Question

Dr Pepper’s preferences can be represented by the utility function u(x,y) = x + y where x is his consumption of Coca Cola (hereafter, referred to as Coke) and y is his consumption of orange juice (hereafter, referred to as OJ).   Initially, both types of drinks are not taxed and with an income of $12 he faces prices ($1, $2). On the advice of nutritionists, the government decides to impose a specific tax of $2 on Coke which leads to its price increasing to $3. OJ remains untaxed and its price is unaffected by the tax on Coke.

Select one:

a. There is no deadweight loss associated with this tax on Coke for Dr Pepper.

b. Somebody called Dr Pepper should not drink Coke.

c. The compensating variation of this price change is the same as the equivalent variation for Dr Pepper.

d. The compensating variation of this price change is twice the magnitude of the equivalent variation for Dr Pepper.

e. The compensating variation of this price change is half the magnitude of the equivalent variation for Dr Pepper.

Answer 1

Both Compensating Variation [CV] and Equivalent Variation [EV] deal with price changes and how they affect utility. As in this case there is a price increase, the CV shows the amount of money that would need to be given to the consumer to get him back to the old level of utility at new prices. The EV shows the amount of money that would have to be taken from the consumer to bring him to the new level of utility at the old prices.

(a) - There is a deadweight loss as total consumption of consumer reduces at new prices following the imposition of the tax

(b) Dr. Pepper does not drink coke anymore because it becomes more expensive that Orange Juice. In the case of perfect substitutes the consumer spends entire income on the good that is cheaper

After calculating the CV and EV as shown below, option (d) is true as CV = $12 and EV = $6

CV shows that the consumer is indifferent between price vector (1,2) with income $12 and price vector (3,2) with income $24

EV shows that the consumer is indifferent between price vector (3,2) with income $12 and price vector (1,2) with income $6