econ.studio
Supply and Demand
Solutions

Supply and Demand

Solutions

Exercise 1
(a) Equilibrium requires quantity demanded to equal quantity supplied. Set Qd=QsQ_d = Q_s: $50−2P=10+2P50 - 2P = 10 + 2PSubtract Subtract 10frombothsidesandadd from both sides and add 2Ptobothsidestocollectallpricetermsontheright: to both sides to collect all price terms on the right: 40 = 4P.Dividingbothsidesby. Dividing both sides by 4givestheequilibriumprice gives the equilibrium price P^* = 10.Substitutebackintoeitherequationtofindquantity:. Substitute back into either equation to find quantity: Q^* = 50 - 2(10) = 30.Theequilibriumis. The equilibrium is (P^, Q^) = (10, 30).(b)Plug. (b) Plug P = 15intoeachequationseparately.Quantitydemanded: into each equation separately. Quantity demanded: Q_d = 50 - 2(15) = 20.Quantitysupplied:. Quantity supplied: Q_s = 10 + 2(15) = 40.Sellerswanttosell. Sellers want to sell 40unitsbutbuyersonlywant units but buyers only want 20,sosupplyexceedsdemand.Thatgap—, so supply exceeds demand. That gap — 40 - 20 = 20units—isasurplus(excesssupply)of units — is a surplus (excess supply) of 20.(c)With. (c) With 20unsoldunitssittingonshelves,sellersfacepressuretocutprices.Asthepricefallsbelow unsold units sitting on shelves, sellers face pressure to cut prices. As the price falls below 15,quantitydemandedrises(buyersrespondtolowerprices)andquantitysuppliedfalls(sellersscaleback).Thetwoquantitiesconvergeuntilthemarketclearsat, quantity demanded rises (buyers respond to lower prices) and quantity supplied falls (sellers scale back). The two quantities converge until the market clears at P^* = 10$.
Exercise 2
(a) The supply curve shifts. The frost is a production shock — it reduces the quantity producers can offer at every price. That is a leftward (inward) shift of the supply curve. The demand curve has not moved; nothing on the buyers' side changed. (b) With supply shifting left, the new supply curve intersects the unchanged demand curve at a higher price and a lower quantity. On the graph, the supply curve moves to the left, and the equilibrium point slides up along the demand curve: P∗P^* rises, Q∗Q^* falls. Draw the original equilibrium, shift the supply curve left, and mark the new intersection. (c) The friend is conflating two different things. A shift of demand would mean the whole demand curve moving — caused by a change in income, tastes, or the price of a related good. That did not happen here. What happened is a movement along the demand curve: because the price rose, the quantity demanded fell. The correct statement is: "The price went up, so the quantity demanded of coffee fell" — demand (the curve) stayed put; quantity demanded (the point on the curve) changed.
Exercise 3
(a) Both curves shift. Rising incomes increase willingness to pay for a normal good, so the demand curve shifts right. Cheaper server technology lowers production costs, so the supply curve shifts right as well. (b) Both shifts push quantity in the same direction. Demand shifting right raises Q∗Q^*; supply shifting right also raises Q∗Q^*. The two effects reinforce each other, so equilibrium quantity certainly rises regardless of which shift is larger. (c) The two shifts push price in opposite directions. Demand shifting right tends to raise P∗P^*; supply shifting right tends to lower P∗P^*. The net effect depends on which shift dominates. If demand shifts further right than supply, price rises. If supply shifts further right than demand, price falls. If both shifts are equal in magnitude, price stays the same. To resolve the ambiguity you would need the specific equations (or at minimum the relative magnitudes) of the two shifts. An exam note: in any double-shift question, one variable is always determinate and the other is always ambiguous — identifying which is which is half the answer.
Exercise 4
