Suppose that Henry's tastes over peanuts (x) and potato chips (y) are summarized by the utility function  u(x,y) = x+y and and p_x = 20, p_y = 30 and m = 300. Now let's suppose that the price of peanuts (p_x) suddenly increases to p_x = 35 while income stays the same. Calculate a change in demand for peanuts due to the substitution effect.

Jim's preferences over goods x and y might be represented by the utility function u(x,y)=x^0.5+2+2y. The price of good x is p_x=1, the price of good y is p_y=8, and Jim's income is m=20. Suddenly, the price of good x increases to p_x=2. What is the change in demand for the good x caused by the income effect of this price change? (Hint: Before you start calculating the effect, take a closer look at the utility function.)

Larry consumes two goods, and and his utility function is . Last week, he bought 16 units of   and 2 units of . But prices have changed. The current prices are  and . What is the minimal amount Larry has to pay for a new consumption bundle this week to be as well off as last week? (Hint: An interior optimum exists, so the optimality condition has to hold in the optimum.)

Suppose that a consumer consumes goods x and y and has monotonic and strictly convex preferences. If the consumer aims to reach a utility level u₀ with the minimum costs, his optimal consumption will be x₀*,y₀*. Now suppose that the price of x increases. In a new consumer's optimum  x₁*,y₁* bringing the consumer the utility level u₀: