The concept of elasticity

1. As additional demanders enter the market for a particular good, the market demand curve shifts outward and becomes flatter at a given price. Does this fact imply that the price elasticity of demand becomes greater at any givenprice? Carefully demonstrate and explain your answer.

2. Susie receives a monthly money income of I = $1,000 and consumes amounts of two goods, food (F) and a composite good (G), facing prices P_F = $2 and P_G = $1. First, construct Susie's budget constraint and graph the budget constraint in a diagram. Assume Susie's consumption optimum is F = 250 and G = 500. Show this consumer optimum combination in your diagram. Second, suppose a Food Coop opens and for a monthly membership fee of $200, members can purchase food at a reduced price of $1 per unit. Would Susie be better off purchasing a Coop membership? Carefully demonstrate and explain.

3. Let individual i have the utility function

U_i(x,y) = x^1/2.y

Suppose the initial endowment is x = 16 and y = 2.

(a) Determine 4 combinations (x,y) for which U_i = 8; and for U_i = 16.

(b) What is the minimum amount of x that i would have to be compensated to induce him to give up 1 unit of y?

4. Let individual i have the utility function

U_i = 2x⁵.y

where x and y are both goods. This utility function implies a marginal rate of substitution of x for y given by

MRS_xy = y/2x

In addition, assume the endowment is x = 4 and y = 8.

If the rate of exchange between x and y is 1 unit ofy for 1 unit of x (and vice versa), what will be his consumptive optimum?