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 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. The equation of the monthly demand for cabin bags is given by: 45-p= 0'5q and the monthly average cost function is: Cme(q) = q²-39'50q+120+¹25, where p ≤ 45 is the unit price and q are the number of units sold. 3.1 What are the price and quantity that maximize the total profit? How much is this profit? 3.2 Calculate the marginal income (revenue) of the 20th unit using marginal income (revenue) and compare it to the actual additional income. 3.3 Calculate the price elasticity of demand for the quantity that maximizes profit and interpret the result obtained.The blue curve on the following graph represents the demand curve facing a firm that can set its own prices. Use the graph input tool to help you answer the following questions. You will not be scored on any changes you make to this graph. Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly. PRICE (Dollars per unit) 100 TOTAL REVENUE (Dollars) 90 80 20 10 0 1250 1125 1000 875 750 625 500 On the previous graph, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 10, 20, 25, 30, 40, or 50 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. 375 250 125 + 0 0 0 Demand 5 10 15 20 25 30 35 40 45 50 QUANTITY (Units) + 5 20 10 15 25 30 35 QUANTITY (Number of units) 40 Graph Input Tool Market for Goods 45 50 Quantity Demanded (Units)…
- 2.- 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.Mango Systems believes that demand for its pet e-mouse follows a linear demand equation: Quantity = 43,911 - 708* Price Mango's variable cost to produce one pet e-mouse is $23.50. Find the maximum total contribution margin (margin per unit times quantity sold) that Mango Systems can possibly achieve on its pet e-mouse. (Rounding: penny.) Your Answer:PS4.2 (a) What Optimal Level of Output (q*) will a Firm Produce given the following? MC(q) = 3 + 2q Price (P) = $9 MC → Marginal Cost q→ Quantity (b) What is a Firm's Producer Surplus assuming the following? Area of Triangle = 1/2* Base * Height (c) Will a Firm be Earning a Positive, Negative, or Zero Profit in the Short-Run given the following? AVC (q) =3+q FC = $3 AVC → Average Variable Cost FC Fixed Cost
- Blue INK is the only cabel service provider in Gazipur. The diagram below depicts the price, output and costs incurred by Blue INK. Use the graph to answer the following questions: What is the Total revenue generated by Blue INK at the profit maximizing level of output?[ Answer in Numerical value only.i;e. 1,2,3,4,5] If the Cable Service Market turns into a Perfectly Competitive Market, what will be the total ammount of the service provided? [ Answer in Numerical value only] If the market turns into a Monopoly market again, what will be the total deadweight loss created? [ Answer in Numerical value only]the 9. You own a bakery and the inverse demand function for your cakes is P = 8 – 1.5Q. If cost of producing cake is C = 0.5Q, determine the profit-maximizing quantity, and the profit-maximizing price.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_________.
- Paulina sells beef in a competitive market where the price is $8 per pound. Her total revenue and total costs are given in the table below. Quantity of Total revenue Total cost beef (lb.) 0 1 2 3 4 ($) 0 8 16 24 32 ($) 4 8 13 19 27 Profit ($) 0 8 pounds Marginal revenue ($) c. What is the profit-maximizing (or loss-minimizing) quantity? Marginal Marginal cost ($) profit ($) a. Complete the table. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. b. At what quantity does marginal revenue equal marginal cost? pounds AUsing the graph on the next page, do the following problems: Determine the profit maximizing level of output when the market price for the good is $75/unit. Show this on the graph by making the appropriate drawing (with a straight-edge). Also, write the number (an appropriate estimate should be made) below the graph. • On the graph, show the maximum total profit that can be generated by the firm based on the market price. Do NOT calculate the value - show the appropriate box on the graph. Be careful in your (straight) lines. Be clear as to the part of the graph that represents the profit. Use shading as appropriate. • Below the graph, write the interpretation of the values of the marginal cost (MC) and the average total cost (ATC) at the profit-maximizing level of output; make sure to use all the appropriate names and units. Write the values and interpretations below the graph. • Answer the following questions: If the market price of the good falls, the profit maximizing level of…11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!
