Consider a consumer with utility function u(x, y) = x + ln(y), where x and y stand for the quantities of goods 1 and 2 respectively. 1. Write down the marginal utility for goods 1 and 2.

2. Are these preferences monotone?

3. Does the consumer have a satiation or bliss point?

4. Write down the MRS between goods 1 and 2.

5. Does the MRS depend on the relative consumption of goods 1 and 2?

6. Graph two indifference curves for the consumer, and identify which one yields higher utility.

7. Are these preferences convex? Support your argument.

8. Suppose that the consumer has an income m = 6, and that the prices for goods 1 and 2 are px = 1 and py = 6 respectively. (a) Write down the budget line for the consumer (b) Graph the budget line for the consumer (c) Identify the optimal consumption bundle for the consumer given their budget constraint; you may do so graphically or analytically.