Suppose the government decides to subsidize (rather than tax) consumption of grits.
A: Consider a consumer that consumes boxes of grits and “other goods”.
(a) Begin by drawing a budget constraint (assuming some exogenous income) with grits on the horizontal axis and “other consumption” on the vertical. Then illustrate a new budget constraint with the subsidy—reflecting that each box of grits now costs the consumer less than it did before.
(b) Illustrate the optimal consumption of grits with an indifference curve tangent to the after subsidy budget. Then illustrate in your graph the amount that the government spends on the subsidy for you. Call this amount S.
(c) Next, illustrate how much the government could have given you in a lump sum cash payment instead and made you just as happy as you are under the subsidy policy. Call this amount L.
(d)Which is bigger —S or L?
(e) On a graph below the one you have drawn, illustrate the relevant MWTP curve and show where S and L can be found on that graph.
(f) What would your tastes have to be like in order for S to be equal to L.?
(g) True or False: For almost all tastes, price subsidies are inefficient.
B: Suppose the consumer’s tastes are Cobb-Douglas and take the form u(x1, x2) = x1α x2(1−α) where x1 is boxes of grits and x2 is a composite good with price normalized to 1. The consumer’s exogenous income is I.
(a) Suppose the government price subsidy lowers the price of grits from p to (p −s). How much S will the government have to pay to fund this price subsidy for this consumer?
(b) How much utility does the consumer attain under this price subsidy?
(c) How much L would the government have had to pay this consumer in cash to make the consumer equally happy as she is under the price subsidy?
(d) What is the deadweight loss from the price subsidy?
(e) Suppose I = 1000, p = 2, s = 1 and α = 0.5. How much grits does the consumer buy before any subsidy, under the price subsidy and under the utility-equivalent cash subsidy? What is the deadweight loss from the price subsidy?
(f) Continue with the values from he previous part. Can you calculate the compensated demand curve you illustrated in A (e) and verify that the area you identified as the deadweight loss is equal to what you have calculated? (Hint: You need to take an integral and use some of the material from the appendix to answer this.)