Practice Worksheet

Explanation Alpha: in 1 hour, Alpha produces either 4 tons steel or 8 bushels wheat. OC(1 ton steel) = 8 ÷ 4 = 2 bushels wheat.

Beta: in 1 hour, Beta produces either 3 tons steel or 2 bushels wheat. OC(1 ton steel) = 2 ÷ 3 ≈ 0.67 bushels wheat.

Explanation Wheat: Alpha (8/hr) > Beta (2/hr) → Alpha has absolute advantage in wheat.
Steel: Alpha (4/hr) > Beta (3/hr) → Alpha has absolute advantage in steel — but just barely.

The correct answer is (b). Alpha dominates Beta in absolute terms for both wheat and steel. This is the Mankiw setup — one producer is faster at everything. The interesting question is what happens when we pivot to comparative advantage: even though Alpha wins both absolute comparisons, Beta will still have comparative advantage in one good (the one where Alpha's lead is smaller). That's the subject of 1c.

Explanation OC of 1 bushel wheat: Alpha gives up 4/8 = 0.5 tons steel. Beta gives up 3/2 = 1.5 tons steel.
Alpha's OC is lower → Alpha has comparative advantage in wheat.

OC of 1 ton steel: Alpha gives up 2 bushels wheat. Beta gives up 0.67 bushels wheat.
Beta's OC is lower → Beta has comparative advantage in steel.

Note that comparative advantages always split between the two producers — never both in the same country. Even though Alpha has absolute advantage in both, Beta still has comparative advantage in one.

Explanation Beta's opportunity cost of 1 ton steel = 0.67 bushels (Beta won't sell below this — it could make the wheat itself cheaper).
Alpha's opportunity cost of 1 ton steel = 2.00 bushels (Alpha won't pay more — it could make the steel itself cheaper).

Acceptable range: 0.67 < price < 2.00 bushels of wheat per ton of steel.

The midpoint is ~1.33. Anything in this range makes both countries strictly better off than going it alone.

Explanation Before trade:
  Alpha: 50×8 = 400 wheat + 50×4 = 200 steel.
  Beta: 50×2 = 100 wheat + 50×3 = 150 steel.

After trade:
  Alpha produces all wheat: 100×8 = 800 bushels wheat, 0 steel.
  Beta produces all steel: 100×3 = 300 tons steel, 0 wheat.
  Exchange: Beta gives 60 steel to Alpha; Alpha gives 60 wheat to Beta.
  Alpha consumes: 800 − 60 = 740 wheat, 60 steel.
  Beta consumes: 60 wheat, 300 − 60 = 240 steel.

Gains:
  Alpha: Δwheat = 740 − 400 = +340; Δsteel = 60 − 200 = −140.
  Beta: Δwheat = 60 − 100 = −40; Δsteel = 240 − 150 = +90.

Each country gives up some of one good to consume much more of the other.

Alpha gains 340 extra wheat after trade and loses 140 steel; at the 1:1 trade price, the 340 extra wheat is more than enough to replace the 140 lost steel, so Alpha is strictly better off.
Beta gains 90 extra steel and loses 40 wheat; at 1:1, the 90 extra steel is more than enough to cover the 40-bushel wheat loss, so Beta is strictly better off too. Both gain.

Explanation Tutoring: Jake 20 min < Alex 30 min → Jake has absolute advantage in tutoring.
Mowing: Alex 45 min < Jake 60 min → Alex has absolute advantage in mowing.

Mixed absolute advantage — each person is faster at one thing. Even with the "who's faster" question split between them, comparative advantage (opportunity cost) still determines who should specialize where.

Explanation Jake: 1 lawn takes 60 minutes. Those 60 minutes could produce 60 / 20 = 3 tutoring sessions.
Alex: 1 lawn takes 45 minutes. Those 45 minutes could produce 45 / 30 = 1.5 tutoring sessions.

