Suppose that you have tastes for grits and “other goods” (where the price of “other goods” is normalized to 1). Assume throughout (unless otherwise stated) that your tastes are quasilinear in grits.
A: The government decides to place a tax on grits—thus raising the price of grits from p to p +t.
(a) On a graph with grits on the horizontal axis and “other goods” on the vertical, illustrate the before and after tax budget.
(b) Illustrate your optimal consumption bundle after the tax is imposed — then indicate how much tax revenue T the government collects from you.
(c) Illustrate the most L you would be willing to pay to not have the tax.
(d) Does your answer depend on the fact that you know your tastes are quasilinear in grits?
(e) On a graph below the one you have drawn, derive the regular demand curve as well as the MWTP curve.
(f) Illustrate T and L on your lower graph and indicate where in the graph you can locate the deadweight loss from the tax.
(g) Suppose you only obseserved the demand curve in the lower graph—and you knew nothing else about tastes. If grits were actually a normal good (rather than a quasilinear good), would you under- or over’s time that deadweight loss by assuming grits are quasilinear?
B: Suppose that your tastes could be represented by the utility function u(x1, x2) = 10x10.5 +x2, with x1 representing weekly servings of grits and x2 representing dollars of other breakfast food consumption. Suppose your weekly (exogenous) budget for breakfast food is $50.
(a) Derive your uncompensated and compensated demand for grits.
(b) Suppose the tax on grits raises its price from$1 to $1.25 per serving. How does your consumption of grits change?
(c) How much tax revenue T does the government collect from you per week?
(d) Use the expenditure function for this problem to determine how much L you would have been willing to pay (per week) to avoid this tax?
(e) Verify your answer about L by checking that it is equal to the appropriate area on the MWTP curve. (For this you need to take an integral, using material from the appendix).
(f) How large is the weekly deadweight loss?
(g) Now suppose that my tastes were represented by u(x1, x2) = x10.5+ x20.5. How would your answers change?
(h) Under these new tastes, suppose you only observed the regular demand curve and then used it to calculate deadweight loss while incorrectly assuming it was the same as the MWTP curve. By what percentage would you be overestimating the deadweight loss? (Hint: You again need to evaluate an integral. Note that the integral of 1/(p(1+p))with respect to p is lnp− ln(1+p).)