Problem Set 1 - d Suppose the government sets a price...

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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.
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b. Calculate the price elasticity of supply when the price is $120.
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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....
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