# Econ 302 Homework

**Econ 302 Homework #1 McLeod**

**Due in class Wednesday, September 13th.**

**Name ______________________________________________________**

**ID # ________________________________________________________**

**Instructions: Please Read Carefully**

**Please print out this form. After you have written your answers, please staple the seven sheets together at the top left-hand corner.**

**The first sheet is intended only as a cover sheet. Do not write anything on the first sheet except your name and ID #.**

**Please answer each question on the page provided. If you need extra space, you may use the back of the sheet.**

**There are 50 possible points on this homework assignment. You may work together, but you MUST WRITE UP YOUR OWN WORK and TURN IT IN, IN PERSON, AT THE BEGINNING OF CLASS on Wednesday, September 13th.**

**YOU MUST TURN IN THE HOMEWORK IN THE CLASS IN WHICH YOU ARE REGISTERED!!**

**Late homework will not be accepted.**

**PLEASE STAPLE YOUR HOMEWORK!!**

1. (18 points) For each of the following situations, i) Find the Marginal Rate of Substitution at the given bundle, and ii) use a graph to **indicate the given bundle,** and **accurately draw the indifference curve** that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis.

a) The consumers utility function is given by U(X,Y) = X1/2*Y1/2, and the given bundle is X = 16 and Y = 4.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

b) The consumers utility function is given by U(X,Y) = MIN(X, 4Y), and the given bundle is X = 3 and Y = 1.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

c) The consumers utility function is given by U(X,Y) = 4X + 2Y and the given bundle is X = 1 and Y = 3.

i) MRS = __________________________________________________

ii) Draw your graph in this space:

2) (18 points) For each of the following situations, draw the consumer’s budget constraint and indicate the consumer’s optimal bundle on the budget constraint. Make sure your graph is accurate and clearly labeled.

a) U(X,Y) = X1/4Y3/4. The consumer has $24 to spend and the prices of the goods are PX = $2 and PY = $3. **Note that the MUX = (1/4)X-3/4Y3/4 and the MUY = (3/4)X1/4Y-1/4.**

b) U(X,Y) = MIN(5X,Y). The consumer has $24 to spend and the prices of the goods are PX = $3 and PY = $1.

c) U(X,Y) = 2X + 3Y. The consumer has $20 to spend and the prices of the goods are PX = $2 and PY = $4.

3. (14 total points) Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she must have exactly three spoonfuls of coconut oil for each cup of coffee. Let C be the number of cups of coffee, and O be the number of spoonfuls of coconut oil. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on coffee and coconut oil. Also, the price of coconut oil is $.20 per spoonful.

Graph Lynn’s Price consumption curve for prices, PC = $.60, PC = $.90, and PC = $1.80. Please put the number of cups of coffee (C) on the horizontal axis, and the number of spoonfuls of coconut oil (O) on the vertical axis. Be sure to label your graph carefully and accurately.

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