4. Pot & Gold Inc. makes and sells Christmas ornaments in a perfectly competitive market. Its production function is given by f(x, z)=√√x+2, where x denotes the amount of plastic and z denotes the amount of wood. The price of plastic is w₁ and the price of wood is w₂. Let y denote the amount of Christmas ornaments produced and p denote the price of Christmas ornaments (p>0).
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a) when w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc
b) Suppose that Pot & Gold Inc has to pay a quasi-fixed cost of $50. When w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc
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- The following graph plots the marginal cost (MC) curve, average total cost (ATC) curve, and average variable cost (AVC) curve for a firm operating in the competitive market for sun lamps. COSTS (Della) 72 04 8 56 24 16 . 0 Price (Dollars per lamp) MOD 8 12 36 48 60 10 ATC AVC 40 00 QUANTITY (Thousands of lamps) For every price level given in the following table, use the graph to determine the profit-maximizing quantity of lamps for the firm. Further, select whether the firm will choose to produce, shut down, or be indifferent between the two in the short run. (Assume that when price exactly equals average variable cost, the firm is indifferent between producing zero lamps and the profit-maximizing quantity of lamps.) Lastly, determine whether the firm will earn a profit, incur a loss, or break even at each price. Quantity (Lamps) ? Produce or Shut Down? Profit or Loss?3. Suppose the production function of a firm is given by f (x1, x2) = min {x1, x2}. (a) Calculate the conditional demand functions of the firm assuming w₁ = 2, w2 = 4, and y = 8. (b) Calculate the minimum cost of the firm to produce 8 units of the good when w₁ = 2 and w2 = 4.Isabella grows pumpkins. Her average variable cost (AVC), average total cost (ATC), and marginal cost (MC) of production are illustrated in the figure to the right. Assume the market for pumpkins is perfectly competitive and that the market price is $5.00 per box. How many pumpkins should Isabella grow? Isabella should produce integer value.) thousand boxes of pumpkins. (Enter your response as an Price ($ per box) 10.00- MG ATC AVC 9.00- a 8.00- G 7.00- 6.00- 5.00- 4.00- 3.00- 2.00- 1.00- 0.00- 0 2 3 5 6. Quantity (boxes in thousands)
- 15. The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x (20x² + 60x), where x is the amount of cheese sold, in hundreds of pounds. The "profit" is - $50 when no cheese is sold. a. Find the profit function. b. Find the profit from selling 300 pounds of Brie cheese. a. Find the profit function. P(x) = b. Find the profit from selling 300 pounds of Brie cheese. The profit from selling 300 pounds of Brie cheese is $Suppose that the market for microwave ovens is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. 100 90 80 ATC 70 60 50 40 30 AVC 20 10 MC 5 10 15 20 25 30 35 40 45 50 QUANTITY (Thousands of ovens) For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down, it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.) Price Quantity Total Revenue Fixed Cost Variable Cost Profit (Dollars per oven) (Ovens) (Dollars) (Dollars) (Dollars) (Dollars) 25.00 1,600,000 70.00 1,600,000 $25.00 100.00 1,600,000 $35.00 If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's…2. The market for a slice of pizza in Oakland is highly competitive. The market demand for a slice of pizza can be summarized by the function: D(p) = 1200 — 200p. Consider each pizza shop to be an individual firm with the 1 same cost function C(q) = FC + - q2, where FC represents fixed cost of renting a space from which to sell pizza, and the variable costs reflect the cost of the labor involved in producing and selling pizza. a. In the short-run (e.g. the six months following the signing of a lease for a space from which to sell pizza) determine the quantity each pizza shop would produce for any price in the market. b. In what way does your answer to part (a) depend on the fixed cost? Explain your answer in no more than two sentences. c. Suppose initially there are 100 pizza shops selling pizza in Oakland. Derive an expression for the short-run market supply for pizza. d. Find the short-run equilibrium price and quantity in the Oakland pizza market. How does this equilibrium depend on…
- Question 2. The price - demand equation and the cost function for the production of HDTVS are given respectively by x = 6000 – 30 p and C(x) = 72000+ 60 x where x is the number of HDTVS that can be sold at a price of $p per TV and C(x) is the total cost (in dollars) of producing x TVs. A. Express the price p as a function of the demand x, and find the domain of this function. B. Find the marginal Revenue at a production level of 1500 and interpret the result c. Sketch a graph of Revenue and Cost functions. Indicate interval in which Profit occurs and loss occurs.Consider the competitive market for titanium. Assume that, regardless of how many firms are in the industry, every firm in the industry is identical and faces the marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves shown on the following graph. (? 80 72 64 56 48 ATC 40 32 24 AVC 16 MC O + + + + + 4 8 12 16 20 24 28 32 36 40 QUANTITY (Thousands of pounds) COSTS (Dollars per pound)Calculate Edison's marginal revenue and marginal cost for the first seven frying pans he produces, and plot them on the following graph. Use the blue points (circle symbol) to plot marginal revenue and the orange points (square symbol) to plot marginal cost at each quantity. COSTS AND REVENUE (Dollars per frying pan) O 35 30 25 20 15 10 1 2 QUANTITY (Frying pans) Marginal Revenue -4 Marginal Cost Edison's profit is maximized when he produces frying pans. When he does this, the marginal cost of the last frying pan he produces is s which is than the price Edison receives for each frying pan he sells. The marginal cost of producing an additional frying pan (that is, one more frying pan than would maximize his profit) is than the price Edison receives for each frying pan he sells. Therefore, curves. Because Edison is a price which is Edison's profit-maximizing quantity corresponds to the intersection of the taker, this last condition can also be written as
- Suppose that the market for air fresheners is a perfectly competitive market. The following graph shows the daily cost curves of a firm operating in this market. (? 40 36 Profit or Loss 32 28 24 АТС 16 12 AVC MC 4 4 8 12 16 20 24 28 32 36 40 QUANTITY OF OUTPUT (Air fresheners) PRICE AND COST (Dollars per air freshener) 20Suppose that the market for dress shirts is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. 50 18, 42 45 40 35 30 ATC 25 20 15 AVC 10 MC 2 4 6 8 10 12 14 16 18 20 QUANTITY (Thousands of shirts) For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down, it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.) Price Quantity Total Revenue Fixed Cost Variable Cost Profit (Dollars per shirt) (Shirts) (Dollars) (Dollars) (Dollars) (Dollars) 12.50 7,500 135,000 27.50 135,000 45.00 135,000 If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's fixed cost is…If a perfectly competitive firm which produces two commodities, has the cost function C = 2Q² + 2Q? where Q1 and Q2 denote the production level of commodity 1 and commodity 2 respectively. (Note: There are 3 questions in the test regarding the information given above) If the prices of commodities are P and P2 respectively, find the optimal levels of output that the firm should produce to maximize its profit O a. Q 1/4P and Q b. Q; 1/6P and Q = 1/4P2 Oc. Q; =1/6P and Q; = 1/6P2 O d. Qi 1/4P, and Q = 1/6P, ; = 1/4P,