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- University of Michigan - Ann Arbor
- Economics
- Economics 101
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- Problem Set #6

Sierra E.

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Economics 101 Section 400 Winter 2009 Assignment Six: Elasticities and Trade Policy For discussion in section on March 5 & 6 Question One Suppose that demand for insulin is perfectly inelastic. The supply function is given as: Qs(P) = a + b P where b > 0. If a tax of $t per 10mL of insulin is levied on producers, what will happen to the equilibrium price received by producers? What will happen to the equilibrium price paid by consumers? What will happen to the equilibrium quantity of insulin purchased in the market? How will your answers be affected by the value of the coefficient b? Suppose the supply of wheat is infinitely elastic. The demand function for wheat is of the form: Qd(P) = a + b P where a > 0 and b < 0. If a subsidy of $s/bushel is offered to wheat farmers, how will the price paid by consumers be affected? What effect will this have on the price received by producers? What effect will this have on the equilibrium volume of wheat produced? How will these answers depend on the value of the coefficient b? Suppose the demand function for widgets is Qd(P) = a + b P where a > 0 and b < 0. Also suppose that supply function is Qs(P) = ? + ? P where ? > 0. If a tax of $t/widget is levied on consumers, what will happen to the equilibrium quantity of widgets sold in the market? How will this depend on the values of the coefficients b and ?? How will the deadweight loss associated with Question Two Suppose the following describes demand for frosted shredded wheat squares in a various regions, over the course of a month: Qdi = 1250 ? 300 Pi + 25 Yi + 1000 Popi + 100 Pci ? 50 Pmi. In this function, Qdi is the quantity of frosted shredded wheat squares demanded in the month in region i (measured in hundreds of boxes), Pi is the price of frosted shredded wheat squares in region i (measured in $/box), Yi is median household income in region i (measured in thousands of dollars per annum), Popi is the population in region i (measured in millions), Pci is the price of cornflakes in region i (measured in $/box) and Pmi is the price of milk in region i (measured in $/gallon). Are cornflakes a complementary or substitute product for frosted shredded wheat squares? How do you know? Is this what you would have expected? Is milk a complementary or substitute product for frosted shredded wheat squares? How do you know? Is this what you would have expected? Suppose the following is known about Region 1: median income is $40,000 per annum, population is five hundred thousand, cornflakes cost $4/box and milk costs $3/gallon. Write quantity of frosted shredded wheat squares demanded only as a function of price. Also draw the demand curve. If the price of frosted shredded wheat squares is $5/box, how many boxes of frosted shredded wheat squares will be demanded this month in Region 1? What is the price elasticity of demand for frosted shredded wheat squares in Region 1 when this price prevails? If the price of frosted shredded wheat squares is $5/box, what is the income elasticity of demand for frosted shredded wheat squares in Region 1? If the price of frosted shredded wheat squares is $5/box, what is the elasticity of demand for frosted shredded wheat squares with respect to the price of cornflakes? What is the elasticity of demand for frosted shredded wheat squares with respect to the price of milk? If the price of frosted shredded wheat squares was $4.50/box in Region 1, do you think that demand will be more or less or equally price elastic when compared to the elasticity you calculated if the price was $5/box (in part (d))? What if the price was $5.50/box? Calculate the price elasticity of demand for each of these prices to verify your answers. Suppose that the following is known about Region 2: median income is $32,000 per annum, population is two hundred and fifty thousand, cornflakes cost $3/box and milk costs $4/gallon. Write quantity of frosted shredded wheat squares demanded only as a function of price. If the price of frosted shredded wheat squares is $4.50/box, what is the price elasticity of demand for frosted shredded wheat squares in Region 2? Suppose the price of frosted shredded wheat squares in both Region 1 and Region 2 is $4.50/box. Would a small increase in price in Region 1 increase or reduce revenue? Would a small increase in price in Region 2 increase or reduce revenue? Without changing total output of frosted shredded wheat squares, could producers increase profits by changing the prices they charge in the two markets? Explain. Question Three Imagine we know that the demand function for Ugg boots is given by: Qd = 200 ? P where P is the price for a pair of the boots and Qd is the quantity of boots demanded (measured in thousands of pairs). When P = 199, what is the price elasticity of demand for Ugg boots? When P = 1, what is the price elasticity of demand for Ugg boots? When P = 100, what is the price elasticity of demand for Ugg boots? Write out an expression for the elasticity that depends only on P. Can you sketch this function, with P on the horizontal axis and ? (the price elasticity of demand) on the vertical axis? The relationship you have just sketched out shows that the price elasticity of demand will vary along the demand curve. Sketch the demand curve, and identify which portion of the demand function is ?elastic?, which portion is ?inelastic? and where, precisely, the demand function has unit elasticity. Can you give an intuitive explanation for why the price elasticity of demand varies in this way along the demand function? Question Four If the price elasticity of demand for some product is -2, is demand for the product elastic or inelastic? What if the price elasticity of demand is -1/2? If the price elasticity of demand is -2, what will happen to the total revenue generated by producers in that market if prices fall slightly? If the price elasticity of demand is -1/2, what will happen to the total revenue generated by producers in that market if prices fall slightly? If the price elasticity of demand is -1, what will happen to the total revenue generated by producers in that market if prices fall slightly? Suppose we have a linear demand function: Qd = 120 ? 2P. Sketch the function, and note what you know about the price elasticity of demand at various points along the demand function. Given the demand function above, when P = 0, how many units of output will be demanded? What will revenue be? If P = 60, how many units of output will be demanded? What will total revenue be? Beneath your sketch of the demand function, draw another diagram with Q on the horizontal axis and total revenue on the vertical axis. Sketch in the two points on this diagram that you identified in part (f). From parts (b), (c) and (d), you know how revenue tends to change when you change prices/quantities slightly as long as you have information about the price elasticity of demand. From part (e), you also know something about the price elasticity of demand when various quantities are being sold in the market. Put these pieces of information together to show the relationship between quantity sold in the market and total revenue in your diagram. At what quantity of output will revenue be highest? What price will be charged if that quantity is to be sold? Revenue is simply the product of quantity sold and price. Rearrange the demand function to express price as a function of quantity. Use this to write an expression for total revenue that is a function only of quantity sold. Sketch a graph of that function. What shape does it have? Does it correspond to the graph you sketched in part (h)? Question Five Consider the domestic market for an imported good. Draw diagrams to show how the following policies will affect quantities produced and consumed, social surplus, consumer surplus, producer surplus and government revenues: a tariff of $x/unit imported is imposed a consumption tax of $x/unit consumed is imposed a production subsidy of $x/unit produced is offered Be careful to determine how and why these policies will impact the price that domestic consumers must pay for the good and the price that domestic producers will receive for the good in equilibrium. Compare the effects of the tariff to the effects of imposing the consumption tax and the production subsidy simultaneously. In an effort to encourage free trade, imagine that the members of the World Trade Organization agreed to dismantle all tariff protection of domestic industries in their respective countries. Do you think that such a commitment will necessarily result in freer trade? Are there alternative means by which these nations can support their domestic industries that have the same effects as tariffs? Are there alternative means of supporting local industries that have lower efficiency cost than tariffs? Why do you think that a government might choose to protect its industry using a tariff rather than simply offering a production subsidy?

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