Final answer:
a. The law of diminishing marginal utility applies to both goods. b. The optimal levels of hamburgers and Cokes consumed are 2 hamburgers and 9 Cokes. c. The optimal levels of consumption increase to 3 hamburgers and 12 Cokes when the consumer income rises to $48.
Step-by-step explanation:
a. The law of diminishing marginal utility states that as a person consumes more units of a good, the additional satisfaction or utility derived from each additional unit decreases. In this case, both the marginal utility of hamburgers (MUH) and the marginal utility of Cokes (MUC) follow this principle because the marginal utility of hamburgers decreases as the quantity of hamburgers consumed increases, and the marginal utility of Cokes decreases as the quantity of Cokes consumed increases.
b. To determine the optimal levels of hamburgers and Cokes consumed, we need to find the point where the ratio of marginal utility to price is equal for both goods. Given that PH = $8, PC = $2, and consumer income is $36, we can calculate the marginal utility to price ratios for hamburgers and Cokes. The formula for the ratio of marginal utility to price is MU/Price. By comparing the ratios, we can find the optimal consumption levels. In this case, the optimal levels are 2 hamburgers and 9 Cokes, which give equal ratios of 2:1.
c. If the consumer income rises to $48 while the prices of hamburgers and Cokes stay the same, the budget constraint line will shift outward. As a result, the consumer can afford to consume more goods. Using the same method as in part b, we can calculate the new optimal levels of consumption. The optimal levels would be 3 hamburgers and 12 Cokes, which also give equal ratios of 2:1.