Dagmar consumes only guacamole and chips. Her income is $800 and her utility function is U(x, y) = max{x, y}, where x is the number of units of guacamole she consumes and y is the number of units of chips she consumes. The price of chips is $5. The price of guacamole used to be $2.50 but is now $10. The equivalent variation of this price change for Dagmar is

Question

Dagmar consumes only guacamole and chips. Her income is $800 and her utility function is U(x, y) = max{x, y}, where x is the number of units of guacamole she consumes and y is the number of units of chips she consumes. The price of chips is $5. The price of guacamole used to be $2.50 but is now $10. The equivalent variation of this price change for Dagmar is

BlackTom AI · Accepted Answer

Because U(x,y) = max{x,y}, Dagmar’s utility equals the larger of the two quantities, so she maximizes that larger quantity by spending all income on the cheaper good.

1) Initial (before price change)
- Prices: p_g0 = $2.50 (guacamole), p_c = $5 (chips). Income m = $800.
- Guacamole is cheaper, so she buys only guacamole: x0 = m / p_g0 = 800 / 2.5 = 320 units, y0 = 0.
- Utility before: u0 = max{320,0} = 320.

2) After the price change
- New guacamole price p_g1 = $10, chips still $5. Now chips are cheaper, so she buys only chips: y1 = m / p_c = 800 / 5 = 160 units, x1 = 0.
- Utility after: u1 = max{0,160} = 160.

3) Equivalent variation (EV) concept and calculation
- EV is the amount of income that, taken away (or given) at the initial prices, would leave the consumer as well off as after the price change. Formally EV = m − e(p0, u1), where e(p0,u) is the minimum expenditure at initial prices p0 to attain utility u.
- To achieve u1 = 160 at the original prices (p_g0 = 2.50, p_c = 5), buy the cheaper good (guacamole): minimal expenditure e(p0,u1) = 160 × 2.50 = $400.
- Therefore EV = original income − required expenditure = 800 − 400 = $400.

Why other possible confusions are incorrect:
- Some might compute the difference in quantities (320 − 160) or compare incomes before/after (which is zero); these ignore the expenditure function and definition of EV.
- Compensating variation (a different measure) would be e(p1,u0) − m = (320 × 5) − 800 = 1600 − 800 = $800, which is not the requested EV.

Conclusion: The equivalent variation of the price change for Dagmar is $400, matching the provided answer.

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