(a) Marginal cost. Markets match marginal benefit to marginal cost — the efficiency condition that runs the whole course.

(b) “I should specialize in doing the task that I do best.” This is the keyed answer, and it needs a gloss, because read carelessly it sounds like absolute advantage.

“The task I do best” means best among my own activities — the one I am relatively strongest at, which is exactly the one with my lowest opportunity cost. It does not mean the task I do better than other people. Option (ii), specializing in everything you do better than others, is the absolute-advantage trap and is wrong.

Do not overthink this one. If the same wording appears again, circle “the task that I do best.” If a question instead asks you to explain comparative advantage in words, answer with opportunity cost, as in Unit 2.

(c) “All of the above.” The keyed answer is (iv), not the narrow physical-capital definition.

The course uses capital in all three senses: physical productive assets (machines, structures — the sense used in the production function and in MRP_K), financial capital (the funds raised by issuing stocks and bonds to buy that physical capital), and accumulated savings that cross borders (the capital inflows of Unit 24). Class 14 opens on exactly this ambiguity, noting that capital means physical productive assets and can also mean wealth.

Rule of thumb: on a multiple choice that lists several real senses of a term used in this course, “all of the above” is usually right. In a written answer, still lead with physical productive assets, then name the others.

(d) The yen appreciated and the dollar depreciated. A dollar buys fewer yen.

(e) All of the above — rule of law, property rights, and protection from government.

(f) Raises price and reduces quantity.

(a) The real price increased. CPI rose by 2.5×, the Big Mac by 3.5×, so it outpaced the basket. With income growing at the rate of inflation you can buy fewer Big Macs today.

(b) No — it requires workers and a facility. So mechanization cannot reduce costs much, unlike manufactured goods where factory automation has driven marginal costs steadily down. That is precisely why its real price rose while the real price of, say, a desktop computer collapsed.

(c) The price falls. The payments F_t are fixed, so raising i increases every denominator in PV = F₁/(1+i) + F₂/(1+i)² + F₃/(1+i)³, shrinking the total.

(d) With i = 0, every (1+i)^t = 1, so p = PV = F₁ + F₂ + F₃.

(e) The price falls. A unit of capital is worth the present value of its future MRP_K = MR × MP_K. If less labor is expected to be available, capital's future marginal product falls, shrinking the numerators and pulling the price down today.

(a) PAE = 10 + (1/3)Y + 6 + 5 − 1 = 20 + (1/3)Y. At Y = 0, PAE = 20.

(b) Set PAE = Y: 20 + (1/3)Y = Y ⟹ 20 = (2/3)Y ⟹ Y = 30 trillion.

(c) Axes Y and PAE. 45° line labelled Y = PAE. PAE line with vertical intercept 20 and slope 1/3, crossing the 45° line at Y = 30. Label the intercept, the crossing, and both axes.

(d) PAE′ = 8 + (1/3)Y + 5 + 5 + 0 = 18 + (1/3)Y. At Y = 0, PAE′ = 18.

(e) 18 = (2/3)Y ⟹ Y = 27 trillion.

(f) Both lines parallel with slope 1/3, intercepts at 20 and 18, crossing the 45° line at 30 and 27. Label all four values.

(g) PAE fell by $2 trillion. Autonomous consumption fell 2, investment fell 1, net exports rose 1. Net: −2. It shows as a vertical drop in the PAE line.

(h) GDP fell by $3 trillion, from 30 to 27. Because the PAE line slopes upward, its intersection with the 45° line falls and shifts left by more than the vertical drop.

(i) Different — GDP's change is larger. The reason is the nonzero marginal propensity to consume, here 1/3, which creates a multiplier of 1/(1 − mpc) = 1.5, and 2 × 1.5 = 3.

(j) Raise G by $2 trillion. The shock reduced PAE by 2, and G enters autonomous spending one-for-one. As long as the mpc is unchanged across the two shocks, an equal and opposite change in autonomous spending offsets it exactly. Match the shift in PAE, not the change in GDP.

(a) The world price P_w must be above the autarky price — otherwise producers sell at home. Draw it as a horizontal line above the domestic crossing. At P_w, Q_S^US is large and Q_D^US is small, and the horizontal gap is exports. Place P_w so that gap is about half of Q_S.

(b) With the crop planted and no storage, supply is perfectly inelastic — vertical at Q_S^US. With export demand gone, the whole crop must clear domestically, so the price falls all the way to the domestic demand curve read at Q_S^US — a really big reduction. Mark that price P_tw on the graph.

(c) Labor demand is MRP_L = MR × MP_L. The trade war collapsed the price of soybeans, which is MR, so the entire labor demand curve shifts inward/downward. Wages and employment both fall. Draw D₁ and D₂ with an unchanged upward-sloping supply, and mark both (W, L) pairs.

(d) They suggest the US lost this round and China won. Even after reaching an agreement, the US government still felt it had to compensate the losers — a one-time $12 billion payment to soybean farmers. And China reported a record trade surplus, suggesting its goods found new buyers.

The asymmetry that makes this work: Chinese exports to the US are durable manufactured goods, while US exports to China are perishable agricultural ones. Industrial goods do not degrade while you wait out a dispute; soybeans do. Honest caveat: we know less about the Chinese side, where there may have been losers too.