Assignment 3, Math for Economics III (28 points)Due Friday, September 25, in recitationWrite neat solutions for the problems below. Show all your work. If you only write the answer with no work, youwill not be given any credit. Please do not forget to write your name and recitation section number and staple yourhomework if you have multiple pages!1. (4 points) LetF(x,y) = (1 +xy)exyi+x2exyj. Find a functionfsuch that∇f=F, and use this to evaluateRCF·dralong the curvex= cost,y= 2 sint,0≤t≤π2.2. (3 points) LetF() = 2y3/2i+ 3x√yj. Find the work done byFin moving an object from (1,1) to (2,4).3. (3 points) Is the vector ﬁeldFgraphed below conservative? Justify your answer.-2-112x-2-112ySolution: We showFis not conservative by showingRCF·dr6= 0 for some smooth simple closed curveC.IfCis the natural ellipse passing through (±2,0) and (0,±1), traversed clockwise, thenCfollows the cur-rent given byF. That is to say, the dot product ofr0(t) withF
Econ 340Home Work Assignment 3Department of EconomicsCal State FullertonDue: March 18 at 11:55 pmProblem 1:Consider the following estimated demand function for chicken for ahousehold in Fullerton, California over a period of 25 months.ptttPPQ03.019.009.56SE=(29.18) (0.07) (0.019)81.02Rand 805.02adjRNumber of observations = 25Here, tQis the quantity demanded for chicken (in pound), tPis the price ofchicken (in $), ptPis the price of pork (in $). Suppose, someone claims that theprice of chicken and the price of pork together have no e±ect on the quantitydemanded for chicken.(a) Formulate the Ftest to provide evidence against the claim. (Hint:Formulate the Null and the Alterative hypotheses, and then calculate thevalue of the F statistic. You can then arrive at a decision by comparingthe critical value of F with the calculated value of F.) Explain the resultsof the F statistics. (10)HO: β2=β3=0Ha: β2≠0, β3≠0F-Value= (.81/(3-1))/((1-.81)/(25-3))= 46.89474Critical F-Values Using 2 for numerator degrees of freedom and 22 asdenominator d.f.