Assignment

1. Sterling consumes 2 goods, x₁ and x₂. His utility function is U(x₁, x₂)= x₁ x₂² and his income is m. The price of good x₁ is p, and the price of good x₂ is 1.

a. Write down Sterling's budget constraint. What is the slope of his budget constraint?

b. Find Sterling's marginal utilities of each good, and find his marginal rate of substitution (MRS).

c. Write down an equation showing the relationship between Sterling's MRS and the slope of his budget constraint that must hold if Sterling is maximizing utility.

d. Use the equation from part (c) and the budget constraint from part (a) to find Sterling's demand functions for each of the two goods.

e. Suppose m=300 and p=1. How much of each good does Sterling consume? Draw a graph showing Sterling's budget constraint and indifference curve passing through his chosen consumption bundle.

f. Suppose m=300 and p=2. How much of each good does Sterling consume? On the same graph from part (e), show Sterling's budget constraint and indifference curve passing through his new chosen consumption bundle.

g. On the same graph, show the (hypothetical) budget constraint that is tangent to the indifference curve from part (e) but parallel to the budget constraint in part (f).

h. On the same graph, show the income and substitution effects of the increase in p from 1 to 2 on Sterling's consumption of good x₁. Is good x₁ a normal or inferior good?

i. Find the equation representing the (hypothetical) budget constraint drawn in part (g). Hint: you know this budget constraint has the same prices as in part (f), so you need to find the income level m that makes the budget constraint just tangent to the indifference curve passing through Sterling's chosen consumption bundle in part (e).

j. Find the amount of each good that Sterling would consume if is his budget were the one found in part (i). What are the numerical values of the income and substitution effects shown graphically in part (h)?