Suppose that Sam has a utility function u(x, y)= xy2 where x is the amount of good 1 and y is the amount of good 2. The price of good 1 is $10 and price of good 2 is $20, and the income is $ 90. The price of good 1 is denoted by px and the income is donated by m. Derive the equations for income-offer curve, Engel curve for good 1, demand curve for good 1 and solve for the optimal consumption of (x, y).

Floyd's utility function is given by U(X,Y)=2XY. MUx=2Y and MUy-2X. The price of good X is Px=2, while the price of good Y is Py = 1. Floyd's income is 1,000. Which of the following is true given that the price of good X falls to 1? The substitution effect for good X results in an increase of X consumption by about 1,043 units and a decrease in Y consumption by about 14 units. The substitution effect for good X results in X consumption of about 250 units. The substitution effect for good X results in X consumption of about 500 units. The substitution effect for good X results in an increase of X consumption by about 250 units and no change in Y consumption.

The utility function of a consumer is given as follows. U(x, y) = x²y³, MU, = 2xy3 and MU, = 3x?y?. a. Derive the demand functions for good x and good y. b. Draw a demand curve. Draw an Engel curve. Is good x a normal good? С.

Assume the demand for cherries is elastic and that the producer of cherries increases the price of cherries. As a result? A convex indifference curve implies what type of behavior? If a consumer always wishes to consume peanut butter and jam in fixed proportions, he treats these two goods as if they are? Assume PX= $3 and PY = $6 and income = $30. What is the relative price of an additional unit of good X in terms of the amount of good Y that has to be given up? Assume there are only two goods (X and Y). Assume the relative price of good X, is 2 of good Y. If income doubles, the price of X doubles and the price of Y doubles, what will be the relative price of good Y?

Zack's preferences can be represented by the utility function 1 u(x, y) = r + 2J. x +2/y. 1. Assume Zack has income m = 27 and faces pricesp= 6 per unit of the first good and q = 3 per unit of the second good. Find Zack's optimal bundle. 2. Assume Zack has income m = 36 and the price of the second good is q = 4. Find Zack's demand for the first good, x(p).

Consider two consumers, A and B, who consume two goods, x and y. Assume that the utility function for A is U₁ = A₁ and the utility function for B is UB = XBYB. Consumer A is endowed with 10 units of x an 10 units of y. Consumer B is endowed with 10 units of x and 40 units of y. Assume the price of y is set to $1. What is the expression for Consumer A's demand for x? XA 10p, +10 Pr 10p, +40 Pr 10pz +10 4pz 10p, +40 4pz

Imagine a market that sells two goods: food, and energy, selling at prices PF and PC, respectively.  In a graph, plot an indifference curve and explain how you derive the optimal level of consumption of food and energy using the budget constraint.    In 2022/2023, the UK government introduced the Energy Bill Support Scheme, which gave every household a discount on their energy bills for winter in the form of an income subsidy. Replicating the graph above, indicate how the indifference curve changes in the presence of the subsidy. How much of the change in the demand of each good is due to an income effect and how much to a substitution effect?  Now suppose the subsidy is removed, and we return to the initial indifference curve (point a.). Imagine then that energy prices decrease by 10%, while food prices remain constant. How does the equilibrium presented graphically in part (a.) changes? As before, indicate how much of the change in quantity of each good consumed is due to the…

A consumer has preferences over two goods, denominated by x and y, given by the utility function U(x,y) = min{αx,y} with α > 0. The prices of the good are px = 2 and py = 5. The consumer has an income of I > 0. (a) Provide an intuition for this utility function. Specifically, are these goods substitutes or complements? If x is bicycle tires and y is bicycle frames, what is the value for α? (b) For what values of α will the consumer demand (i.e., Walrasian demand) more x than y. (c) For what values of α will the consumer spend more on x than on y (given her Walrasian demands).

Consider a consumer who has utility function U(x,y)= x + 2y, where x is the amount of good 1, and y is the amount of good 2, and income of 90. Suppose the price of good 1 is 5 dollars per unit, and the price of good 2 is 15 dollars per unit. What is the consumer's quantity demanded of each good? I.e. which consumption bundle (x,y) that the consumer can afford maximizes their utility? O(4.5,3) O (20,6) (18,0) O (0,6)

Bob has utility function U(x,y)=x2+y over goods x and y a) Do we have a name for this type of utility function? Are Bob's preferences well-behaved? b) Let Bob have budget I=$60, and let prices be Px=$30, Py=$10. Find Bob's optimal basket of goods x and y. Is this an interior or corner solution? c) What will happen if the price of good y doubles? [Think about: can we use this utility function to describe preferences over pet snakes and pet mice?]