Problem 2. (SW 12.8.) Consider a product market with a supply function Q = Bo + B₁ P₁ + už, a demand function Q = %o +u, and an equilibrium condition Q = Q, where u and u are mutually independent i.i.d. random variables, both with a mean of 0. (a) Show that P₁ and us are correlated. OLS (b) Show that the OLS estimator of ₁ is inconsistent. Hint: The standard strategy for showing inconsistency: first, argue that Cov(QP), second, use Var(P) calculations to show that Cov(Q²,P) #B₁. will converge in large samples to Var(P)
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Just part B. Please write it out on paper. Typing it back to back is difficult to understand what you mean.
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- Please solve questions 15, 16 and 17. The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = 10000 - 25Pg + 20Ph + 30Pr - 15dv - 35Psc - 10Pmm + 0.05Ag + 0.03A -25C + 0.1Y Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is…A large company in the communication and publishing industry hs quantified the relationship between the price of one of its products and the demand for this product as Price = 160 -0.01 xDemand for an annual printing of this particular product. The foxed costs per year (ie. per printing) = $4T 000 and the variable cost per unit = $35. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 7,000 units per year. The maximum profit that can be achieved is S. (Round to the nearest dolar.) The unit price at the point of optimal demand is S per unit (Round to the nearest cent)The soft goods department of a large department store sells 184 units per month of a certain large bath towel. The unit purchase cost of a towel to the store is $2.5 and the cost of placing an order has been estimated to be $11. The store's inventory carrying cost is 33% of the purchase cost of the goods. Suppose that the demand rate is a constant and the EOQ model is used. What is the optimal annual cost of placing orders and holding inventory?
- k : ces As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-400Q and P= 500,000 -225Q, respectively. Your cost function is CQ) = 165,000+ 243,750Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $1The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = 10000 - 25Pg + 20Ph + 30Pr - 15dv - 35Psc - 10Pmm + 0.05Ag + 0.03A -25C + 0.1Y Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is standard, but upgrade options are 10…(a) The sales of a book publication are expected to grow according to the functionS = 300000(1 − e−0.06t), where t is the time, given in days.(i) Show using differentiation that the sales never attains an exact maximum value.(ii) What is the limiting value approached by the sales function?(b) A poll commissioned by a politician estimates that t days after he makes a statementdenegrating women,the percentage of his constituency (those who support him at the time hemade the statement) that still supports him is given by S(t) =75(t2 − 3t + 25)t2 + 3t + 25The election is 10 days after he made the statement.(i) If the derivative S’(t) may be thought of as an approval rate, derivate the a functionfor his approval rate.(ii) When was his support at its lowest level?(iii) What was his minimum support level?(iv) Was the approval rate positive or negative on the date of the election?(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curvefor the bast will be…
- You are the owner of QuantCrunch Corporation, a company that recently spent $15,000 to develop a statistical software package. To date, you only have one client. A recent internal study revealed that this client’s demand for your software is Qd = 300 – 0.2P and that it would cost you $1,000 per unit to install and maintain software at this client’s site. Your assignment is to construct a report that compares (1) the profit that results from charging this client a single (profit-maximizing) per-unit price with (2) the profit that results from charging $1,450 for the first 10 units and $1,225 for each additional unit of software purchased. Answer the following questions in your report: What type of pricing strategy is (1)? What type of pricing strategy is (2)? Compare at least three strategies discussed in this module (including 1 and 2) in making your recommendation? Show your calculations.Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S = 100N/(N + 1), where N is the number of ads. If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits? A) 2,853. B) 1428. C)98 D) 477.The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is standard, but upgrade options are 10 inch extra sharp, 12 inch, 12 inch extra sharp, Each also has a touch-screen option. The upgrades…
- R(p) = pN(p).| Bob is currently selling tires for 60 dollars each. His weekly sales are running at 130 tires per week, so N(60) = 130. His marketing department estimates that he will lose 2 sales per week for each 10 dollar increase in unit price, so N'(60) = -0.2. Estimate Bob's increase in weekly revenue for each one dollar increase in tire price. Revenue increase =1 dollarsAs the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 70 percent chance of low demand and a 30 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 -450Q and P = 700,000 -325Q, respectively. Your cost function is C(Q) = 135,000 + 172,500Q. How many new homes should you build, and what profits can you expect?As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 80 percent chance of low demand and a 20 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 −300Q and P = 800,000 −200Q, respectively. Your cost function is C(Q) = 180,000 + 260,000Q. How many new homes should you build, and what profits can you expect? Give typing answer with explanation and conclusion