The consumer's budget constraint is $6 = 0.50G + P, where G is packs of gum and P is bags of pretzels. The marginal utility of pretzels is MU_P = G^0.5, and the marginal utility of gum is MU_G = 0.5G^-^0.5P. The consumer's utility function is U = G^0.5P. the utility-maximizing bundle consists of _____ packs of gum and _____ bags of pretzels. A) 8; 2 B) 4; 4 C) 2; 5 D) 6; 3

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Quizplus · Accepted Answer

To maximize utility, the consumer should equate the marginal rate of substitution (MRS) to the price ratio. The MRS is MU_G/MU_P = (0.5G^(-0.5)P)/(G^0.5) = 0.5P/G. The price ratio is 0.50/1. Setting MRS = price ratio gives 0.5P/G = 0.50/1, which simplifies to P = G. Substituting P = G into the budget constraint 6 = 0.50G + P gives 6 = 0.50G + G, which simplifies to 6 = 1.5G, so G = 4 and P = 4.

The Consumer's Budget Constraint Is $6 = 0