第一部分 消费者理论 1. 当11xx 时,加数量税t,画出预算集并写出预算线 预算集:).....(..........112211xxmxpxp ).........(..........)(1112211xxxtmxpxtp 2. 如果同样多的钱可以买(4,6)或(12,2),写出预算线。 mxpxp2211 则有 mpp2164,mpp21212 不妨假设12 p,则可解得:8,211mp。 预算线为82121 xx 3.(1)0.4100xy (2)0.2100........... ..300.4106........... ..30xyif xxyif x (3)0.4106xy 4. 证明:设两条无差异曲线对应的效用分别为21,uu,由曲线的单调性假设,若21uu ,则实为一条曲线。若21uu ,假设两曲线相交,设交点为 x,则21)(,)(uxuuxu,可推出21uu ,存在矛盾,不可能相交。 5. -5(把一元纸币放在纵轴上)或者-1/5(把一元纸币放在横轴上), 6. 中性商品是指消费者不关心它的多少有无的商品 商品 2 如果也是中性商品那么该题就无所谓无差异曲线,也无所谓边际替代率了. 商品 2 如果不是中性商品: 边际替代率是 0(把中性商品放在横轴上)或者 (把中性商品放在纵轴上) 7. (1)x1 is indefinitely the substitution of x2, and five units of x1 can bring the same utility as that one unit of x2 can do. With the most simple form of the utility function, 125u xxx, and assume that the prices of those two goods are p1 and p2 respectively and the total wealth of the consumer is m, the problem can be written as 121 112max,. .u x xs t p xp xm ③ Because 5p1=p2, any bundle 12,x xwhich satisfies the budget constraint, is the solution of such problem. (2) A cup of coffee is absolutely the complement of two spoons of sugar. Let x1 and x2 represent these two kinds of goods, then we can write the utility function as 12121,min, 2u x xxx The problem of the consumer is 121 112max,. .u x xs t p xp xm Any solution should satisfies the rule that 1212xx, and the budget constraint. So replace x1 with (1/2)(x2) in the budge...