# Problem Set 1

Due by 11:59 PM Wednesday, February 17, 2021 by PDF upload in Blackboard AssignmentsNote this has been changed from Sunday February 14, to give you more time to be able to come to office hours or ask questions. Normally assignment deadlines will remain Sundays at 11:59PM.

Please type your answers to the following questions in a document and save as a PDFIn MS Word, or Pages, or most word processing software, File -> Save As -> PDF, or File -> Export -> PDF.

to upload on Blackboard under Assignments. You may handwrite answers if you will be able to scan/photograph & convert them to a single PDF, if they are easily readable, but this is not preferred. See my guide to making a PDF - an essential skill in the modern world. If you are handwriting answers, you may print the pdf above and write on it, or just write on a piece of paper (we only need your answers).

For the few questions that ask you to draw a graph, try to do so on your computer (use MS Paint, the drawing tools in MS Word or MS Powerpoint, plot points in MS Excel, drawing/notetaking apps, etc.), and save it as an image to include on your homework document. Again, they need not be perfect or to scale, just show that you understand the broad idea. Being able to understand and sketch the graphs is still a very important and useful skill! If all else fails, I will be lenient in grading graph questions if you are unable to technologically include a graph.

You may work together (and I highly encourage that) but you must turn in your own answers. Your TA, under my supervision, will grade homeworks 70% for completion, and for the remaining 30%, and one question will be graded for accuracy - so it is best that you try every problem, even if you are unsure how to complete it accurately.

## Concepts and Critical Thinking

### Question 1

How can we use utility functions, which have actual numbers that can be measured and compared, to model preferences and still say with a straight face that preferences are subjective? Hint: what does it mean for a utility function to be ordinal or cardinal? Why can multiple utility functions describe the same preferences?

### Question 2

Describe, in your own words, what the marginal rate of substitution between two goods means. How is it different from the slope of the budget constraint?

### Question 3

Describe, in your own words, what happens at the optimum consumption point. Why is it the optimum? What does the equality of the slope of the indifference curve and the slope of the budget constraint mean, in English?

## Problems

### Question 4

#### Part E

Find the optimal combination of $$x$$ and $$y$$ where the consumer maximizes utility subject to income. Label this point $$A$$ on the graph.

### Part F

How much utility does the consumer earn at the optimum?