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- 2. A refrigerator manufacturer is planning capacity expansions. They have determined that their capacity cost follows the equation below, where f(y) = kya, is the cost of a plant that can produce y units annually. f(y) = 0.0107y⁰.62 They have determined that when a = 0.62, using a = u/(e" - 1) gives a value u = 0.89. Their demand for refrigerators is growing at a rate of 5000 units annually, and they use a 16% interest rate for discounting. At the optimal capacity addition level, what does each capacity installation cost?11. A company produces a certain good for which the (inverse) demand function is given by p = 15 - 2q, where p is the unit price (expressed in some monetary unit) and q is the quantity sold (expressed in some non-specified unit). The fixed costs amount to 6.5 monetary units and the variable costs amount to 1 monetary unit per non-specified unit of the good. We assume that all goods produced are sold. a. Find the function equation for the profit functionP in terms of the quantity q. b. Find the domain of the profit function P. c. Determine for which production levels q the company makes a profit.1) Use the attached graph #1 to model the following. a. What is the price and quantity of this market? b. What is the profit or loss in this market for this firm? c. Is this a competitive market or monopoly? d. What is the deadweight loss in this market, if any? e. How does a firm decide to increase or decrease output? i. What do they do when marginal revenue is less than marginal cost? ii. What do they do when marginal revenue is more than marginal cost? f. When does a firm decided to shut down verses temporarily stopping production? g. In this market the demand curve is what? i. Short run ii. Long run h. In this market the supply curve is what? i. Short run ii. Long run 2) Use the attached graph #2 to model the following. a. What is the price and quantity of this market? b. Is this a competitive market or monopoly? c. What is the profit or loss in this market for this firm? d. What is the deadweight loss in this market, if any? e. In this market the demand curve is what? i. Short run…
- (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..2. Refer to the following graph to answer Question #1 40 35 30 25 20 16 15 12 10 5 I 10 20 MC ATC P₁ AVC P₂ P3 30 45 50 60 70 80 90 100 110 a) What is profit if the price is P1? b) What is profit if the price is P2? c) What is the profit maximizing level of output if the price falls to P3?1.Which of the following explains why marginal cost curves are upward sloping? Increasing marginal benefit Total costs increase as output increases Diminishing marginal product of inputs This statement is true only for inferior goods 2. If a firm generates $232844 in revenue, earns $95728 in economic profit, and its explicit costs are $80,000, how much are its implicit costs? $152844 $57116 $137116 $175728 3. Consider the table of firm costs and revenue below. It may be useful to calculate the missing values. Q MC MR TC TR 1 3 5 13 5 2 2 5 15 10 3 3 5 4 5 5 5 8 5 6 12 5 If the firm chooses Q to maximize short-run profit, what will the profit be? ?=−6\pi = -6 ?=−3\pi = -3 ?=3\pi = 3 ?=6
- 3 Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.003x° +0.01x +0.5x. Currently, Pierce sells 70 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 75 lawn chairs were sold each day? c) What is the marginal revenue when 70 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(71), R(72), and R(73). ..... a) The current revenue is $ b) The revenue would increase by $. (Round to the nearest cent.) c) The marginal revenue is $ when 70 lawn chairs are sold daily. d) R(71) - $ R(72) $ R(73) $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 Hawkeye has total cost and total revenue equations, but cannot figure out what the firm should do, Use your knowledge of profit-maximization to find the profit-maximizing quantity (X), the Total Revenue at that quantity, the Total Cost at that quantity, and the maximum profits earned. Total Cost X+4*X2 +100*X+100 Total Revenue --X2+500*X Profit-maximizing Quantity = Total Revenue at Profit-maximizing Quantity= Total Cost at Profit-maximizing Quantity= Maximum Profit Earned: =
- A manufacturer knows that: His TR is given by Revenue = 23Q – Q2 /4 His total cost of production is; Cost = 36 + 2Q + 0.1Q2 Where Q is the weekly production in thousands a) Economists define MR as the rate of change of Total revenue. Derive an expression for Marginal Revenue (MR) b) How do you think Economists’ would define ‘Marginal Cost’? Derive an expression for marginal Cost (MC) and at what output will make marginal Revenue equal Marginal cost? c) Find the total profit and the value of Q that maximizes profitIn 2016, Netflix increased prices for their U.S. subscribers from $7.99 to $9.99 per month.1Following the price increase, the rate of subscription growth decreased significantly, from 1.56 (in the fourth quarter of 2015, before implementing the price increase) to 0.40 (in the third quarter of 2016, after implementing the price increase). In addition, the stock price of the company fell by about 16% (price dropped in July 2016, after releasing the second quarter earnings, to $85.84 per share, from $102.23 on March 31, 2016). How much is the price elasticity of demand for Netflix subscription in this case, using the midpoint method when calculating the percentage change.4. Suppose a manufacturer and its retailer face the problem of double marginalization described in my notes, Section 11.1. If the manufacturer sets the wholesale price equal to its marginal cost c and in addition, requires the retailer to pay a fraction a (between 0 and 1) of its profit. Write down the retailer's profit maximization problem. Will this practice solve the double marginalization problem? (That is, will this 4.a practice maximize their joint profit?) 4.k Suppose the retailer is required to pay a fraction of a of its sales (i.e., total revenue). Write down the retailer's profit maximization problem. Will this practice solve the double marginalization problem?