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Consumer Equilibrium

Currently, a consumer is buying both sorbet and gelato each week. His MRSGS [marginal rate of substitution of gelato (G) for sorbet (S)] equals 0.75. The price of gelato is €1 per scoop, and the price of sorbet is €1.25 per scoop.

• Determine whether the consumer is currently optimizing his budget over these two desserts. Justify your answer.
• ​Explain whether the consumer should buy more sorbet or more gelato, given that he is not currently optimizing his budget.
Solution to 1:

In this example, the condition for consumer equilibrium is MRSGS = PG/PS. Because PG/PS = 0.8 and MRSGS = 0.75, the consumer is clearly not allocating his budget in a way that maximizes his utility, subject to his budget constraint.

Solution to 2:

The MRSGS is the rate at which the consumer is willing to give up sorbet to gain a small additional amount of gelato, which is 0.75 scoops of sorbet to gain one scoop of gelato. The price ratio, PG/PS (0.8), is the rate at which he must give up sorbet to gain an additional small amount of gelato. In this case, the consumer would be better off spending a little less on gelato and a little more on sorbet.

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5. CONSUMER EQUILIBRIUM: MAXIMIZING UTILITY SUBJECT TO THE BUDGET CONSTRAINT
on is less than the price ratio—meaning that the price for that additional unit is above her willingness to pay. Even though she could afford bundle c, it would not be the best use of her income. EXAMPLE 5 <span>Consumer Equilibrium Currently, a consumer is buying both sorbet and gelato each week. His MRS GS [marginal rate of substitution of gelato (G) for sorbet (S)] equals 0.75. The price of gelato is €1 per scoop, and the price of sorbet is €1.25 per scoop. Determine whether the consumer is currently optimizing his budget over these two desserts. Justify your answer. Explain whether the consumer should buy more sorbet or more gelato, given that he is not currently optimizing his budget. Solution to 1: In this example, the condition for consumer equilibrium is MRS GS = P G /P S . Because P G /P S = 0.8 and MRS GS = 0.75, the consumer is clearly not allocating his budget in a way that maximizes his utility, subject to his budget constraint. Solution to 2: The MRS GS is the rate at which the consumer is willing to give up sorbet to gain a small additional amount of gelato, which is 0.75 scoops of sorbet to gain one scoop of gelato. The price ratio, P G /P S (0.8), is the rate at which he must give up sorbet to gain an additional small amount of gelato. In this case, the consumer would be better off spending a little less on gelato and a little more on sorbet. 5.2. Consumer Response to Changes in Income: Normal and Inferior Goods The consumer’s behavior is constrained by his income a