Question

A person's utility fromm goods A and B is U(A,B)= A x B. The marginal utilities of each goods are MUa=B and MUb=A. The person has $120 income to spend on the two goods and the price of both goods equals $1.

a) Write the equation for the budget line and sketch it on a graph – identifying relevant intercepts and slope – placing good A on the horizontal axis.

b) Find the quantities of A and B that maximize utility; show your work and illustrate your answer graphically.

c) Sketch out the income-consumption curve.

d) Holding constant income (at $120) and the price of A (at $1), what is the demand for B? Can you write out an equation representing the demand for B? Plot out a couple of points on the demand curve for B.

e) A tax of $1 per-unit is placed on A (i.e., increases price of A to $2). Find the new utility maximizing amounts of A and B. Show your answers graphically.

f) How much tax revenue is collected? Calculate and show graphically.

g) A lump-sum tax (fixed $-amount income taken from the person), set at the same dollar amount as the per-unit tax revenue generated in part (e), replaces the per-unit tax. Show the new budget constraint (i.e., with the lump-sum tax) on your graph.

h) The taxes in (e) and (f) both collect the same amount of tax revenue; which, if either, would the person prefer (achieve higher level of utility)?

Answer 1