Solutions To Exchange Rate Problems

Solutions To Exchange Rate Problems - University of North...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: University of North Carolina Chapel Hill KenanFlagler Business School BA281 Microeconomics Answers for Practice Problem Set 4 Prof. Robert A. Connolly September 27, 2005 Problem 1: Exchange Rates Affect Costs (or Do They?) Suggested Answers: a) In the shortrun, what happens to the ATC and MC of the subsidiary if the new process is implemented at a onetime cost of $600,000, an increase in fixed costs of about ten per cent? MC falls here, but ATC increases. b) In the shortrun, what happens to the cost of the other inputs that the subsidiary buys locally? There is no change in costs. c) In the long run, the firm's planning group expects the Euro () to depreciate from 1/$1 to 1.15/$1. Provide a short description (use a bullet point format) of the impact on local currency costs, prices, and profits of the rate depreciation. Assume the change in technology occurred at the same time. costs don't change. value of $ costs increases. Total costs increase. prices don't change profits decrease The use of $valued inputs should fall In the end, the net effect depends on the change in DM costs vs. the changed usage of $ valued inputs. d) Using a bullet point format, describe the set of longrun adjustments that will occur given the change in technology and the exchange rate movement. (Treat this like the summary powerpoint slide that you might prepare for senior managers. Long, rambling answers are inappropriate for them and as an answer here.) If the change in quantity of $valued inputs dominates, the firm should expand. Expect that other firms will try to mimic. If the change in costs dominates, the firm should find optimal output is decreasing since cutting back production will reduce marginal costs. 2 Problem 2: Exchange Rates Affect Industries (Don't They?) Suggested Answers: The Chilean peso appreciation increases the U.S. dollar costs of the Chilean manufacturer. This shifts the Chilean firm's cost curves up (again, measured in U.S. dollars). The old marginal (average total) cost is marked as MC (ATC) and the new marginal (average total) cost is marked as MC' (ATC'). Note that the market price does not increase in this case. Why? Remember, this firm produces an undifferentiated product, and it is small by comparison with the whole market. That's what it means to be in a competitive market. If the market was initially in equilibrium with the market price equal to the marginal cost of selling output (in U.S. dollars), the Chilean firm now finds the market price to be below the unit cost of production. Accordingly, the Chilean firm will sustain losses until the exchange rate appreciation is reversed, the market price rises (for some other reason), its costs measured in dollars can be reduced, or this Chilean firm abandons the market altogether. Market Chilean Firm U.S. Firm Price (in US$) ATC' MC' S MC New ATC P ATC Old Old, New MC Market Quantity (in equilibrium) D Q When would cost control matter for the U.S. firm? Suppose this case revolved around Chilean Peso depreciation against the U.S. dollar. Now, the Chilean firms find their costs measured in U. S. dollars are lower than before the depreciation. If they are small relative to the market, there is no appreciable impact on U.S. firms, because the market price (measured in U.S. dollars) does not change. If these producers are a large segment of the market, the market supply curve will shift out the right, the market price will decrease, the Chilean firms will be able to operate profitably (since their costs in U.S. dollars are lower), and the U.S. firms will be making losses because their costs haven't decreased. Note the three elements that create difficulties for U.S. producers in their home market: U.S. dollar appreciates (foreign currency depreciates), U.S. firm costs are unchanged, and foreign firms constitute a substantial portion of total market supply. 3 Problem 3: Exchange Rates Affect Optimal Prices (Don't They?) Suggested Answers: a) The inverse demand function is found by substituting a /$ exchange rate into the demand function Q fc = 225 - .25Pfc - .35(/$) , converting the last term to a number, combining this number with the intercept, and solving for the price. At 85/$1, this produces an inverse demand function of Pfc = 781 - 4Q fc and at 130/$1, this yields an inverse demand function of Pfc = 718 - 4Q fc . In turn, the marginal revenue functions are MR fc = 781 - 8Q fc at 85/$1 and MR fc = 718 - 8Q fc at 130/$1. b) At 85/$1, setting MR fc = MC means 781 - 8Q fc = 100 so that Q fc = 85.125. At 130/$1, the same operation yields Q fc = 77.25. c) Since MC = 100 and it is constant regardless of how many seats are being filled in the U.S. or Tokyo, the problem alluded to in part b) does not exist in this setting. If MC depended on the number of seats being filled, then we would have to solve for the optimal price and quantity in each market simultaneously. Why? Solving separately assumes that the solution in each market segment leaves the costs for the other segments unchanged. Here, the (very special) assumption of constant marginal cost makes that work, but in settings where marginal cost is increasing in the amount of output made and sold, this assumption fails. What about exchange rates? The exchange rate does not affect the way the problem is solved, but as we saw in part b), the exact solution value does depend on the exchange rate. d) The solution method does not depend on the value of the exchange rate. If the marginal cost function depends on the number of seats being filled in each part of the airplane, the solution principle is clear: solve so that marginal revenue and marginal cost are equated across the different market segments simultaneously. This is the standard price discrimination problem. Problem 4: Exchange Rates Affect Profits (or Do They?) Suggested Answers: a) Marginal cost in Canadian dollars found by converting MC in U.S. dollars to Canadian dollar terms: dC/dQ(US$) = .5 + .3Q. To get MC in Canadian dollars, multiply U.S. dollar MC by the exchange rate: MC(C$) = (.5 +.3Q) 1.3517 = .676 + .406Q. Find TC in Canadian dollars in the same way. TC(US$) = .5Q + .15Q2 4 TC(C$) = (.5Q) + .15Q2) 1.3517 = .676Q + .203Q2 Find ATC in Canadian dollars by directly by dividing by Q: ATC(C$) = .676 + .203Q. b) Now, find the Canadian NAP demand curve measured in U.S. dollars: QC = 40 4P(C$) so P(C$) = 10 .25QC. [I use this: P(C$) (US$/C$) = P(US$)] Now, P(US$) = (10 .25QC) .7398 so QC = 40 5.407P(US$). c) MC(C$) = .676 + .406QC QC = 40 4P(C$) P(C$) = 10 .25QC MR(C$) = 10 .5QC. Set MR = MC to get QC so 10 .5QC = .676 + .406QC (P(US$) = 5.494). QC = 10.297 and P(C$) = 7.426 d) Canadian dollar profits are given by (C$) = P(C$) QC (.676QC + .203Q2) = 7.426 10.297 (.676 10.297 + .203 (10.297)2) = 48.006 (US$) = 48.006/1.3517 = 35.515. (in U.S. dollars) e) The answer is precisely the same. The optimal quantity is still 10.297, but the Canadian NAP price measured in U.S. dollars is $5.494. This is the same as C$7.4257/1.3517. We have this outcome because optimal behavior (how much to produce and what price to charge) is independent of the measurement units. f) Since the exchange rate is now C$1.5545/US$, the MC(C$) =.77725 + .46635QC. The MR schedule which is measured in C$, is unchanged. The new optimal quantity and price is given by solving .77725 + .46635QC = 10 .5QC. QC = 9.544 TR(C$) = 72.668 P(C$) = 7.614 TC(C$) = 28.657 Solving this yields In U.S. dollars, (C$) = 44.011. = 4.898 TR(US$) = 46.747 P(US$) (US$) = 28.312. Canadian dollar depreciation yields smaller sales and profits in the Canadian market. This is because the cost curves shift up against stationary demand and marginal schedules producing a lower optimal quantity, a higher C$ price, and lower C$ economic profits. ...
View Full Document

This note was uploaded on 03/24/2008 for the course BA 281 taught by Professor Connolly during the Spring '08 term at UNC.

Ask a homework question - tutors are online