3. (This problem is due to Dave Kreps.)Suppose there are two goods (X=R2+) andthe consumer has a vNM utility index over consumption bundles ofv(x) =f(x1+x2)wheref:R→Ris a strictly increasing function. Letp= (1,3) andp0= (3,1). Letq=.5p+.5p0= (2,2). In Regime 1, there is a 1/2 probability that the realized pricewill bepand a 1/2 probability that the realized price will bep0, so her expected utilityis.5 maxx∈Bp,wf(x1+x2) +.5 maxx∈Bp0,wf(x1+x2).In Regime 2, the price isqwith certainty, so her expected utility ismaxx∈Bq,wf(x1+x2).Prove that, for any strictly increasingf, the consumer is expected to be better off inRegime 1.

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Econ 201AFall 2010

4.MWG 5.B.6 (a), (b), (d): There are three goods. Goods 1 and 2 are inputs. Thethird, with amounts denoted byq, is an output.Output can be produced by twotechniques that can be operated simultaneously or separately. The techniques are notnecessarily linear.The first (respectively, the second) technique uses only the first(respectively, the second) input. Thus, the first (respectively, the second) techniqueis completely specified byφ1(q1) (respectively,φ2(q2)), the minimal amount of inputone (respectively, two) sufficient to produce the amount of outputq1(respectively,q2).The two functionsφ1(·) andφ2(·) are increasing andφ1(0) =φ2(0) = 0.(a) Describe the three-dimensional production set associated with these two techniques.Assume free disposal.