# Microeconomics: Quiz # 1 October 30, 2006 1. (a) MRS XY = MU X

```Microeconomics: Quiz # 1
October 30, 2006
1. (a) M RSXY = M UX /M UY = (1/x)/1 = 1/x.
(b) M RSXY = PX /PY and PX &middot; x + PY &middot; y = IA . Therefore, x = 2 and y = 4.
(c) Under the new prices, x′ = 1 and y ′ = 4. To decompose the substitution and income effects,
we need to know the original utility level, which is u = ln 2 + 4. We want to know the
consumption basket (x′′ , y ′′ ) such that u(x′′ , y ′′ ) = ln 2 + 4 and M RSXY (x′′ , y ′′ ) = PX′ /PY′ .
Therefore, x′′ = 1 and y ′′ = ln 2 + 4. The substitution effect is x′′ − x = −1, and the income
effect is x′ − x′′ = 0.
(d) M RSXY = PX /PY and PX &middot; x + PY &middot; y = IA imply XA (PX ) = 10/PX .
(e) d XA (PX )/d PX = −10/PX2 . ε = (d XA (PX )/d PX )(PX /XA (PX )) = −1.
(f) M RSXY = PX /PY and PX &middot; x + PY &middot; y = IB imply XB (PX ) = 30/PX .
(g) X(PX ) = XA (PX ) + XB (PX ) = 40/PX .
(h) X(PX ) = SX (PX ). Therefore, PX = 2. They need to import SX (2) = 20 units of food.
2. Island A is better for him. (I will draw the graph in our next class.)
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