Microeconomics

khan tucker conditions

Explain your work and properly label any diagram. 1. An economics paper says that the consumer's problem can be written as maxU(a:1, 332) st. p113] +p2332 E y z1,32 Where it is assumed that prices and income are strictly positive and that preferences are a) continuous b) monotonic, and c) strictly convex. Explain in our own words (i.e., in simple, clear language) why the authors would have made these assumptions. 2. What are the Kuhn-Tucker conditions of the problem max2lnx1 +332 at. 431 | 232 g 24 1'1 n-Tz Explain each condition in simple language 3. What are the Marshallian demands for the indirect utility function? V(p1,p2=y) : 0.4ln2 0.61n3 + 0.Gln[y p26) (1.2]an 0.4]np2 4. Consider the indirect utility function V(p1:p2,y) = 0.1 + 0.2111121 * 0.5)]an * 0.41113; Does it satisfy the properties of an indirect utility function? Explain 5. You have household level data on maize and sorghum expenditures, EM and E3, in a variety of locations throughout Malawi as well as their prices, PM and P3, at these locations. Indicate the share equations that you would estimate based on the (linear approximation) Almost Idea] Demand system. Discuss how each variable would be constructed. Also discuss what restrictions should be placed on parameters to ensure that the share equations and indirect utility function have the correct properties and why each restriction is put in place