Marvin has a Cobb - Douglas utility function(U= 90.5 1 q0.5 2), his income is Y = 10, and he faces prices of p2 = 2. (a) Find the uncompensated demand (marshallian demand) curves for good 1. (b) Find the compensated demand (hicksian demand) curves for good 1. (c) Find the expenditure function (E(p1, p2, u)) From now on, suppose the price of good 1 increases from p1 = 1, to p '1 = 2 (d) Find the change in consumer surplus(ACS), Using uncompensated demand (marshallian demand) function. (e) Find the compensating variation (CV). (f) Find the compensating variation (EV).

Problem 2 Joan has the following utility function: u(x, y) = 5x + 3y. (a) Find Jane's marshallian demands. (b) Find Jane's hicksian demands. Consider that income is I = $8, and prices are given as p = $4, Py = $2. (c) Does Jane have enough money to attain a utility level of 20? Justify your answer. (d) Assume thè price of y marginally increases. Find the total, income and substitution effect for r due to the change in py.

Suppose that an individual with income I cares about two goods, X and Y. The prices of the two goods are px and py. The individual has the utility function U(X,Y)= 5 ln X + 3 ln Y. (a) Derive the Marshallian demands for the two goods. (b) Find the indirect utility function.

Do not use chatgpt. Thank you!

Suppose an individual has the following utility function: U(X,Y)= min{X, 2Y}, and they choose marshallian demands gx,gy. Suppose you have an increase in px. Which of the following is true about the change in demand for good X, gx? (a) No substitution effect, because they only consume one of the goods. (b) No substitution effect, because they always consume the goods in fixed proportion. (c) No income effect, because they only consume one of the goods. (d) No income effect, because they always consume the goods in fixed proportion. Which of the following production functions exhibits constant returns to scale? (a) f(k,l) = 0.310.7 (b) f(k, l) = kl (c) f(k, 1) = ln(k)+ln(1) (d) f(k, l) In(k) + In(1) =

Let X; denote the amount of good X demanded by person i given her income is M; and the price of good X is Px. Sofia's demand function for good X is given by XS =0.14 Ms / Px. Tanya's demand function for good X is given by Xt = 0.79 Mt / Px. Zara's demand function for good X is given by X₂ =0.32 M₂ / Px. The portion of income Tanya spends on good X is equal to ...

Repeat Question 1 with the utility function u(x₁, x₂) = x₁x2. (a) Determine the (Walrasian) demand functions for goods 1 and 2, x1(p1, p2, 1) and X2(P1, P2, I). Are goods 1 and 2 gross substitutes, gross complements, or neither. (b) Suppose that prices are p₁ = 1, p2 = 4 and income is I = 64. Compute the utility associated with the optimal choice of the consumer. (c) Then due to a tax of 3 dollars per unit, the price of good 1 increases to p₁ = 4. Compute the utility associated with the optimal choice of the consumer. (d) Determine the compensating variation in income CV. (e) Determine the equivalent variation in income EV.