Question1.

Use the supply and demand analysis, discuss the impact of worker shortage, which is nowadays widely observed in many Chinese cities, on prices and consumers' living costs. Try to consider the effect of workershortage on firm production and consumer demand.

Question 2: Consumer utility maximization problem

Assume that there are two goods: good 1 and good 2. The prices for each good is p1 and p2, respectively. Define the quantity of consumption for each good as x1 and x2. The income for the consumer is defined as M. The consumer tries to maximize his utility by choosing the number of quantities in consumption for each good, where the utility function is defined as U = 5x1x2 2 (1)

1. What does it mean by marginal rate of substitution in consumption? Given the consumer's utility function (1), calculate the marginal rate of substitution.

2. What does it mean by the law of diminishing marginal rate of substitution. Based on the utility difference curves, try to confirm whether the consumer's utility satisfies diminishing marginal rate of substitution or not.

3. Write down the consumer's budget line.

4. The consumer maximizes his utility under the budget constraint. Solve for the consumer's utility maximization problem. Please write down the calculation results step by step. (note: I recommend you to use the Lagrangian method following the Appendix in Chapter 4.)
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5. Suppose both the income and prices for both goods are scaled by t where t > 1. How would the consumer change in the consumption of both goods given the new income and prices? Is the utility function homethetic or not?

Question 3: Demand curves

Based on the same settings as in Question 2, we reconsider the changes in individual demand.

1. What does it mean by the income-consumption curve? Draw the curve when the prices of goods are (p1, p2) = (1, 1) .

2. What does it mean by the Engel curve? Show the demand for good 1 when the consumer's income changes and the prices of goods are (p1, p2) = (1, 1).

3. Explain the price elasticity of demand in both math expressions and economic intuitions. Solve for the price elasticity of demand for good 1.

4. Explain the income elasticity of demand in both math expressions and economic intuitions. Solve for the income elasticity of demand for good 1.