Even though Jake is faster at tutoring, he gives up MORE tutoring time per lawn than Alex does — Jake's 60 min/lawn = 3 sessions forgone, vs Alex's 45 min/lawn = 1.5 sessions forgone. So each lawn costs Jake more in lost tutoring than it costs Alex. That's the key asymmetry: Alex has comparative advantage in mowing.

Explanation Alex has the comparative advantage in mowing. Each lawn costs Jake 3 lost tutoring sessions; each lawn costs Alex only 1.5 lost tutoring sessions. Alex gives up less to mow, so he's the "cheap mower."

Conversely, Jake has the comparative advantage in tutoring: his OC of a tutoring session is 1/3 of a lawn, vs. Alex's 2/3 of a lawn.

Note the twist: Alex is actually the faster mower in absolute terms, AND he also has comparative advantage there. Comparative advantage lives in opportunity-cost space — whoever gives up the least is the right person for the job, regardless of absolute speed.

Explanation Alex's OC of 1 lawn = 1.5 sessions. He won't mow for less (he could just tutor that time and do better himself).
Jake's OC of 1 lawn = 3 sessions. He won't pay more (he'd rather mow it himself than give up 3+ sessions).

Acceptable range: 1.5 < price < 3.0 sessions per lawn.

Anywhere in this range, both are strictly better off. A split of 2.25 sessions (halfway) would share the total gain-from-trade evenly. Closer to 1.5 = Jake captures more of the gain; closer to 3 = Alex captures more.

Explanation Jake tutors all 180 min → produces 180 / 20 = 9 sessions.
Alex mows Jake's 1 lawn, so Jake pays Alex 2 sessions (price = 2 sessions/lawn).
Jake's tutoring consumption = 9 − 2 = 7 sessions.

Compare to no-trade baseline: Without trade, Jake mowed his own lawn (60 min) and tutored the remaining 120 min → 1 lawn + (120/20) = 6 sessions. Under the trade, Jake still gets his 1 lawn (Alex mowed it) AND has 7 sessions — a gain of +1 session. Jake is strictly better off because the trade price (2 sessions) sits inside the viable range 1.5 < price < 3 you found in 2d.

(Quick sanity check: at a price closer to 1.5 Jake captures almost all the gain; at prices near 3 Alex does. 2 sessions/lawn is toward Jake's end of the range — he gets the bigger slice here.)

Alex's side: Alex spends 45 min mowing his own lawn + 45 min mowing Jake's lawn = 90 min mowing, leaving 90 min to tutor → 90/30 = 3 sessions produced. Plus the 2 sessions Jake pays him = 5 sessions consumed. Compare to Alex's no-trade baseline (45 min mowing his own + 135 min tutoring = 135/30 = 4.5 sessions, plus 1 lawn): Alex consumes 5 sessions vs 4.5 — a gain of +0.5 sessions. Both strictly better off.

Explanation(b) is correct. Comparative advantage belongs to the producer with the lower opportunity cost. That producer gives up less of the other good to make one unit of this one.

(a) describes absolute advantage. (c) is impossible — no single producer can have comparative advantage in every good (mathematical necessity: if OC is low in one good, it's high in the other).

Explanation(b) 1/2 of a cake. Making 10 bread takes 1 hour; that same hour could make 5 cakes. So 10 bread ↔ 5 cakes, meaning 1 bread = 5/10 = 1/2 cake.

Watch out for (a): 2 cakes is the opposite direction — the OC of 1 cake in terms of bread. Direction matters.

Explanation(b) 3 bottles. For both to gain, 2 < price < 5. Only 3 falls in this range.

At 1 bottle (a), the car-seller (X) rejects — they could make the car at a cost of 2 bottles themselves. At 6 bottles (c), the car-buyer (Y) rejects — they could make the car at a cost of 5 themselves.

Explanation(c) is correct. Absolute advantage in both ≠ comparative advantage in both. Comparative advantage always splits: if OC(X) is low, OC(Y) must be high (they are inverses). So the "slower" producer still has the lower OC in one good — and both parties gain when each specializes.

