Question

1. Consider an alternate universe where you have a (or another) roommate named Jamie who binge watches TV seasons bought on services like itunes. In modeling Jamie’s preferences, we will assume that they are Cobb-Douglas over TV seasons (x-axis good) and a numeraire Good which always has a price of $1.00 (note: we use the notion of a numeraire good to represent spending on all other consumption goods – in this example, that means everything other than TV seasons – its price is always $1).

a. Jamie lives off a monthly income of $1,000. Last month, when the price per season was $50, Jamie bought 8 seasons. Using what we know about the relationship between the parameters of the Cobb-Douglass utility function and expenditure shares, write down the specific utility function for Jamie - i.e. put in the appropriate numbers for ? and (1 − ?).

b. We can use the utility function identified in part a to find the associated expenditure function for any target utility level. This expenditure function is given by: ??? =

̅ .4 .6

? ∗ (? /0.4) ∗ (? /0.6) . Use this expenditure function to derive the hicksian??

demands for TV Seasons.

c. It is predicted that a proposed end to net neutrality will increase the market price of seasons from $50 to $ 100. Use the implied change in the expenditure function to compute Jamie’s Compensating Variation for this potential price increase.

d. What is the Change in Marshallian Consumer Surplus that would be associated with this price increase? Hint: review the solved problem 5.2 on page 147 of the text book.

e. Recall that we can also compute CV as the integral under the compensated demand curve (setting utility equal to the baseline utility). Verify your answer to part c using this approach.

Answer 1

a) Monthly income of Jamy= $1000 and price per person=$50

Jamie bought 8 seasons=1000/50*8 =160 characters

Utility function at an associated function=a(1-a)=a(1-160)

a=159

b)Expenditure function= (? /0.4) ∗ (? /0.6)=2p/0.24 units = 2*159/.24=318/0.24=Rs 1325

c).The potential price increase=$50+$100*1325 =$150*1325=$198750

Expenditure function. In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods.

The expenditure function is the minimal expenditure needed to attain a target utility level. ... The expenditure function is given by the lower envelope of {ηx1,x2 (p1) : u(x1,x2) = u} Since the minimum of linear functions is concave, the expenditure function is therefore concave.

d) The marshallian consumer surplus is the proportion of income spent on any commodity is small then the income effects are small. If n is the number of goods, we show, under certain assumptions on preferences and prices, that the order of magnitude of the norm of the income derivative of demand is 1/√n. As a corollary we get that for the case of a single price change the percentage error in approximating the Hicksian Deadweight Loss by its Marshallian counterpart goes to zero at least at the rate 1/√n and that demand is downward sloping for n large enough.