Her demand equations can be found from the general Cobb-Douglas equations by substituting `C_0` for `Q_x`, `C_1` for `Q_y`, PVI for M, $1 for `P_x` and `($1)/1.2` for `P_y`:
Since `PVI_t > PVI_n`, she's better off taking the training. Her consumption in the two periods will be:
`C_0 = (0.5*$180000)/($1) = 90,000`
`C_1 = (0.5*$180000)/(($1)/1.1) = 99,000`
Her consumption in period 0, $90,000, is larger than her net income in that period, $50,000, so she's borrowing the difference: $40,000.
The graph is shown below:
To describe what's going on in words: in period 0 she pays $20,000 in tuition (moving along the `C_0` axis from $70,000 down to $50,000) and then borrows $40,000 (moving along the `C_0` axis from $50,000 to up to $90,000). In period 1 she gets a $33,000 raise (along the `C_1` axis from $110,000 to $143,000) and then repays $44,000 (from $143,000 down to $99,000).
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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 11/06/2020