201 Econ Problem set 1 PDF

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Problem set 1...

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University of San Diego School of Business Economics 201

Problem Set 1 (due Weds, 2/12/20 at the beginning of class) The key to getting full points on problem set and exam questions is the quality of your explanation. Every question has a tool or concept associated with it, and you need to use that tool in your answer. But just writing a formula or drawing a graph isn’t enough: you need to explain what that graph or formula tells you, and how it gives you an answer to the question. Full points are awarded for the combination of correct use of the tool and correct explanation of the logic. I can only judge you on what you actually write down – “that’s what I meant” doesn’t cut it. Last but not least, be sure to show your work on any calculations.

1) Suppose the market for gigantic mylar birthday balloons could be described by QD = 40 - 6P + 0.2I QS = 2P - 2PM

(Q = Qty of Balloons in 1000s; I = Ave. Income in $1000s) (P = Price of Balloons in $; PM=Price of 1 kg of mylar)

a) Briefly explain the economics of the signs of each coefficient. For example, does an increase in the price of Mylar increase or decrease the quantity supplied? Why does that make sense economically? b) Assume that average income is $50,000 and the current price of mylar is $7/kg. Calculate the equilibrium price and quantity in this market, and draw a graph of the equilibrium (be sure to label the intercepts and the equilibrium with the correct numbers). c) Now assume that the price of mylar falls from $7/kg to $3/kg. Calculate the new equilibrium and show it in your graph. Also, briefly explain what “market forces” will come into play to move this market from the old equilibrium to the new equilibrium. After the change in the price of mylar, start by thinking about the quantities supplied and demanded at the original price. 2) Elasticity Questions a) At the original equilibrium in question 1b (ie PM=$7), calculate the price elasticity of demand, and the price elasticity of supply. At this point, is the demand curve price elastic, or price inelastic? Explain what these terms mean. Remember to exploit our simplification of the elasticity formula for linear S/D curves. b) For each of the following relationships, describe in 1-2 sentences whether you would expect it to be elastic or inelastic, positive or negative, and why. Some of these topics we discussed in lecture; others are from the Chapter 2 readings.

-- The price elasticity of demand for gasoline in the short run -- The price elasticity of demand for washing machines in the long run -- The income elasticity of demand for Top Ramen (is EI positive or negative?) -- The E-book cross price elasticity of demand for E-Book readers (How does the price of E-books affect demand for E-book readers? Is EX > 0?) c) Briefly explain how the price elasticity of demand will change as we move down a linear demand curve. Linear = constant slope, and “move down” means lower prices and higher quantity demanded. 3) Consumer Preferences and Utility Maximization Homer’s utility function for donuts and… beverages is U= ½ ln(D) + ln(B), where D is number of boxes of donuts and B is 40 oz. cans of… beverage. Homer has $300 to spend this semester on these two items. Donut boxes cost $10, and each can costs $5. Homer is currently consuming 6 donut boxes and 48 beverages this semester. a) Graph Homer’s budget constraint, and show that this is a feasible bundle for Homer (on or inside his budget constraint). Put beverages on the x-axis. b) Use the utility function to calculate Homer’s Marginal Rate of Substitution at the current bundle. Use the MRS and the slope of the budget constraint to show that Homer’s current consumption is not optimal. Draw an indifference curve through the current bundle that reflects the MRS you calculated and the suboptimality of the bundle. You don’t need a precise graph of the indifference curve as long as your graph captures the slope of the IC relative to the slope of the budget line. Lastly, based on the MRS and the slope of the budget constraint, propose a shift in consumption that will increase Homer’s utility. c) Now consider our “bang for the buck” measure MU/P. Use this measure to prove Homer’s current consumption is suboptimal, and describe how the consumption shift from 3b will change Homer’s “bang for the buck.” d) Solve for Homer’s optimal level of consumption. Draw a new indifference curve in your graph that shows that this new bundle is optimal. As in lecture, proceed in two steps. First, use either criteria for the optimal bundle to derive an optimal relationship between D and B, then plug that relationship into the budget constraint to solve for specific values....