Economics-The US President has announced plans to impose a “Build in USA” policy that would impose a tariff of 𝜏 = 50% on imports to the US of products made outside the US. At present (Period 0), it is not known whether

1. The US President has announced plans to impose a “Build in USA” policy that would impose a tariff of 𝜏 = 50% on imports to the US of products made outside the US. At present (Period 0), it is not known whether he will make good on those threats., but it is believed that the tariff will be imposed with probability 𝜃 = 60%. A British firm is the world’s only supplier of diet Irn-Bru, which is a (strangely) popular product among the President’s US supporters. Currently, the firm manufactures the beverage at its plant in Turnberry, Scotland. The product costs 𝐶 = £2 per unit to make; shipment to the US costs an additional 𝜎 = £8 per unit. The inverse demand curves for the UK and US markets are:

𝑃𝑈𝐾 = 𝐴𝑈𝐾 − 𝐵𝑈𝐾 ∗ 𝑄𝑈𝐾 = 50 − 2 ∗ 𝑄𝑈𝐾

𝑃𝑈𝑆 = 𝐴𝑈𝑆 − 𝐵𝑈𝑆 ∗ 𝑄𝑈𝑆 = 200 − 𝑄𝑈𝑆

The fixed cost of building a plant in the US is 𝐹𝑈𝑆 = £10000; the average variable cost

 

of production using this plant is 𝐶𝑈𝑆

 (𝑄) = 𝛼 − 𝛽𝑄 = 10 − 𝑄. The riskless rate of return

2

 

is 𝑟𝑓 = 5%. The company’s stock is currently trading at 𝑃⁰ = £100; if the tariff is imposed it will fall to  𝑃^𝜏 = £68.55; otherwise it will rise to  𝑃^𝑁𝑇 = £147.17.

 

[For avoidance of doubt, the firm faces no tariff in Period 0, but may face a tariff in Periods 1,2,… If it does face a tariff, it will compute a new price and quantity for its exports to the US market. There are no recurrent fixed costs (beyond the one-off cost of constructing a US plant). For each situation, find the quantity produced and corresponding price using the inverse demand curve 𝑃(𝑄) and total cost curve 𝑇𝐶(𝑄) by maximising 𝑃(𝑄)𝑄 − 𝑇𝐶(𝑄) w.r.t. 𝑄. The situations are: US plant supplying US market; UK plant supplying US market without tariff; UK plant supplying US market with tariff; and UK plant supplying UK market. The US plant, if built, will only be used to supply the US market and starts producing from the period in which it is built.]

2. Find the profit-maximising prices and quantities for the two markets in period 0 and the corresponding Period 0 profits (8 marks)
3. using the UK plant and
4. building a plant in the US to supply the US market.
5. If the President implemented the “build in USA” policy in period 0, would the firm build the US plant?
6. Suppose that i) with probability 𝜃, the tariffs will be imposed starting in Period 1 and lasting forever ( with probability 1 − 𝑝 the tariffs will never be imposed),

ii) the US plant has to be built today (or never) and iii) the UK and US (if built) plants would operate forever. Would the plant be built today? What is the WACC? (12 marks)

7. Suppose the firm could buy an option to delay the decision until Period 1 (when the tariff choice will be known), but doing so would raise the cost of constructing the US plant to 𝐺𝑈𝑆. Find the value of the option as a function of 𝐺𝑈𝑆. (8 marks)
8. How would your answers to b and c change if the tariffs were randomly imposed

in each future period, but the US plant could only be built in Period 0 (as in part b) or either in Period 0 or Period 1 (as in part c)? For the purposes of this question, you should assume that:

9. There will be no tariff in Period 0;
10. The tariff will be applied in Period 1 with probability 𝜃;
11. If the tariff is applied in Period 1, it will be applied in all subsequent periods with probability 𝜃^𝑈 > 𝜃; and
12. If the tariff is not applied in Period 1, it will be applied in all subsequent periods with probability 𝜃^𝐷 < 𝜃.

