Question

1. Erika has preferences that are complete, transitive, continuous, monotonic, and convex. Her utility function is U(x1, x2), where goods 1 and 2 are the only goods she values. Her income is M, and the prices of the goods are p1 and p2; assume M, p1 and p2 are positive numbers.

a. Suppose M decreases, good 1 is normal, and good 2 is inferior. Using a graph, show what happens to the demand for each good.

b. Is it possible for both goods to be inferior? If so, use a graph to show what happens to the demand for each good when M decreases. If not, show or explain why this is impossible.

Answer 1

Erika has preferences that are complete, transitive, continuous, monotonic, and convex. Her utility function is U(x1, x2), where goods 1 and 2 are the only goods she values. Her income is M, and the prices of the goods are p1 and p2.

a. When , M decreases and good 1 is normal, and good 2 is inferior , then :

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E ffect n Demamd w mermal geod) inperior good DI dlemand As M alls, demand fot X, cu As M talls, demand for otted demand cves DD

ndittrence cwuwe :- budget Lum , s eguat),on :- As M alls the 20 MN to CD The meuu imd Hexente cunve and uw budget line Satisy tangene condition at point E where nt cev sumption crx, a ballon to x and censuumption

b. No, it is not possible for both the goods to be inferior. Since ,Erika has monotonic preferences and consumes only two goods , it’s not possible that as income declines , she would increase consumption of all goods, because now, her purchasing power has declined.

EXPLANATION THROUGH DIAGRAM :

If her income decreases , then her budget set will shift leftwards. In the diagram , red budget set is the new budget set when income has decreased. If both goods are inferior , then with fall in income, demand for both goods should increase. Any equilibrium point that lies on the red budget set will indicate fall in demand of at least one good.( please see diagram) which means that both the goods cannot be inferior.

et set when M dall 2. NV