A. → Use Hessian Matrix to classify the stationary point of the function - π = 50Q₁-20 +9502-40²-3Q1Q₂¶ B. → Write down the associated Hessian-matrix and hence determine the nature of. the stationary point of this function- Z = X² + y² - 2X - 4Y + 15
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- Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?Bell Greenhouses has estimated its monthly demand for potting soil to be the following: N=400+4X where N=monthlydemandforbagsofpottingsoil X=timeperiodsinmonths(March2006=0) Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: Forecast Bell Greenhouses demand for potting soil in March, June, August, and December 2007. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast.The forecasting staff for the Prizer Corporation has developed a model to predict sales of its air-cushioned-ride snowmobiles. The model specifies that sales S vary jointly with disposable personal income Y and the population between ages 15 and 40, Z, and inversely with the price of the snowmobiles P. Based on past data, the best estimate of this relationship is S=kYZP where k has been estimated (with past data) to equal 100. If Y=11,000,Z=1,200, and P=20,000, what value would you predict for S? What happens if P is reduced to $17,500? How would you go about developing a value for k? What are the potential weaknesses of this model?
- The demand function for a product is given by P = 4000/ln (x+10), where P is the price per unit in dollars when x units are demanded.i. Find the rate of change of price with respect to the number of units sold when 40 units are sold ii. Find the rate of change of price with respect to the number of units sold when 90 units are sold.iii. Find the second derivative to see whether the rate at which the price is changing at 40 units is increasing or decreasing.Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ millionKusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour. a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained above
- The demand function for Newton’s Donuts has been estimated as follows:Qx = -14 – 54Px + 45Py + 0.62Ax where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company’s goal)? Should Newton’s Donuts spend…A multiple regression model, K = a + bX + cY + dZ, is estimated regression software, which produces the following output: a. Are the estimates of a, b, c, and d statistically significant at the 1 percent significance level? b. How much of the total variation is explained by this regression equation? c. Is the overall regression equation statistically significant at the 1 percent level of significance? d. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take?21. Consider a firm subject to quarter-to-quarter variation in its sales. Suppose that the following equation was estimated using quarterly data for the period 2011–2018 (the time variable goes from 1 to 32). The variables D1, D2, and D3 are, respectively, dummy variables for the first, second, and third quarters (e.g., D1 is equal to 1 in the first quarter and 0 otherwise). Qt =a+bt+c1D1+c2D2+c3D3 The results of the estimation are presented here: a. Calculate the intercept in each of the four quarters. What do these values imply? b. Use this estimated equation to forecast sales in the fourth quarter of 2019.
- Bell Greenhouses has estimated its monthly demand for potting soil to be the following: Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: MONTH ADJUSTMENT FACTOR (%) March +2 June +15 August +10 December −12 a. Forecast Bell Greenhouses’ demand for potting soil in March, June, August, and December 2007. Answer b. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast. YEAR FORECAST ACTUAL 2007 500 515 2006 452 438 2005 404 420 2004 356 380 2003 308 320Suppose you regress the annual percentage stock price returns on Russell 2000 small cap index for on a the percentage annual returns for a market index. Use the following output from this linear regression to answer questions a. - f. a. What is the formula for the Russell 2000's characteristic line? b. You forecast a market return of 6% next year. According to the market model, what is next year's expected return for the Russell 2000 index? c. What is the correlation between the return on the Russell 2000 and the return on the market Index? d. How much of the variation in the Russell 2000's returns are explained by the model? e. Based on these regression results, the Russell 2000 index would be considered what kind of an investment, defensive, aggressive, or market neutral? f. Does this regression have much explanatory power? Why or why not?Consider the following numerical example of the IS-LM model: C= 100 + 0.3Yd ; I = 150 + 0.2Y – 1000 i ; G = 200 ; T = 100. Derive the IS relation. I've got the answer written down as =400+0.5Y-500i can someone please provide solutions as to how it is this.
