A multi-sector model Consider a version of the manufacturing bid-rent curve, but with two sectors. Let x1 and x2 be the distance that firms in sector 1 and sector 2 locate away from the city center. Firms face freight, labor, and land costs ? but no intermediate goods cost. To simplify the algebra, lets also assume that firms in each sector use only one unit of land (and thus the land cost, LC(xi) = P(xi) for i = 1,2. The labor costs for each firm (as a function of distance to center) is given by:

L(x1) = 20 ? A1 ? x1

L(x2) = 30 ? A2 ? x2

The freight costs for each firm as a function of distance is given by

F(x1)=(B1 +3)?x1

F(x2)=(B2 +3)?x2

A) Write out the profit function for a firm in each sector. You should provide two equations.

Do not assume that revenue is equal in each sector. (1 points)

B) Use your answer from part A to derive the bid-rent curves for manufacturing firms in each sector. (1 points)

C) For each sector, find the point at which the WTP for land is zero (this won't be a number, but a function of the model's parameters). (2 points)

D) Interpret your answer from part C. How does the distance you calculated for sector one change with A1? Provide economic intuition for your answers. (1 point)

E)

Now assume that A1 =5,A2 =6,B1 =7andB2 =4. Furthermore, you may now assume that TR1 = TR2 = 40. Find the range of distances from the center each sector will be located. Hint: draw a graph of these lines. Remember: land is always allocated to the highest bidder. Don't worry about units and note that your answer may include fractions. (2 points)

Definition 1 Consider the linear model y = XB + e, E(e) = 0, X ( R"XP, BE RP. A vector value linear function of B, say AB, is estimable if ATB = PT XB for all B E RP, for some matrix P. Notation Throughout if A is matrix C(A) denotes its column space. 1. Consider the data: Y, = Bo + B1 + e; where e1, . ... en are uncorrelated errors with mean zero and variance o?. (a) (.5 pts) Write this model in the form Y = XB + e with 3 = (30, B,). Specify the matrix X. (b) (.5 pts) Write down the normal equations. Find a solution to them. Is the solution unique? (c) (.5 pts) What is the least squares estimate of Bo + Bi? (d) (.5 pts) Is B, estimable? (e) (.5 pts) Consider now another observation Yn+1 = Bo + 281 + en+1 where e1, . . .; en+1 are uncorrelated errors with mean zero and variance o'. Write this model in the form Y = XB+e and calculate the least squares estimate of B.For a sample n = 166 college students, the following variables were measured: (a) Height (cm) (b) Mother's height (cm) (c) Father's height (cm) (d) Gender of student (M or F) (e) Race (white, black, Asian, Hispanic) As a researcher, you want to know if parents' height, gender, and/ or race predict height accurately. These are the measurements for the first five students sampled: . Student 1: 151, 165, 189, Female, White . Student 2: 155, 169, 183, Female, Hispanic . Student 3: 175, 157, 191, Male, Hispanic . Student 4: 176, 181, 177, Male, Asian . Student 5: 173, 148, 162, Male, Black (c) Write out the regression model in matrix format for the first five students sampled.2. One of the core principles I want students to take away from the class is what we've called the "economic decision-making rule," and informs our theory of individual behavior. a. Write what the economic decision-making rule is and define marginal analysis. b. Define sunk costs and opportunity costs and discuss which of the two should be included when engaging in marginal analysis. c. Explain three contexts where we have seen the economic-decision make rule, interpret it in these contexts, and explain how they inform optimal decision-making (for example, a perfectly competitive firm sets P=MC to maximize profits, which is an application of the economic decision-making rule).Experiments show that at any given time, the rate of decomposition of a radioactive substance is proportional to the amount of substance present at that time. The amount of time needed for half of a radioactive sample to undergo decay is known as the half-life. A radioactive isotope of the element carbon-14 (C#) has a half-life of 5730 years. The amount of this isotope in living organisms begins to decline when the organism dies. If the amount present at the time of death was 2.5 grams what would be the amount remaining after, 2,000 years?2/14 question Jol 10. Step 1 of2 Correct Inco A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table. Test Scores Student First Test Grade Second Test Grade 2 73 64 70 4 50 5 73 70 6 68 65 70 68 72 67 65 10 75 63 65 13 73 14 45 91 92 65 78 Skip Try Similar