 

How does this increased instability affect the value of the option to delay? (12 marks)

13. A Canadian firm is hiring an executive to run its US export business. It also has to approve the advertising budget requested by the new executive. The profitability of the advertising will depend on the extent to which US customers are willing to buy Canadian products; this will be known by the executive after they take up the post, but is not known to the firm. You may assume that the profitability of the advertising is given by a random variable 𝜋, uniformly distributed on the interval [𝑃₀, 𝑃₀ + 𝑋]. The firm believes the profitability of setting a budget of 𝐵 is 𝑈_𝐹(𝐵|𝜋) = 1 + 𝜋𝐵 − 𝐵². However, the executive also gets kickbacks from US media outlets for placing ads; if perfectly-informed about advertising effectiveness, the executive would value 𝐵 at 𝑈_𝑒(𝐵|𝜋) = 1 + (𝜋 + 𝛽)𝐵 − 𝐵² where 𝛽 is a non-negative constant. After the executive has had time to study the market, the firm asks the executive to report on advertising effectiveness (𝑝) and purchases the quantity that maximises the firm’s expected utility given this report. Other than 𝑈_𝑒(𝐵|𝜋), the executive gets no remuneration.
14. How would you set up this problem? Can the executive be sure of purchasing the optimal quantity (according to their preferences)? If so, how? If not, why not? How does your answer depend on the size of 𝛽? (6 marks)
15. Suppose that the minimum effectiveness is 𝜋₀ = 25%, 𝑋 = 50% and that

𝛽 = 5%. Find the ‘babbing equilibrium’ for this situation – what budget will the firm approve and what expected utilities will the firm and the executive get? (10 marks)

16. Now construct a two-part equilibrium – depending on the report from the executive, the approve either a low budget 𝐵^𝐿𝑜𝑊 or a high budget 𝐵^{𝐻𝑖𝑔ℎ}. At what reported level of effectiveness will the firm switch its order size, and what are the values of 𝐵^𝐿𝑜𝑊 and 𝐵^{𝐻𝑖𝑔ℎ}? (10 marks)
17. Now consider a more detailed budgeting process; the executive reports

𝑝, which may or may not be the true value 𝜋. The firm has announced a ‘menu’ {𝑝_𝑜, 𝑝₁, … , 𝑝_𝐾}, where 𝑝₀ = 𝑃_𝑜 and 𝑝_𝐾 = 𝑃_𝑜 + 𝑋 and corresponding budget levels {𝐵_𝑜, 𝐵₁, … , 𝐵_𝐾} – if the report 𝑝 ∈ [𝑝_𝑖, 𝑝_𝑖+1) then the approved budget level is 𝐵_𝑖, which maximises the firm’s expected utility conditional on the true value being uniformly distributed over [𝑝_𝑖, 𝑝_𝑖+1). Derive the conditions under which the executive will report honestly and show that there is a maximum value of 𝐾 which is inversely related to the size of 𝛽. You need not derive an explicit equation relating the maximum 𝐾 to 𝛽 but can show this by example. Does a higher 𝐾 lead to higher expected utility for the firm? For the executive? (12 marks)

18. What would happen if, instead of trusting the executive, the firm announced that they would accept any report leading to a budget less than or equal to a ceiling 𝐵̅; otherwise, they’d only authorise a budget of

𝐵̅. Find the executive’s optimal reporting strategy (𝑝 as a function of the true state 𝜋). Is there an optimal value for 𝐵̅? If so, what is it? How do the expected utilities compare to those found in parts b and c? (12 marks)

19. Finally, how would your answer to e change if the firm announced that it would accept any report leading to a budget less than or equal to 𝐵̅, but

 

would audit any report that would lead to a larger budget. If the auditor found that the true value 𝜋 ≠ 𝑝, the firm would fine the executive 𝛽𝐵, where 𝐵 is the budget corresponding to the report 𝑝 (in other words, the budget that maximises 𝑈_𝐹(𝐵|𝜋))? (10 marks)