Question

3. Keiko spends all her money on airtime for her mobile phone and gasoline for her car. Her preferences correspond to the utility function U(G,W) = W+ 20/G, where G stands for gallons of gasoline and W stands for mobile (wireless) minutes used in a week. (Remember, for that utility function, the marginal utility of gasoline is 10/VG, and the marginal utility of mobile minutes is 1.) Keiko can spend S40 and mobile minutes cost $0.50 per minute. Suppose the price of gasoline rises from $I to S2.50 per gallon (a) What is the effect (uncompensated price change) on her purchases of gasoline and mobile minutes? (b) Break up this effect (uncompensated price change) into the substitution effect (compensated price change) and income effect. (c) How much compensation does the substitution effect involve? (d) Sketch the budget constraints, the relevant indifference curves, the optimal con- sumption bundles, and the decomposition of the income and substitution effects.

Answer 1

Solution: Part-1) When price equals Pg-1, budget constraint is G+0.5W-40 Optinal consumption bundle satisfies MUc/MUw -Pe/Piw, 10/G-1/0.5 or G-25 W-(40-G)/0.5 30 The utility derived from the consumption bundle is 30+20 25 130 As optimal consumption bundle satifies MUc/MUw Pc/Pw, 10/G 2.5/0.5 or G-4 W- (40-4 0.25) /0.5 60 The utility derived from the consumption bundle is 60+20 4-100 Thus, when the price of gasoline increases from $1 to $2.5, the gasoline consumption falls from 25 gallons to 4 gallons, and the mobile phone usage rises from 30 minutes to 60 minutes Part-2) As MUc/MUw Pc/Pw, 10/G 2.5/0.5 or G-4 To reach the utility level of 130, the utility level before the price change, W-130 20*-90 The compensated price effect shifts the consumption level from (25, 30) to (4, 90) The income effect shifts the consumption bundle level from (4, 90) to (4, 60) Part-3) The income required to buy the compensated consumption bundle (4.90) is 4 * 2.5 + 90 * 0.5 = 55 Thus, the compensation of the substitution effect is $55- $40 $15 PART-D) GRAPH 1,90) 2.5G+ 00) 25+5W-40 10