This is the central insight of Chapter 3: trade benefits both even when one party is better at everything.

Explanation(b). A straight-line PPF has constant slope, so opportunity cost is the same regardless of how much you already produce. This is the Mankiw farmer/rancher setup — each unit always costs the same.

A bowed-out (concave) PPF shows increasing opportunity cost, because resources are specialized — some workers are better at one good than the other, and reallocating them becomes more painful at the extremes.

Explanation(b). Kaitlyn has the comparative advantage: her OC of mowing ($50) is far lower than LeBron's OC ($30,000). The mutually beneficial price range is $50 < price < $30,000. Any price in that range makes both better off.

LeBron has the absolute advantage in mowing (2 hours < 4 hours), but that doesn't matter — specialization is driven by comparative, not absolute, advantage.

Explanation(b). The necessary and sufficient condition for gains from trade is different opportunity costs. If OCs are identical across producers, neither has a comparative advantage in anything — and there's no gain to be had. But as long as OCs differ (in at least one good), each producer has comparative advantage in something, and specialization + trade expands the economic pie.

Explanation(b). The US has absolute advantage in both goods (5 > 4 cars; 10 > 2 wheat). But for comparative advantage: OC of 1 car = 2 wheat (US) vs. 0.5 wheat (Japan). Japan's OC is LOWER → Japan has comparative advantage in cars. OC of 1 wheat = 0.5 cars (US) vs. 2 cars (Japan) → US has comparative advantage in wheat.

So the US exports wheat; Japan exports cars. Both gain. (This is famously opposite to the intuition from absolute advantage.)

ExplanationFalse. This is the classic Ch 3 trap. Even when one producer is faster at both goods, comparative advantage still tells her to specialize in the good where her OC is lowest, and trade for the other. The partner has comparative advantage in SOMETHING — it's a mathematical necessity. Both gain.

ExplanationTrue. Comparative advantage compares opportunity costs across producers. Only one can have the lower OC in a given good (barring ties). They always split — one has comparative advantage in good X, the other in good Y.

ExplanationTrue. Both parties compare the trade price to their own opportunity cost of producing that good. The seller accepts only if price > her OC; the buyer accepts only if price < his OC. So the deal happens iff seller's OC < price < buyer's OC.

ExplanationFalse. This is essentially the same trap as 4.1, at the country level. The more productive country still has comparative advantage in only some goods (the ones where its productivity lead is biggest). Specialize where comparative advantage is strongest; import the rest. Both trading partners gain.

ExplanationTrue. Opportunity costs in opposite directions are reciprocals. If 1 A = k units of B, then 1 B = 1/k units of A. This is why comparative advantage always splits: if one OC is high, its reciprocal (the OC of the other good) is low.

ExplanationFalse. A bowed-out PPF has increasing opportunity cost — the slope gets steeper as you move right. This reflects that resources are specialized: to produce each additional unit of one good, you must reallocate workers who are increasingly ill-suited to that task. Only a straight-line PPF (as in Mankiw Ch 3) has constant opportunity cost.

Model Answer Even if one person is faster at both goods (absolute advantage), opportunity costs still differ between them. The person who can produce every good faster still has to give up something to produce any one good — so each person's OC mix is unique. Whoever has the lower opportunity cost in a good has the comparative advantage there, and the other person automatically has comparative advantage in the other good (because opportunity costs are reciprocals). When each specializes where their comparative advantage lies and trades, total production of both goods rises — and that extra output can be split so that both consume more than they could producing alone.

Model Answer The acceptable trade price for a good must lie between the two producers' opportunity costs for that good. The seller (the one with the lower OC, i.e., comparative advantage) needs to receive at least their own OC — otherwise they'd rather produce the good themselves. The buyer (higher OC) won't pay more than their own OC — otherwise self-production is cheaper. If the proposed price sits outside this range, one side rejects the deal. Within the range, both strictly gain; where exactly the price lands inside the range determines how the gains are split.