Consider a country that produces two goods wheat (W) and cotton (C) with two factors of production: land (T) and labor (L). The technology for wheat and cotton are as follows. Each unit of wheat requires 10 units of labor and 1 unit of land. Each unit of cotton requires 30 units of labor and 1 unit of land. Denote the wage by w and the rent of land by r.

a. Suppose a country has 500 units of labor and 20 units of land. Determine the allocation of labor and land between the two goods algebraically and then show it diagrammatically. How much of wheat and cotton are produced in the economy?

b. Now suppose that the labor supply increases to 540 units. Determine the allocation of labor and land between the two goods algebraically and then show them diagrammatically. Verify the Rybczynski's theorem.

c. Now Suppose Malaysia has 500 units of labor and 20 units of land, while Indonesia has 80 units of land and 8000 units of labor. Which country has a comparative advantage in cotton? Which country has a comparative advantage in wheat? What is going to be the pattern of trade between these two countries?

d. Denote the price of cotton by PC and the price of wheat by PW. Suppose the autarky prices in the two countries are as follows. Malaysia: PC =100, Pw =40. Indonesia: PC = 80, Pw = 60. Calculate the autarky levels of wage and rent in both countries.

e. Now, suppose the world trading price of the two goods is PC =90, Pw =50.

Calculate the factor prices in both countries in a trading equilibrium. Verify the

Stolper-Samuelson theorem.

11.40 In the preliminary studies of a new drug, a pharmaceutical firm needs to obtain infor- mation on the relationship between the dose level and potency of the drug. In order to obtain this information. a total of 18 test tubes are inoculated with a virus culture and incubated for an appropriate period of time. Three test tubes are randomlyr assigned to each of six different dose levels. The 18 test tubes are then injected with the randome assigned dose level of the drug. The measured response is the protective strength of the drug against the virus culture. Due to a prob- lem with a few of the test tubes. only two responses were obtained for dose levels 4. 8. and 32. The data are given here: Dose level 2 4 8 16 32 64 Response 5,1 3 10. 14 15, 1'7 20, 21 , 19 23, 29 23, 31. 30 a. Plot the data. b. Fit a linear regression model to these data. c. From a plot of the residuals. does there appear to be a possible lack of t of the linear Iruadel'?I Let (1, Y1), ..., (50, Y50) be draws from a simple linear model where Yi ~ N(Bo + B1i, 32) for i = 1, ..., 50. (a) Find r E R such that P(Bo E (Bo -r, Botr)) = 0.95, where Bo is our least squares estimate of Bo. (b) Find r E R such that P(B1 E (B1-r, Bitr)) = 0.95, where B1 is our least squares estimate of B1. (c) Find r E R such that P(Bo + 3B1 E (Bo + 3B1 - r, Bo + 3/1 + r)) = 0.95, where Bo, B1 are our least squares estimates. (d) Give a test statistic and rejection region for a test that B1 + 0 with size 0.01 (o = 3 is known).D Question 1 Given f (x) = -4x2 + 20x + 25 at what value of x is the function optimized? D Question 2 Given f (x) = -4x2 + 20x + 25 what is d2 f ( I) ? dz2 D Question 3 Given f (x) = -4x2 + 20x + 25 at the value of x that optimizes the function, it is a relative min max neither min or maxProblem 2. Consider the model 311 : #'tl 92 = #+52 313 : +3 with ER.) : 0, E(2) : 02, E(ieJ) : 0 when 22 7E j, for all i,j : 13,3. If we let 6 = [61, 62, E3]T, we can also write these conditions as E(e) = 0, E(ET) = 02]. Note that Normality is not being assumed. Answer each of the following questions. You have to show all your work to get full credit. i) Find the eigenvalues of H : X (X TX )'1XT. ii) Find E (6TH 6). Justify your answer. Recall that Normality is not assumed. Question 1 0.5 pts Econometrics is the branch of economics that develops and uses statistical methods for estimating economic relationships applies mathematical methods to represent economic theories and solve economic problems studies the behavior of individual economic agents in making economic decisions deals with the performance, structure, behavior, and decision-making of an economy as a whole