Let the utility function be given by u(x1, x2) = √x + √₂. Let m be the income of the consumer, p₁ and p2 the prices of good 1 and good 2, respectively. Write down the budget constraint and illustrate the set of feasible bundles using (a) a figure. (b) Suppose that m = 24, p₁ = 2 and p2 = 4. Find the optimal bundle for the consumer. In other words, find the combination of ₁ and 2 that maximizes the consumer's utility when the prices are p2 = 2 and p₁ = 4, and her income is m = 24. (c) Determine the Marshallian demand function.

2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂

A consumer’s preferences over pizza (x) and steak (y) are given by u(x,y) = x2y (HINT: MUx = 2xy and MUy = x2) and his income is I = $120 and py = $1. (a) Calculate his optimal bundle when pX = $8 (call this bundle A) and separately when pX = $1 (call this point C). (b) Finding the decomposition bundle B, calculate the income and substitution effects on the amount of pizza of a decrease in the price of pizza from pX = $8 down to pX = $1. (c) Forget about the decomposition bundle and the two effects. In (a), the price of pizza decreases, hence the agent ends up better off. Let’s quantify how much “better off” the agent becomes after this price drop, in dollars. For this, instead of the price drop, suppose the agent is given some money $m and he optimize utility with this additional gift included to his budget. What should m be, so that his optimal utility with his expanded budget is exactly equal to his utility at the bundle C (the bundle he chooses optimally when pizza price drops to…

A consumer has utility (see image) on ice creams (x) and cakes (y).   (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x).  (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.

Suppose the function for the utility from good c is denoted as U(c)=2c1/2 .  Which of the following expressions indicates the marginal utility of c?