Victoria has the following utility function: U(x,y) = x½y½ and faces the budget constraint: M = Px + Py. Suppose M = 120, Px = 4 and Py= 1. Find the optimal x and y.
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Victoria has the following utility function: U(x,y) = x½y½ and faces the budget constraint: M = Px + Py. Suppose M = 120, Px = 4 and Py= 1. Find the optimal x and y.
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- She has the following utility function: U (x, y) = x/2y1/2 and faces the budget constraint: M = Px + P,y. Suppose M = 120, P, = 1 and P 4. Find the optimal x and y.Suppose there are two goods, x and y. If one good has a negative price, and the other good has a positive price, then the slope of the budget constraint will be positive. is this true or false?Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (
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- If a consumer consumes two goods (q1 and q2) and demand function of q1 is U/P1, which portion of his budget goes to q1.Anthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?Which of the following utility functions represent preferences which do not satisfy monotonicity? 1 U= - x+y 1 U= - 5ху Ou=xy O u= y