MS&E
Problem Set 1

# Problem Set 1 - Stanford University Department of...

• Homework Help
• 2

This preview shows pages 1–2. Sign up to view the full content.

Stanford University Department of Management Science and Engineering MS&E 241 Economic Analysis Winter 2016 Problem Set 1 Due Date: 01/13/16 In Class Problem 1 Explain whether the following problems are convex and solve them. Please demonstrate how you reached your results. Hint: Try to first graph the feasible set and the level sets of the objective functions. This should help you visualize each problem ’s solution . a. 𝑚?𝑥?𝑚?𝑧𝑒 𝑥 1 1/2 +𝑥 2 1/2 ????𝑒?? ?𝑜 𝑥 1 +2𝑥 2 ≤ 6 𝑥 1 , 𝑥 2 ≥ 0 b. 𝑚?𝑥?𝑚?𝑧𝑒 𝑥 1 +𝑥 2 ????𝑒?? ?𝑜 𝑥 1 +2𝑥 2 ≤ 6 𝑥 1 , 𝑥 2 ≥ 0 c. 𝑚?𝑥?𝑚?𝑧𝑒 𝑥 1 2 +𝑥 2 2 ????𝑒?? ?𝑜 𝑥 1 +2𝑥 2 ≤ 6 𝑥 1 , 𝑥 2 ≥ 0 Problem 2 Consider a competitive market for which the quantities demanded and supplied at various prices are given as follows: Price (Dollars) Demand (Millions) Supply (Millions) 60 22 14 80 20 16 100 18 18 120 16 20 a. Calculate the price elasticity of demand when the price is \$80.

This preview has intentionally blurred sections. Sign up to view the full version.

b. Calculate the price elasticity of supply when the price is \$120.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: d. Suppose the government sets a price ceiling of \$80. What will be the resulting shortage (in millions)? Problem 3 Suppose that a country produces and consumes goods A and B. The domestic supply and demand of good A is given by: ? ° = 15.90 + 0.72? ± + 0.05? ² ? ³ = 0.02 − 1.8? ± + 0.69? ² Where ? ± , ? ² are the prices for good A and good B respectively. a. Suppose the price of B is \$50. What is the free-market price for good A? (round to pennies: \$X.xx) b. Graphically illustrate how the equilibrium prices and quantities of good A change with different prices for good B. Hint: in one graph ? ± , ? ± draw the demand and supply functions for two different values ? ² c. Based on the information given in the problem, is good A a complement or substitute for good B in consumption? d. Now suppose that unlimited quantities of good A can be imported at \$4.5. What will the level of imports be? Illustrate graphically....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern