Question

1. The State of Florida currently budgets $10,000/year for two goods—voting machines (which cost $1,000 each) and voter education programs (which cost $500 each). Their wise governor, Jeb, knows his constituency well enough to know their indifference map over the two goods. Now, consider bundle A which consists of 5 voting machines and 10 education programs. The slope of Florida's indifference curve at bundle A is –3 (assume voting machines are on the horizontal axis).

a. Is this combination of goods the optimal bundle of goods for the State of Florida?

b. If so, explain why. If not, carefully explain how Florida can re-arrange its expenditures (i.e., choose another bundle) to reach a higher level of utility (you do not need to determine exactly which bundle they would choose).

c. Show how a $5,000 grant from the federal government would affect Florida's budget constraint. d. Suppose the federal government restricts the state to spend this $5,000 grant on voting machines only. Re-draw the state's budget constraint, reflecting this requirement.

2. Suppose that the demand curve of a good is vertical over a given range of prices. Draw the corresponding indifference curves and budget lines (assume the indifference curves of this good meets the four assumptions of preference, and the budget line is linear). Is this good a normal good? (Hint: draw the diagram of the process of getting a demand curve, figure out what substitution effect and income effect should be, and whether income effect is positive or negative.)

3. Jeff has a monthly income of $400, which he spends each month on dinners (which cost $20 each) and movies. He finds that he maximizes his utility by spending half his income on dinners and ha lf on movies. His marginal rate of substitution at this bundle of goods is 0.4 (measured with dinners on the horizontal axis).

a. Given this information, what is the price of movies?

b. Draw Jeff's budget constraint and indifference curve at this optimal bundle. Label both axes appropriately.

c. Write an equation—in slope- intercept form—for Jeff's budget constraint.

d. What is the opportunity cost, in terms of dinners, of an additional movie? e. Now suppose the price of dinners changes to $25. Show on your diagram how the budget constraint will change. Can Jeff still afford his initial bundle from part b?

Answer 1

Sol 1 :

(A) There are two condition to find the optimal combination of two goods which are as follows :

Condition 1 : MRSXY(Marginal Rate of Substitution) = Price x / Price of y (Budget line)

Condition 2 : IC ( Indifference curve should be Convex at the point of equilibrium)

Price of Voting Machine (X)= $1000

Price of Voter education programme (Y) = $500

so , MRT (Px/Py) = 1000/500

                            = 2

where as , MRS(Slope of indifference curve) is given = - 3

So, condition 1 is not fulfilled here and Florida's combination of goods are not optimum or are not deriving maximum utility. (MRSxy > Px/Py)

(B) So, if the Florida's Combination of goods are nit optimum mentioned in case (A) where , MRSxy > Px/Py .it means that florida is willing to pay more for goods x ( Voting Machine) than the market wants Florida to pay. So , Florida will buy or consume more of goods X(Voting Machine) than the Voter education programme. So this will reduce the MRS(Slope of indifference curve). and florida's new bundle of goods will restore to the equilbirum point.

(C) If the government provides the grant of $5000 then this would increase the budget constraint from $10000 to $15000 . It will lead to shift the budget line from B1 to B2.

The shift will be as follows

(D) In this case , if the government restricts to spend the grant of $5000 on Voting machine only , then budget line or budget constraint will shift only for voting machine (i.e on X axis) because with increase in budget for voting Machine, now he will b e able to buy more of voting machine with the same amount on voter education fund.

The Shift in Budget Constaint will be as follows :