econ11_08_ps3_sol

# econ11_08_ps3_sol - Eco11 Fall 2008 Simon Board Economics...

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Eco11, Fall 2008 Simon Board Economics 11: Solutions to Practice Problems 3 (Week 4) October 23, 2008 1. Budget Sets There are two goods: x 1 and x 2 with prices p 1 = 2 and p 2 = 2. Suppose the government subsidises the ﬁrst 10 units of x 1 by \$1. Draw the budget curves for m = 8, m = 12 and m = 16 Solution When m = 8, it is as if p 1 = 1 and p 2 = 2. When m = 12 or m = 16, there is a kink at x 1 = 10. The slope is - 1 / 2 to the left and - 1 to the right. The vertical intercept is x 2 = 6 when m = 12 and x 2 = 8 when m = 16. The horizontal intercept is x 1 = 11 when m = 12 and x 1 = 13 when m = 16. 2. Income Eﬀects and Quasilinear Utility Suppose utility has the form u ( x 1 ,x 2 ) = x 1 / 2 1 + x 2 . Let p 1 = 1 and p 2 = 2. Derive the consumer’s income oﬀer curve. Solution Note: Here I use the MRS argument (which is identical to the Lagrange method). We could also use the substitution method. The consumer’s MRS is MU 1 MU 2 = 1 2 x - 1 / 2 1 The price ratio is p 1 /p 2 = 1 2 . The solution is x * 1 = 1, which is feasible if m 1. If m < 1 then MRS > p 1 /p 2 , so the consumer will spend all her money on good 1. 1 1 Equivalently, the bang–for–the–back from good 2 is MU 2 /p 2 = 1 / 2. This is less than the bang–for–the–back from good 1 if x 1 < 1. 1

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Eco11, Fall 2008 Simon Board We thus ﬁnd that x * 1 = m for m < 1 and x * 1 = 1 for m 1. More concisely, x * 1 = min { m, 1 } . 3. Price Changes
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econ11_08_ps3_sol - Eco11 Fall 2008 Simon Board Economics...

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