CSUF2011 FallEcon531Homework 01Instructions: Please answer Question #6 and any four questions from Question 1 through Question 5. Please submit your answer (attach your file electronically) before 11:59 PM, Monday, September 26. Please show your work in all cases. Good Luck!1.This question is about producer surplus and consumer surplus.a.Given a linear demand curve, if domestic consumption changes by10%, does consumer surplus also change by 10%? Why or why not?What is the relationship between change in domestic consumption andconsumer surplus?b.Is there a difference between producer surplus and profit? Explain.2.Suppose Robinson Crusoe produces fish (F) and coconuts (C). Assume thatduring a certain period, he has decided to work 200 hours and is indifferent to whether he spends this time fishing or gathering coconuts. RobinsonCrusoe’s production function for fish is given by:And his production function for coconuts is given by:where L F and L C are the number of hours spent fishing or gathering coconuts. Consequently:200Robinson Crusoe’s utility for fish and coconuts is given by: √ .(a) Write an equation for Crusoe’s PPC.(b) Show that (explain in words) if Robinson Crusoe cannot trade with rest of theworld, he will choose to allocate his labor such that slope of his PPC will equal the slope of his indifference curve (i.e., his marginal rate of product transformation (MRT) will equal his marginal rate of substitution (MRS) on the consumption side.).(c) Specifically, for this case, show that his:(d) What will the optimal values of his F and C be?(e) Suppose now that trade opens up to Robinson Crusoe and he can now trade fish and coconuts at a price of one fish for two coconuts. If Robinson Crusoe continues to produce the same quantities of F and C as before, what will he choose to consume once he is given the opportunity to trade?3.Assume that good X is a labor-intensive good and good Y is a capital-intensive good; country A is labor-abundant and country B is capital-abundant. But suppose that as w/r rises, after a point, good X in factbecomes more capital-intensive than good Y.a.Is this "factor intensity reversal" plausible? Explain.b.Show this phenomenon on the Fountain Diagram.c.Show this phenomenon on the Edgeworth Box diagram.d.Show this phenomenon on the Iso-quants drawn over K and L.4.The following equations describe the long-run situation for prices and costs,where the numbers indicate the amounts of labor and land needed to producea unit of corn and toys.P corn = 80W + 40RP toys = 100W + 30Ra.If the price of corn is initially 200 and the price of toys is initially 200,what are the values for the wage rate W and the rental rate R?b.The price of corn now increases to 240. The price of toys stays thesame. What are the new values for W and R after adjustment to thenew long-run situation?c.What is the change in the real wage (purchasing power of laborincome) with respect to each good? Is the real wage higher or lower"on average"? What is the change in the real rental rate (purchasingpower of land income) with respect to each good? Is the real rentalrate higher or lower "on average"?d.Is there a magnification effect (i.e., does the percentage real return ofthe rental rate rise change more than the percentage change in theprice of corn)?5.Consider a simplified version of the Krugman-Obstfeld model ofmonopolistic competition where each monopolistic firm faces the following demand curve:p = (α/n) – (β/s) qWhere p is the firm’s product price, n is the number of firms, s is the market size, q is the firm’s output and α, β are parameters in the demand function. The corresponding total cost curve is:Total Cost = f + cqWhere f is the fixed cost and c is the constant marginal cost. Using this model, prove that if the market size doubles, number of firms will not double and some firms will be forced out of the market.6. Briefly explain or provide short answers to ANY FIVE of the following (draw diagrams, if necessary – no need to write more than four or five sentences in each case):a)In a typical Ricardian model, if Good X is produced under monopoly in one ofthe countries, is free trade still the optimal policy?b)Usefulness of the Gravity Theory in the economics of international trade.c)Internal inconsistency of mercantilist thoughts on international trade policy.d)Hydraulic Theory of Economic Developmente)Does a small country gain more from free trade (compared to a large country)?Explain using offer curves.f)O’Rourke’s paper: What is the basic idea?g)If autarky relative prices are P x/P y = 3 in country A and P x/P y = 4 in country B,and if two international prices P x/P y = 3.25 and P x/P y = 3.75 are suggested,country A will prefer 3.75 and country B will prefer 3.25. True or false? Why?h)In the Heckscher-Ohlin trade model, discuss the conditions under which factorprice equalization may not occur.i)Provide a critical look at the Product Cycle Theory.j)In the Ricardo-Lewis model, what happens if the international food prices are not equal initially?。