(a) Set Qd=QsQ_d = Q_s: $100−2P=−20+4P100 - 2P = -20 + 4PAdd Add 20tobothsidesandadd to both sides and add 2Ptobothsides: to both sides: 120 = 6P.Dividingby. Dividing by 6gives gives P^* = 20.Substituteintothedemandequation:. Substitute into the demand equation: Q^* = 100 - 2(20) = 60.Checkingwithsupply:. Checking with supply: Q_s = -20 + 4(20) = 60.Bothsidesagree,confirming. Both sides agree, confirming (P^, Q^) = (20, 60).(b)Thechokepriceisthepriceatwhichbuyersdemandzerounits.Set. (b) The choke price is the price at which buyers demand zero units. Set Q_d = 0:: 0 = 100 - 2P,so, so P = 50.Theminimumsupplypriceisthepricebelowwhichsellersoffernothing.Set. The minimum supply price is the price below which sellers offer nothing. Set Q_s = 0:: 0 = -20 + 4P,so, so P = 5.(c)Eachsurplusistheareaofarighttriangleonthesupply−demanddiagram.Consumersurplusisthetrianglebetweenthedemandcurveandtheequilibriumprice,withbase. (c) Each surplus is the area of a right triangle on the supply-demand diagram. Consumer surplus is the triangle between the demand curve and the equilibrium price, with base Q^* = 60(runningalongthequantityaxis)andheightequaltothegapbetweenthechokepriceandtheequilibriumprice, (running along the quantity axis) and height equal to the gap between the choke price and the equilibrium price, 50 - 20 = 30:: CS=12×60×30=900CS = \frac{1}{2} \times 60 \times 30 = 900Producersurplusisthetrianglebetweentheequilibriumpriceandthesupplycurve,withthesamebase Producer surplus is the triangle between the equilibrium price and the supply curve, with the same base Q^* = 60andheightequaltothegapbetweentheequilibriumpriceandtheminimumsupplyprice, and height equal to the gap between the equilibrium price and the minimum supply price, 20 - 5 = 15:: PS=12×60×15=450PS = \frac{1}{2} \times 60 \times 15 = 450Totalsurplusisthesum: Total surplus is the sum: TS = CS + PS = 900 + 450 = 1350$. This represents the total gains from trade — the value buyers receive above what they pay, plus the revenue sellers receive above their minimum acceptable price.
Exercise 5
(a) A price ceiling is binding only when it is set below the equilibrium price — a ceiling above P∗P^* has no effect because the market would never reach it on its own. Here Pˉ=15<P∗=20\bar{P} = 15 < P^* = 20, so the ceiling is binding. The legal maximum of \15preventsthemarketfromclearingat prevents the market from clearing at $20.(b)Whenabindingceilingholdsthepricebelowequilibrium,quantityisdeterminedbytheshortsideofthemarket—sellerswillnotsupplymorethantheyarewillingtoatthecontrolledprice.Quantitysuppliedattheceiling:. (b) When a binding ceiling holds the price below equilibrium, quantity is determined by the short side of the market — sellers will not supply more than they are willing to at the controlled price. Quantity supplied at the ceiling: Q_s(15) = -20 + 4(15) = 40.Quantitydemandedattheceiling:. Quantity demanded at the ceiling: Q_d(15) = 100 - 2(15) = 70.Thequantityactuallytradedis. The quantity actually traded is 40(whatsellersoffer).Theshortageis (what sellers offer). The shortage is Q_d - Q_s = 70 - 40 = 30units.(c)Deadweightlossmeasuresthesurplusdestroyedbecausemutuallybeneficialtradesthatwouldhaveoccurredatthefree−marketequilibriumnolongertakeplace.Those units. (c) Deadweight loss measures the surplus destroyed because mutually beneficial trades that would have occurred at the free-market equilibrium no longer take place. Those 20losttransactions—thegapbetween lost transactions — the gap between Q^* = 60andthecontrolledquantity and the controlled quantity Q = 40—involvebuyerswhosewillingnesstopayexceedstheminimumsupplyprice.Thedemandpriceat — involve buyers whose willingness to pay exceeds the minimum supply price. The demand price at Q = 40tellsuswhatthemarginalbuyeriswillingtopay:from tells us what the marginal buyer is willing to pay: from Q_d = 100 - 2Pweget we get P = (100 - 40)/2 = 30.Thesupplypriceat. The supply price at Q = 40istheceilingitself, is the ceiling itself, $15.Thedeadweightlossistheareaofthetrianglewithheight. The deadweight loss is the area of the triangle with height 30 - 15 = 15andbase and base 60 - 40 = 20:: DWL=12×20×15=150DWL = \frac{1}{2} \times 20 \times 15 = 150$ (d) Two real-world symptoms the model predicts for rent-controlled housing: first, waiting lists and queues for available units — excess demand cannot be cleared by price, so it is rationed by time instead. Second, deteriorating housing quality — landlords cannot raise rents to cover maintenance costs, so upkeep declines and the quality of the stock falls over time.