-3A and let the cost function of the apple orchard be CA(H, A) = where H and A are the number of units of honey and apples produced, respectively. The price of honey is $7 and the price of apples is $5 per unit. Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner. Calculate A₁ and A₂. 2.2 A₂ is equal to 2. Let the cost function of the honey farm be Cu(H, A) = 100
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- A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.Q)Assume that a competitive firm has the total cost function: TC=1q^3−40q^2+740q+1600 Suppose the price of the firm's output (sold in integer units) is $650 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. A. How many units should the firm produce to maximize profit? B. What is the total profit at the optimal output level? Please specify your answer as an integer.The graph below shows a particular firms marginal revenue (mr) marginal cost (mc) and average total cost (atc) curves, where the market is competitive. Suppose that a new management team is brought in and that this team is initially less concerned about maximizing profits than it is simply about making a profit. What range of production quantities will allow the firm to operate while earning a profit? Give you're answer by dragging the qmin to Qmax lines into their correct positions. The output will need to lie somewhere between those limits.
- 4. Assess which of the following is true and which is false.A firm’s profit equation is given by π = -100 + 160Q – 20Q2. Therefore,a) The firm’s fixed cost is 100.b) The firm’s fixed cost is 40 and variable cost is 20.c) Marginal profit is Mπ = 160 – 20Q.d) The firm’s profit-maximizing output is Q = 4.e) Marginal profit is Mπ = 160 – 40Q and it is positive for quantities that are lower than theprofit-maximizing quantity.Y6 questions1. A firm produces TVs and ovens witha joint cost function that takes the form:C(x,y) = 3x^2 + 2y^2 + 2xy where x and y are the firm's output of TVs and ovensrespectively. Suppose the cost function is subject to the constraint on the total output ofthe firm in the form 2x + y = 35.a) Find the optimum values x and that minimize the firm's total cost.b) Check your answer in (a) by using the bordered Hessian matrix.c)Determine the optimum value of the Lagrange multiblier À. Interpret your answer.Modified True or False: State whether each statement is true or false. If the statement is false, briefly explain why it is so, and then restate it to make it true. The shapes of long-run cost curves follow directly from the assumption of a fixed factor of production, which implies diminishing returns. The optimal scale of plant is the scale of plant that maximizes average cost. In the long-run competitive equilibrium, each individual firm chooses a scale of operations that minimizes its long-run average cost. Answer correctly and explain within 30mins will give you positive feedback.
- Question four Suppose that a firm's total cost equation is TC= 10,000+ 1000 + 0.25Q2 Where TC is total cost and Q is the level of output. (a) What output level will minimize the firm's average total cost? (b) Calculate the average and marginal cost at the average cost minimizing output levela. Find the input demand (x), output supply (y), and profit function for the technology, y = ln(x), where y = 0 for x ≤ 1. b. Use Hotelling’s Lemma on the profit function in part (a) to find the input demand for x and the output supply for y.In the graph below, you can see the iso-cost curve and the iso-quant curve for the firm to produce q = 1000 units of output. Note that the vertical axis shows the quantity of capital while the horizontal axis shows the quantity of labor. Suppose that the firm is producing 1000 units of output at point A, using 200 units of capital and 100 units of labor. (i) As an outside consultant, what actions would you suggest to management to improve profits? (ii) What would you recommend if the firm were operating at point B, using 100 units of capital and 200 units of labor? Explain your answer.
- Assume that a competitive firm has the total cost function: TC=1q3−40q2+880q+2000 T C = 1 q 3 - 40 q 2 + 880 q + 2000 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. How many units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal output level? Please specify your answer as an integer.Your Uncle plans to open a business that will operate five stores in the Mississauga area. Four of these firms will operate with production functions q = K1/4L1/4 while the fifth store, the Heartland Superstore will have production function q = 2K^(1/4)L^(1/4). a. Derive the long-run marginal cost curve for the business. (all five stores combined). b. He will be paying competitively determined input prices of PL = $16 and PK = $1 and can sell output for P = $32. (Do not use this information in Part a.) How many persons should he hire for each store? How many units of capital should be installed in each store? Calculate his profits.Assume that the cost data in the following table are for a purely competitive producer: TotalProduct AverageFixed Cost AverageVariable Cost AverageTotal Cost Marginal Cost 0 1 $60.00 $45.00 $105.00 $45.00 2 30.00 42.50 72.50 40.00 3 20.00 40.00 60.00 35.00 4 15.00 37.50 52.50 30.00 5 12.00 37.00 49.00 35.00 6 10.00 37.50 47.50 40.00 7 8.57 38.57 47.14 45.00 8 7.50 40.63 48.13 55.00 9 6.67 43.33 50.00 65.00 10 6.00 46.50 52.50 75.00 Instructions: If you are entering any negative numbers be sure to include a negative sign (−) in front of those numbers. Select "Not applicable" and enter a value of "0" for output if the firm does not produce. a. At a product price of $56.00 (i) Will this firm produce in the short run? (Click to select) No Yes (ii) If it is preferable to produce, what will be the profit-maximizing or loss-minimizing output? (Click to select) Not applicable Loss-minimizing…