1. **State the problem:** Donna consumes tulips and pizzas. Prices are 5 per tulip and 10 per pizza. Currently, she consumes 18 tulips and 9 pizzas. We need to calculate the marginal utility per dollar for pizzas from 8 to 9 units, decide if she should change consumption to increase utility without increasing spending, and find the total utility at the optimal bundle. 2. **Calculate marginal utility per dollar for pizzas from 8 to 9:** - Utility at 9 pizzas = 227 utils - Utility at 8 pizzas = 212 utils - Marginal utility (MU) = 227 - 212 = 15 utils - Price per pizza = 10 - Marginal utility per dollar = $\frac{15}{10} = 1.5$ utils per dollar 3. **Calculate marginal utility per dollar for tulips at current consumption (18 tulips):** - Utility at 18 tulips = 93.7 utils - Utility at 20 tulips = 96.4 utils - MU = 96.4 - 93.7 = 2.7 utils - Price per tulip = 5 - Marginal utility per dollar = $\frac{2.7}{5} = 0.54$ utils per dollar 4. **Compare marginal utility per dollar:** - Pizzas: 1.5 utils per dollar - Tulips: 0.54 utils per dollar Since pizza gives more utility per dollar, Donna should consume more pizzas and fewer tulips to increase total utility without increasing spending. 5. **Find the optimal consumption bundle:** We look for the bundle where marginal utility per dollar is equal for both goods. - Check MU per dollar for pizzas from 9 to 10: MU = 240 - 227 = 13 utils MU per dollar = $\frac{13}{10} = 1.3$ - Check MU per dollar for tulips from 16 to 18: MU = 93.7 - 89 = 4.7 utils MU per dollar = $\frac{4.7}{5} = 0.94$ - Check MU per dollar for tulips from 14 to 16: MU = 89 - 81 = 8 utils MU per dollar = $\frac{8}{5} = 1.6$ - At 14 tulips and 10 pizzas: MU per dollar tulips = 1.6 MU per dollar pizzas = 1.3 Tulips have higher MU per dollar, so increase tulips and decrease pizzas. - At 16 tulips and 9 pizzas: MU per dollar tulips = 0.94 MU per dollar pizzas = 1.5 Pizzas have higher MU per dollar, so increase pizzas and decrease tulips. - At 15 tulips and 9.5 pizzas (interpolated), MU per dollar would be closer. By checking the table, the optimal bundle is around 16 tulips and 10 pizzas. 6. **Calculate total utility at optimal bundle (16 tulips, 10 pizzas):** - Utility tulips = 89 utils - Utility pizzas = 240 utils - Total utility = 89 + 240 = 329 utils **Final answers:** - a. Marginal utility per dollar from 8 to 9 pizzas = 1.5 utils per dollar - b. Donna should choose more pizzas and fewer tulips to increase total utility without increasing spending. - c. Total utility at optimal bundle (16 tulips, 10 pizzas) = 329 utils