Suppose consumer are always ready to trade k units of good X for w units of good Y. Then, which of the following utility function represents this preference? U(X,Y) = min{wX + kY). O U(X,Y) = wX + kY. O U(X,Y) = min{kX, wY}. O U(X,Y) = kX + wY.
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- QUESTION 1 x0.80Qy(1-0.80); and the budget 153 = 11Qx + 12Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.9. as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1). Qx For the utility function U = Please enter your responsethe option is a &cJames works for a delivery company in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=5; James is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station. James’s utility function is U(x,y)=x1/3y2/3 and his income in College Station is $2500. What happens to James’ utility if he accepts the transfer (James’ utility maximization is always characterized by the tangency rule)?
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- Subpart 4,5,6 only.Consider a consumer whose preferences are represented by a utility function u(x, y) = a0.5y Are these preferences convex? O Yes O NoZeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…
- Find marginal utility MU for a consumer consuming x amount of a given commodity, where his total utility function is TU = x²ln (x² + 1).You go to the store in search of laundry detergent, to discover that they offer two varieties: Myst and Breez. Your preferences between Myst and Breez can be represented by the following utility function: U(M. B) = 16M + 32B Myst costs 4$ unit. Breez costs 10$ per unit for the first 5 units, but all units after 5 only costs $6. Find your Engel Curve for Breez.(a). What kind of preferences are represented by a utility function of the form u(x₁, x₂) = √√x₁ + x₂? What about the utility function v(x₁, x₂) = 13x₁ + 13x₂? Compute the slope of the two indifference curves. Do their slopes depend on the bundle? (b). What kind of preferences are represented by a utility function of the form u(x1, x₂) = x₁ + √√x₂ ? Compute the slope of the indifference curve. Does it depend on the bundle? In which way? (c). Consider the utility function u(x₁, x₂) = √x₁x2. What kind of preferences does it represent? Is the function v(X₁, X2) = X₁X2 a monotonic transformation of u(x₁, x₂)? Compute the slope of the indifference curve. Does it depend on the bundle? In which way?