The demand curve for milk can be represented by the following equation: Q = 6000 – 800P There are only two producers and the marginal cost to produce one unit of milk is $6 %3D (There is no fixed cost). If the capacity of each firm is 600 output, calculate the price range of milk under the Bertrand-Edgeworth Model.
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- For a certain company, the cost function for producing x items is C(x)=30x+250 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 140 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answers to some of the questions are given below so that you can check your work. Assuming that the company sells all that it produces, what is the profit function? P(x)= . Hint: Profit = Revenue - Cost as we examined in Discussion 3. What is the domain of P(x)? Hint: Does calculating P(x) make sense when x=−10 or x=1,000? The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose? Profit when producing 70 items = Profit when producing 80 items =…In the specific factor model in a market equilibrium the mobile factor's productivity must be the same for the production of all goods. True FalseConsider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. (a) Write down the definition of a competitive equilibrium for the above economy 1 (b) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, lump-sum tax, T , and output, Y in equilibrium. (c) Solve for the optimal allocation of leisure, l, the consumption, c, employment, N, output, Y . Contrast these quantities with those…
- Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. Answers for part b below: A consumer's choice of optimizing its consumption and labor hours (h - l ) is given by the point where , MRS(c , l) = wage rate Now , MRS (c, l) = MU(c) /MU(l) MU(c) = dU/d c = a/c MU(l) = dU /dl = (1-a )/l MRS = a (l)1−a (c)a (l)1-a (c) Putting this in optimal condition we have : a (l)(1−a) (c)a (l)(1-a) (c) = w --- (i) l = w…Hello, I would like to request help with the below discussion question for my Quantative Analysis class. For a certain company, the cost function for producing x items is C(x)=50x+150 and the revenue function for selling x items is R(x)=-0.5(x-130)^2+8,450. The maximum capacity of the company is 180 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit! Answer to some of the questions are given below so that you can check your work. 1. Assuming that the company sells all that it produces, what is the profit function? P(x)=_____________ 2. What is the domain of P(x)? 3. The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose? Profit when producing 80 items = _____________ Profit when producing 90…Consider the three-sector model Y = C + I C = aYd+ b T = tY + T * I = cr + d i) Show that Y = b + d- aT* + cr/1-a(1-t) If a = 0.8, b = 100, t = 0.25, T * = 250, c = -60, d = 1700 & r = 8, calculate the equilibrium level of income. (b)(i) Find the marginal cost of a firm’s different products when the total cost function is c = 5x2+ 7x + 2.5xy + 6 y + 3y2 (ii)Determine the marginal cost of y when x = 3, y = 5
- For a competitive equilibrium in a two-period model, must the government's present-value budget constraint hold?You are the manager of a firm that specializes in small single-board widgets. Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable Z Total Benefits B(Z) Total Cost C(Z)0 0 01 200 102 380 303 540 604 680 1005 800 1506 900 2107 980 2808…According to data from Yelp, more than 55 percent of the 132,500 businesses listed on the site that closed during the pandemic will remain shuttered permanently. Although government relief bought some companies time, businesses that are now closed will likely remain that way for the long term. Restaurants account for the greatest share of permanent and temporary closures, followed closely by retailers and then beauty salons and spas. “Businesses are needing to decide, ‘Do I renew my lease on my space for another year?’ It is really hard to make a one-year commitment to paying rent when businesses are closing down for the second time and there’s no end in sight to this virus,” said Michael Stepner, a postdoctoral researcher at Harvard University. “The longer these temporary closings go on, the more of them will turn permanent.” States that depend heavily on tourism like Hawaii and Nevada have experienced the most closures per capita. As businesses close across the country, it becomes…