This problem set tells the story of four friends Alice, Bob, C'arol, who are consumers, andFanny, who owns a firm. Alice, Bob and Carol have preferences over two goods, Dumplingsand Eggs. Fanny's firm produces eggs. In what follows you should use m; for i = A, B, C todenote the income of each of the three consumers and p; for j = D, E to denote the pricesof each of the two goods. Similarly, d; and e; denote the consumption of dumplings and eggsrespectively by consumer i = A, B, C. Fanny uses two (non-fixed) inputs, called 1 and 2, toproduce eggs; the price of these inputs is denoted by w; for j = 1,2. 5.Find a utility function representing Carol's preferences and find her cor-responding demands of dumplings and eggs as a function of her income mc and theprices of the two goods (which are again pp and pE).6.Fanny's firm is the only supplier of eggs in the region but she wants to benice to her three friends, so she behaves as a perfectly competitive (i..e. price taker)firm. Her firm has the following technology:f(*1, #2) = (x1)04(x2)06,where x; for j = 1,2 is the amount of each input she uses. Assume that the priceof input 1 is wi =0.4(N + 1) and the price of input 2 is w2 = 0.6(N + 2). What is

5) The consumer only cares about maximum of good a good in each bundle . Let the utility is equal…

Answered: 5. Find a utility function representing…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you believe that population abundance (A) of a particular species is a linear function of vegetation coverage (V) and the presence of a predators (P). Surveys where conducted across 20 sites and found the following information: a) There was an average of cover of .406 (40.6%) of the area, with an average 6.8 predators and 61.55 individuals in our target population. b) ⟨?2⟩=0.231, ⟨? ⟩=76.300, ⟨??⟩=2.933, ⟨??⟩=36.329, ⟨??⟩=379.300 Set up the appropriate system of equations needed for a the linear regression of a model of the form ?=??+??+?. Then estimate the parameters and report the final model.
| 1. We assume that the measured quantity y is a linear function of three independent variables, x1, x2, and x3, i.e., y = b + a1x1 + a2x2 + a3x3 Nine data points are measured by setting three levels for each parameter, and the data are placed into a simple data array as shown to Table 1, Calculate the y intercept and the three slopes simultaneously, one slope for each independent variable x1, x2, and x3. Table 1 data array X1 0 0 0 Questions -1 -1 -1 1 1 1 x ₂ 0 -1 1 0 -1 1 0 -1 1 X3 0 0 -1 -1 1 1 0 -1 1 y 10.472 7.253 14.708 9.861 4.374 10.339 12.082 10.678 14.519
Obtain the regression of demand on price from the following data and estimat demand when the price is 7.5 Price Demand Price Demand 2.0 75 4.5 40 2.5 60 5.0 40 3.0 55 5.5 35 3.5 50 6.0 30 4.0 45 6.5 30
Suppose you believe that population abundance (A) of a particular species is a linear function of vegetation coverage (V) and the presence of a predators (P). Surveys where conducted across 20 sites and found the following information: a) There was an average of cover of .406 (40.6%) of the area, with an average 6.8 predators and 61.55 individuals in our target population. b) ⟨V2⟩=0.231⟨V2⟩=0.231, ⟨P2⟩=76.300⟨P2⟩=76.300, ⟨VP⟩=2.933⟨VP⟩=2.933, ⟨VA⟩=36.329⟨VA⟩=36.329, ⟨PA⟩=379.300⟨PA⟩=379.300 Set up the appropriate system of equations needed for a the linear regression of a model of the form A=aV+bP+cA=aV+bP+c. Then estimate the parameters and report the final model.
1
Suppose an analyst models mortgage application rejection rejection (Reject) as a function of the individual applicant income (Income): Reject i = β0 + β1 Income i + ε i Suppose an individual is characterized as belonging to one of the following three groups: Hispanic, Black, or neither. How would you augment this model to test whether the effect of income on mortage rejection differ based on this race/ethnicity categorization?
Consider the monthly rent (Rent in $) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft). Rent Beds Baths Sqft 645 1 1 500 675 1 1 648 760 1 1 700 800 1 1 903 820 1 1 817 850 2 1 920 855 1 1 900 859 1 1 886 900 1 1.5 1000 905 2 1 920 905 2 1 876 929 2 1 920 960 2 1 975 975 2 2 1100 990 1 1.5 940 995 2 1 1000 1029 2 2 1299 1039 2 2 1164 1049 2 2 1180 1050 2 2 1162 1084 2 2 1163 1100 2 1 1020 1100 2 2 1150 1185 2 2 1225 1245 3 2 1368 1275 2 2 1400 1275 3 2 1350 1400 3 1 1185 1450 2 2 1200 1500 3 2 1412 1518 3 3 1700 1600 3 1 1440 1635 3 3 1460 1635 3 3 1460 1650 3 1.5 1170 1750 3 1.5 1944 1950 4 2.5 2265 1975 3 4 1700 2200 5 4 4319 2400 3 2.5 2700 a. Estimate: Rent = β0 + β1Beds + β2Baths + β3Sqft + ε. (Round your answers to 2 decimal places.) Rent =. ? + ? bed +. ? bath+ ? sqft
The demand functions for two products are given below. P₁, P2, 91, and 92 are the prices (in dollars) and quantities for products 1 and 2. 91 = 1200 - 2p1 - 5p2 92 = 1300 - 5p1 - 3p2 What is the quantity demanded for each when the price for product 1 is $30 per item and the price for product 2 is $10 per item? Demand for product 1: Demand for product 2: Are these two products complementary goods or substitute goods? Select an answer

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5. Find a utility function representing Carol's preferences and find her cor- responding demands of dumplings and eggs as a function of her income mc and the prices of the two goods (which are again pp and pe).