Matching utility functions and indifference curve maps Consider the following 6 utility functions: π‘ˆ1 = √π‘₯ + 2𝑦 π‘ˆ2 = √2π‘₯ + βˆšπ‘¦ π‘ˆ3 = 2π‘₯ 2 + 𝑦 2 π‘ˆ4 = π‘₯ 2 + βˆšπ‘¦ π‘ˆ5 = min(π‘₯, 𝑦) + π‘₯ 2 π‘ˆ6 = 2 ln(π‘₯) + ln(𝑦)

 a) For each, find the expressions for marginal utilities and the marginal rate of substitution, and determine whether monotonicity and convexity are met. Winter 2022, Tocoian 2

 b) Next, try to picture what indifference curves will look like, and see if you can find a matching graph below. [Try not to rely too much on brute force calculations of utility values – what if the grid was not shown and you couldn’t easily identify the coordinates at any given point?

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