Question

8. Edna's preferences over romantic comedes zı and horror flicks z2 is given by u =エ122, which implies MU = z2 and MUr2 = zł. The prices of each are P1 and P2 per movie. Edna's monthly budget for movies is n (a) Solve algebraically for Edna's ordinary demand for romantic comedies P,2,) and for horror flicks = z2(P1,P2, m). The equations to be solved include丑= PL and m = p12 1 +P2X2. エ1 l mark (b) Evaluate these at pp2 1 and 24, find the level of utility, that Edna attains. Draw this equilibrium on a graph, showing the budget line and the choice levels z and 2, and draw in an approximation to Edna's indifference curve (draw it in penci, as you ill get more precise information belo!. Make the graph large enough to accomodate the following questions. Hint: Edna's utility level is uo-144. [1 mlark] (c) Use your answers to part (a) to show what happens tozl and when Pi rises to P1 4, Solve also for the new utility level, , that Edna now is able to attain. Draw the new budget constraint, and indicate the new levels of r and r on your graph. 1 mark (d) Solve algebraically for Edna's expenditure minimizing choices (Hicksian demands) h(, P2,u) and h2 2(p,P2, u) that yield a particular level of utility, u. The equations to be solved are Hint: you are solving for and 2, but you call the solutions hi and h2-r. 1 mark] (e) Now, that you have a general formula for hi and h2, evaluate these at u = uo, with prices P,-P2 1, and at u uo with prices P,-4 aid P2-| . Show that the former exactly equal ะใ and Find the latter, and show these on your indifference curve for u = 10, [1 mark] (f) Now, that you have a general formula for hi and h2, evaluate these at u , with prices pl = 4 and P2 = 1, and at u ul with prices P1 = P2 = 1 . Show that the former exactly equal rl and . Find the latter, and show these on your indifference curve for u = u, [1 mark] (g) Now, draw a second graph which has price P1 on the vertical axis, indicating both P1 = 1 and P1 4 on the vertial axis. On the horizontal axis, locate and and draw (as a linear approximation) the ordinary demand curve that passes through those two points. Then draw the points hi (4,1, t10) and hi (1, 1, u1) on the horizontal axis. Draw (as linear approximations) the associated Hicksian (compensated) demand curves associated with the two utility levels, u and ul. 1 mark (h) Indicate the areas corresponding to the consumers surplus, equivalent variation and compensating variation associated with the price increase in good 1. [1 mark

Answer 1

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