5. For a profit-maximizing firm with a marginal-cost function MC(q) =q³²+ 6, find: (a) PS (producer surplus) at price po = 7 CHAPTER REVIEW 631 (b) PS at price = 70 (c) APS resulting from the price change po = 7 to p = 70. Illustrate your results with a graph.
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- The following graph shows the daily market for small cardboard boxes in San Diego. PRICE (Dollars per small box 10 9 Demand 0 161 6 QUANTITY (Millions of small boxes) 2 Supply 19 10 Suppose that Talero is one of more than a hundred competitive firms in San Diego that produce such cardboard boxes. Based on the preceding graph showing the daily market demand and supply curves, the price Talero must take as given is2.- A company that works in a perfectly competitive market has a total cost function: TC = Q3 - 52.5Q2 + 1,050Q + 6,750 The supply and demand functions in that market are: QS = 2P -704 Qd = 5,260 - 5P d) Calculate the market consumer surplus. e) Validate the utilities by calculating them as the area of the rectangle on the graph.5. Demand functions are X-100-Px and Y=152-2Py Total Cost is C-6x2 + 4y2 +4xy + 110, Optimize the profit using two variable regular optimization formula.
- The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 20 1.00 25 2.00 1.20 30 2.46 1.41 35 3.51 1.71 40 4.11 2.01 45 5.43 2.39 50 5.99 2.75 55 8.47 3.27 Instructions: In part a, enter your answer as the closest given whole number. In parts b-d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds? 2$ c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? 2$ost functions and competitive markets Assume each firm in a competitive market (i.e., they produce the same homogeneous product) has the cost function C(Q) = 1500 + 20Q. The (entire) market faces the demand curve P(Q) = 220 – 0.5Q. What is the equilibrium price in this competitive market? What is the equilibrium quantity? (b)On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.
- Exercises: 1 Given the demand (price) and cost functions P=2000-40Q and C(Q) = 3000+400Q respectively, find the following, using the calculus approach: a. Profit-maximizing output (quantity) b. Profit-maximizing price c. Maximum profit value d. Revenue maximize QuantityCalculate 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 as2. A firm has a cost function of C = 1000+20Q + 1/10Q2 and has a demand function as shown in the graph below: 100 90 80 70 70 60 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 Quantity (Q) -P (demand) a) Estimate the firm's demand function. You may assume that the slope is a whole number, and the intercept is a multiple of 10. (1 mark) b) Find the firm's revenue function. You do not need to draw it. (2 marks) c) Find the marginal revenue function, and draw it on a copy of the graph. (3 marks) d) Find and draw the marginal cost function. (3 marks) e) Use your results from parts (c) and (d) to find the profit-maximising level of output. (3 marks) f) Find the market price at this level of output. (2 marks)
- 4. The demand equation for a product is p = a – bq and the cost function is C(q) = kq² – rq where p is the price of the product, q is the quantity sold and a, b, k and r are positive constants. Find the equilibrium quantity in terms of a, b, k and r.Homework Demand equation of a firm is q = V75 – pp and supply equation of this firm is q = p/2 – 20 , determine consumers' surplus and producers' surplus under the market equilibrium. Sketch the graph.Can you show how Qsc is = 2Pc? Which is the answer for this.