Question

Cat only buys tomatoes (x) and cucumbers (y) and her preferences can be identified with U(x,x)=6x2y. a. What is Cat's marginal utility for tomatoes, and what is her marginal utility for cucumbers? How does Cat's utility change when she consumes more tomatoes? How does her utility change when she consumes more cucumbers? b. Find Cat’s marginal rate of substitution (tomatoes are on the x axis and cucumbers on the y axis). What is the slope of Cat's indifference curve that passes through the point (1,10)? What is the slope of Cat's indifference curve that passes through the point (10,1)? C. What is Cat's budget constraint using Px as the price of x, Pay as the price of y, and I as her fixed income? What is the slope of the budget constraint? How does the slope depend on Cat's income? d. Figure out Cat's optimal consumption bundle given income and prices. Write the equation that characterizes the set of bundles such that the indifference curve is tangent to the budget constraint. What is the intuition behind this equation? What does thi s equation tell us about how much Cat spends on cucumbers relative to how much he spe nds in tomatoes in any optimal allocation?

Answer 1

UCx, y) = 6x²4 a) MUx= 12xy Csomeo mo) Muy = 6x2 (Cucumbers mo) Utility increases as more tondoes 4 Cucumbers are possen b) MRS (1,16) = 2110 20 MAS (10,1)= 20 ='s scope of Budget Consbait =-PxPy ( depends on Fun Slope dosmot 1 x P x +Yby = Income d) At optionality Mes= 2 y = Poppy