Name Key

1. Gore Monde is a food lover who lives on bread and wine. Let his marginal utility of bread, MU_b, be given algebraically by the expression MU_b = 40 - 5b.  Similarly, let his marginal utility of wine be MU_w = 30 - w.  The current prices of bread and wine are Pb = 5 and Pw = 1, respectively.  Gore's income is 40.

a. What is the greatest quantity of bread that Gore can consume? b = 40/5 = 8

b. What is the greatest quantity of wine that Gore can consume? w= 40/1 = 40

c. What is the slope of Gore's budget constraint when you put wine on the horizontal axis and bread on the vertical axis? slope = -8/40 = -1/5

d. Given the prices and Gore's income, how much bread and wine should he consume? Bread = , Wine =

From the hint we know MRS_wb = MU_w/MU_b = P_w/P_b .  Or, (30-w)/(40-5b) = 1/5. This can be rearranged as w = 22 + b.  Whatever w,b choice makes the hint true must be a choice that also satisfies Gore's budget constraint.  Therefore 40 = 5b+(22+b).  Solving for b we get b = 3 and w = 25.

e. Suppose that Gore's income falls to 10. How much bread and wine will he consume now? Bread = , Wine = When we use the same reasoning we find 10 = 6b+22, or b = -2.  This is not possible, so it must be the case that Gore consumes no bread at all, and therefore spends all of his money on wine; w = 10.

2. Al Fabette consumes x's and y's.  With y on the vertical and x on the horizontal, his marginal rate of substitution in consumption is given by MRS = y/x.  At a shop on Sesame Street he can buy his x's and y's at the prices P_x = 5 and P_y = 1.

a. Fill in the boxes below to create Al's income expansion path.

From the hint we know that MRS_xy = MU_x/MU_y = P_x/P_y . Making the appropriate substitutions we can write y/x = 5/1.  This must be true regardless of income, therefore y = 5 x + 0 is the income consumption path.

 b. Suppose that the price of a unit of x falls to P_x=4.  Then Al's income expansion path will become

flatter   steeper no change

3. Put y on the vertical and x on the horizontal. Let Pepe Smith have the marginal rate of substitution MRS = y.  His income is 120 and the price of y is P_y = 1.

 a. In the box below write an expression for Pepe's price expansion path:

Again, the hint is MRS_xy = MU_x/MU_y = P_x/P_y. This time, upon substitution y = P_x/1; this must always be true for every tangency between budget constraint and indifference curve.  Whatever choice of x and y makes this true must also be an x,y pair that lies on Pepe's budget constraint. His budget is 120 = P_xX + P_yY = P_xX + Y. Now substitute in for P_x to get 120 = YX + Y.  The x,y pairs that lie on this line are common to both the MRS_xy = P_x/P_y rule and the budget constraint. Rearranging gives us the price expansion path y = 120/(x+1)

b. In the box below write an expression for Pepe's demand curve associated with the price expansion path you found in part a of the question. Write your expression in the box below:

The demand curve shows Pepe's reservation price as a function of quantity.  Since we know that y = Px, it must be the case that P_x = 120/(x+1) is Pepe's demand curve.

Hints: MRS_xy = MU_x/MU_y = P_x/P_y