a function of time, t. Is this market dynamically stable or unstable? c) If the initial price is P = 50, how close will the price be to its long run equilibrium value, when t= 10?1 One of the characteristics of Hicksian demand is that it is homogenous of degree zero in prices. Check if the following functions can be Hicksian demand functions: a) h„(Pz, Py, U) = p5U/p5 0.5 b) hz(Pz, Py, U) = U c) h(Pz, Py, U) = P„U
- 2. Say we have a profit maximizing firm that produces one output good with two factor inputs. The factor prices are w> 0 for factors i = {1,2}. The production technology is y = f(x1.₂). a. Define the firm's short-run profit maximization problem when 1 is the fixed factor set at level 1 > 0. b. Say in the short-run profit max problem, the technology f(1, ₂) is smooth and strictly concave and has the "increasing difference property" f12(x) > 0. Say (a) #1 increases, (b) we decreases. Show the optimal factor demand (1, Waip, w1) increases when both (a) and (b) happen. c. Show that output in part (b) also increases when both (a) and (b) happen d. Now, use the envelope theorem to show how to construct the Long-run profit maximization problem from this short-run problem. e. Draw a picture of the long-run profit maximization problem, and explain how it relates to the cost minimization problem.Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.006x³ +0.02x² +0.6x. Currently, Pierce sells 90 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 95 lawn chairs were sold each day? c) What is the marginal revenue when 90 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(91), R(92), and R(93). (…) a) The current revenue is $ b) The revenue would increase by $. (Round to the nearest cent.) c) The marginal revenue is $when 90 lawn chairs are sold daily. d) R(91) ≈ $ R(92) $ R(93) $Define Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationshipTC = 20 + 5Q + Q2Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationshipQ = 25 - Pa. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)b. Determine the output level where total profits are maximized.