Consider that there are two goods, good X and good Y, which are perfect substitutes. The consumer has the utility function given by: U(X,Y)= X + aY The prices of the goods are given by px = 3 and py = 6, respectively. The income of the consumer is given by I = 100. a) Choose a value for parameter "a" by yourself. Graphically illustrate the budget line of the consumer and draw some example indifference curves. Then, find the consumption bundle that maximizes the consumer's utility. b) List the possible outcomes for different values of parameter "a". Suppose that there are three goods, good X, good Y, and good Z, and suppose that the consumer has the utility function denoted by U(X, Y, Z) where X, Y, Z denote the quantities of goods. The prices of the goods are denoted by px, px, and pz, respectively, and the income of the consumer is denoted by I. Write down the consumer's optimization problem (formally, as we wrote in the lectures). Apply the Lagrangian method. Find the necessary conditions (NC) for the consumer's optimization problem of allocating budget between consumption of three goods (good X, good Y, good Z). Provide at least two interpretations of the NC (explain what these conditions mean in words). What if there were n goods listed as {X₁, X₂,...,Xn}? What would be the necessary condition for the optimal quantities of any pair of goods X; and X;?

Q: c. How much total consumer surplus will each of them receive at a price of $32?

A: Last parts C and d are answered below:

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Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.