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Now suppose the utility function is given by U(X1, 12) = 1 12 + 10x2. (d) Give the equation for an indifference curve for this utility function, and draw a picture of such an indifference curve. Given your picture, does this look like a quasi-concave utility function? (e) Give the definition of a quasi-concave utility function, for a general utility function. In principle, we could insert this particular utility function into this definition and verify that it holds, i.e., verify that this is utility function is indeed quasi-concave. However, the resulting algebra is quite tedious. Instead, let's look at an example. Calculate the utility of (11, 2) = (2, 2). Now calculate the utility of (x,; x2) = (4, 0). What does quasi-concavity tell you about the utility of (x1, x2) = (3, 1) (= ;(x1, X2) + (21, (2))? Verify that this is the case. (f) Consider the seemingly-similar utility function U($1, 12) = ri + 10x2. Draw a picture of an indifference curve for this utility function. Given these indifference curves, does this look like a quasi-concave utility function? Form the Lagrange function for the associated constrained utility maximization problem and find the associated first-order conditions. Use your picture to argue that you have found not a maximum but a minimum