University of California, Berkeley Economics 230a Department of Economics Fall 2017 Problem Set #1 (due 10/17/17) 1.Consider an economy in which relative producer prices are fixed and a representative household, with a unit endowment of labor, maximizes the following utility function: 𝑈𝑈(𝑐𝑐1,𝑐𝑐2,𝑙𝑙) = (𝑐𝑐1− 𝑎𝑎1)𝛽𝛽1(𝑐𝑐2− 𝑎𝑎2)𝛽𝛽2𝑙𝑙1−𝛽𝛽1−𝛽𝛽2(where c1and c2are consumption goods and lis leisure), subject to the budget constraint: p1c1 + p2c2 + wl = wA.Derive an explicit solution (i.e., in terms of prices and preference terms aiand βi) for the excess burden of taxes on c1, c2, and las a function of the original, undistorted prices of the three goods (𝑝𝑝10, 𝑝𝑝20, and w0), the distorted prices (𝑝𝑝11, 𝑝𝑝21, and w1) and a fixed utility level. B.Show that excess burden equals zero if 𝑝𝑝𝑖𝑖1= (1 +𝜃𝜃)𝑝𝑝𝑖𝑖0, i = 1, 2, and w1= (1+θ)w0some constant θC.Compare the values of excess burden based on utility levels achieved in the absence and in the presence of taxation, 𝑉𝑉(𝑝𝑝10,𝑝𝑝20,𝑤𝑤0)and 𝑉𝑉(𝑝𝑝11,𝑝𝑝21,𝑤𝑤1)D.Using the measure derived in part A, show that the marginal excess burden for an increase in a tax orsubsidy on good 2 is positive. (Hint: relate the change in excess burden to the sign of (𝑝𝑝21− 𝑝𝑝20).) 2.Consider a model of household production, in which the representative household maximizes the utility of market goods Xand home goods Z, U(X,Z). for . .