Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120.

(a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12.

(b) Calculate the optimal basket of X1 and X2 and fully illustrate this optimal choice in a diagram with X1 on the horizontal axis.

(c) Suppose the government introduces a $2 tax on the consumption of each unit of X2 but X1 remains tax-free. Calculate the new optimal basket of X1 and X2. Illustrate this new optimal choice in your diagram above. (d) [7 marks] Calculate the compensating variation needed to return this consumer to her original utility level.

Expert Solution

Rahul Sunny answered 1 year ago

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