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In: Economics

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...

A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget.
1. Draw the budget line for this consumer when M=50 and the budget line when M=100. Put good x on the horizontal axis.

Solutions

Expert Solution

Answer to the question:

To draw the budget line we need to have the Price of two goods (Px and Py) and the income level (M). We have:

Price of X (Px) = 4.

Price of Y (Py) = 2.

And we have 2 income situation:

a. M = 50.

b. M = 100.

The equation of the budget line is:

Let us consider the first situation where the income is 50.

When the X=0,

When Y=0,

Let us now consider the second situation where the income is 100.

When the X=0,

When Y=0,

When, the M = 50, consumer will be able to buy a maximum of 12.5 units of X (when the Y=0) or the consumer will be able to buy a maximum of 25 units of Y (when the X=0). This budget constraint is represent with red color.

Again when, the M = 100, consumer will be able to buy a maximum of 25 units of X (when the Y=0) or the consumer will be able to buy a maximum of 50 units of Y (when the X=0). This budget constraint is represent with red color.

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Rahul Sunny answered 1 year ago

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