Question

A consumer can spend her $20 weekly drink budget on sugar-sweetened beverages (SSBs) or all other beverages. SSBs cost on average $2 each, and all other beverages cost on average $4 each. The city is proposing a 20% tax on SSBs.

1. In two separate graphs, draw the effect of the tax on the consumer's consumption of SSBs and all other beverages for two situations:
   1. The substitution effect and the income effect move in the same direction. What kind of good is an SSB in this situation?
   2. The substitution effect and income effect move in opposite directions. What kind of good is an SSB in this situation?

Answer 1

Solution:

Weekly income with the consumer = $20

Price of sugar-sweetened beverages (SSBs), Ps = $2 each, price of other beverages, Pb = $4 each

So, budget line: Ps*S + Pb*B = I, S is quantity of SSBs and B is quantity of other beverages.

Old budget line: 2*S + 4*B = 20

With tax imposition of 20%, new price of SSBs, Ps' = 2(1 + 20%) = 2(1 + 0.2) = $2.4 each

New budget line: 2.4*S + 4*B = 20

Taking quantity of SSBs on horizontal axis and quantity of other beverages on vertical axis, initial slope of budget line (which equals the price-ratio) = 2/4 = 0.5. New slope = 0.6 (steeper)

For both graphs, we represent initial equilibrium point by X, final equilibrium point by Z, and decomposing point by Y, so that (Y - X) gives the substitution effect and (Z - Y) gives the income effect.

(a) If substitution and income effect move in the same direction: We know that substitution effect is always negative, so with increase in price, SSBs will be consumed less. By moving in same direction, it means that income effect should also result in decreasing the consumption of SSBs further. Note that with taxation, real wealth or purchasing power of consumer decreases, and we have already established that income effect is resulting in decreased consumption of SSBs. Since, the decrease in income has resulted in decreased consumption, we can claim that SSB is a normal good (since income elasticity of demand is positive).

Then, forming the required graph (notice that income and substitution effect, both move in same, leftward direction):

Quantity of other beverages 10 6 05 4 Initialequilibrium Y point eqm 2 Income effect Initial.budget line New Budg 10,0 10 0 2 4 5 6 Quantity of SSBs,S

(b) If substitution and income effect move in the opposite direction: Now, by moving in the opposite direction, it means that income effect should result in increasing the consumption of SSBs (since substitution effect has resulted in decrease in the consumption of SSBs). Again, with taxation since the real income with the consumer has decreased, while with income effect consumption of SSBs has increased, it means that income elasticity of demand is negative. So, we can claim that SSB is an inferior good.

Then, forming the required graph (notice that income and substitution effect move in opposite direction; substitution effect moves in leftward direction, income effect moves in rightward direction):

Quantity of other 10 beverages, 1 6 0,5 5 4 Initial Equilibrium point 2 New eqm poin Income effect nitial budget line Substitution effect budket n (10,0) 0 1 23 4 56788.33 9 10 Quantity of SSBs, S