Consider an economy with three goods. Suppose that a consumer has a continuous

utility function satisfying local non satiation. Suppose also that the consumer's Walrasian

demands for goods 1 and 2 when p3 = 1 satisfy

x1(p1, p2, 1, W) = a1 + b1p1 + c1p2 + d1p1p2

x2(p1, p2, 1, W) = a2 + b2p1 + c2p2 + d2p1p2

(a) State Walras' law and use it to find the Walrasian demand for good 3. (It's fine to

just give the demand when p3 =

(b) State a result about the homogeneity of Walrasian demands and use it to find the

consumer's Walrasian demands at other values of p3.

(c) Note that the Walrasian demands for goods 1 and 2 are independent of wealth. Show

that this makes it very easy to find the Hicksian demands for goods 1 and 2. State the

Compensated Law of Demand. Show that this law puts some restrictions on the possible

values for (a1, b1, c1, d1, a2, b2, c2, d2).

(d) Define the Slutsky substitution matrix. What properties must it have if demands

are derived from maximizing a continuous, locally non satiated, and strictly quasiconcave

utility function? Give at least one additional restriction on (a1, b1, c1, d1, a2, b2, c2, d2) that

this implies.

4. (25 Minutes - 23 points)

Let X = {x1, x2, . . . , xn} be a finite set of states. Let ?(X) be the set of lotteries with

outcomes in X. Write ?xi for the lottery in which xi is realized with probability one.

Let P be a preference on ?(X). Assume that P is transitive and that ?x1 P ?x2 P

. . . P ?xn .

(a) State the Archimedian axiom.

(b) The preference P is said to satisfy monotonicity if a?x1 +(1?a)?xn P b?x1 +(1?

b)? if and only if a ? b. Show that monotonicity implies that ? ?xn x . n x1 P

Question The data in the table shows the price and quantity demanded for reclining chairs. Using the Midpoint Method, what is the price elasticity of demand from point C to point D? Note: Remember to take the absolute value of the result and round to the nearest hundredth. Rounding should be done at the end of your calculation. Point Price Quantity A $10 500 B $13 480 C $16 460 D $20 440 E $22 420 Provide your answer below:QUESTION 7 Exhibit 4-5 - 52 50 51 Price Quantity Refer to Exhibit 4-5. A change from Point A to Point B represents a(n): a. decrease in quantity supplied. b. increase in quantity supplied c. increase in supply. d. decrease in supply.QUESTION 1 The law of demand illustrates a(n) relationship between price and O a. inverse; demand Ob. direct; quantity demanded O c. inverse; quantity demanded O d. direct; demand QUESTION 2 Because personal tastes differ, what are substitutes for one person need not be substitutes for another person. True False QUESTION 3 A decrease in consumer incomes will: a. decrease the demand for an inferior good. Ob. decrease the supply of an inferior good. c. increase the demand for a normal good d. do none of the aboveQuestion 9 A rent ceiling results in a shortage of apartments. As a result, there is Not yet answered Select one: Marked out of O a. only a loss of consumer surplus for tenants. 1.00 Flag question O b. a gain of both consumer and producer surplus. O c. only a loss of producer surplus for landlords. O d. a loss of both consumer and producer surplus