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Lorelais choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on snap to optimal bundle to see the optimal choice. Click on show indifference curve map. Draw the lowest four indifference curves as you see from the graph 3. Find the marginal utility of x1 and x2. What is the maximum number of x so that MU, is bigger than or equal to MU 4. Given her income of $40, how many units of x can she buy? Would she buy any positive number ofx2 in light of the answer from Q2.3? Find the optimal bundle.
5. Suppose instead her income is $50. Would she buy any positive number of x2? Find the optimal bundle using the tangency condition. 6. Find the optimal bundle with an income of $100 using the tangency condition. What happens to the consumption amount of x1 compared to the consumption of x1 with an income of $50? (Hint: In econgraphs, play around by moving an income slide bar and see how the optimal bundle changes.) 7. Will the optimal bundle be the same or different if the utility function were u(x1, x2) -9ln(xi) +x2? What if the utility function were u(xi , X2)-X exp(x2 )? Explain.
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