1) For the following utility functions, draw a graph of two indifference curves with xon the horizontal axis and y on the vertical axis, corresponding to ulx, y) = 2 and Ux, y) = 4

1)

(a) u(x, y) = min{2x, y} [z is misprinted here]

Now, this is an example of perfect complement. The indifference curves are L shaped along the line: 2.x = y.

Now, u(x, y) = 2

Either, 2.x = 2 => x = 1

or, y = 2

Hence, the kink point on the indifference curve u=2 is at (1, 2).

Also, u(x, y) = 4

Either, 2.x = 4 => x = 2

or, y = 4

Hence, the kink point on the indifference curve u=4 is at (2, 4).

The following diagram shows the two indifference curves.

The two indifference curves are U=2 and U=4.

(b) u(x, y) = 2.x + 3.y

Now, this is an example of perfect substitute. The indifference curves are negatively sloped straight lines. The slope of the indifference curves is (-2/3).

Now, u(x, y) = 2

or, 2.x + 3.y = 2

or, x + y/(2/3) = 1

Hence, horizontal intercept is 1 and vertical intercept is (2/3).

Also, u(x, y) = 4

or, 2.x + 3.y = 4

or, x/2 + y/(4/3) = 1

Hence, horizontal intercept is 2 and vertical intercept is (4/3).

The following diagram shows the indifference curves at u = 2 and u = 4.

Please use this google drive link to download the answer file.       

answer 1.https://drive.google.com/file/d/18tFDk9whLJ4y99Ah6AbAZi-gFZfFdu1k/view?usp=sharing

answer 2.https://drive.google.com/file/d/1ndKKW9APK9T1NFlO-8mqTYzi1ThmbJ4H/view?usp=sharing

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https://helpinhomework.org/blog/how-to-obtain-answer-through-google-drive-link 

3)It is impossible to estimate the opportunity cost without the cost of production of the products shown in the graph.

4)please see the attached file.