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Supply and demand practice problems

Eight supply and demand problems with complete worked solutions — equilibrium algebra, identifying curve shifts, price controls, subsidies, and elasticity along a linear demand curve. These are the mechanics every introductory economics exam tests. Draw the diagram for each problem before computing; the graphical intuition is half the answer. Free to use, no signup.

Problem 1

A market has demand QD=200−4PQ_D = 200 - 4P and supply QS=50+2PQ_S = 50 + 2P. Find the equilibrium price and quantity.
Show worked solution
Set QD=QSQ_D = Q_S: 200−4P=50+2P200 - 4P = 50 + 2P, so 150=6P150 = 6P and P∗=25P^* = 25. Then Q∗=50+2(25)=100Q^* = 50 + 2(25) = 100. Check: 200−4(25)=100200 - 4(25) = 100. Equilibrium is P∗=25P^* = 25, Q∗=100Q^* = 100.

Problem 2

Consumer incomes rise, and the good in question is normal. Which curve shifts, in which direction, and what happens to equilibrium price and quantity?
Show worked solution
Demand shifts right (at every price, consumers want more of a normal good when income rises). Supply is unchanged. The new intersection has a higher equilibrium price and a higher equilibrium quantity. The supply curve does not shift — quantity supplied rises as a movement along the supply curve in response to the higher price.

Problem 3

The price of a key production input rises. Trace the effect on the market: which curve shifts, and what happens to price and quantity?
Show worked solution
Higher input costs shift supply left (at every price, producing any quantity is now costlier, so less is offered). Equilibrium price rises and equilibrium quantity falls. Consumers respond to the higher price with a movement along the demand curve — demand itself does not shift.

Problem 4

Demand and supply both increase simultaneously. What can you conclude about the new equilibrium quantity and price?
Show worked solution
Quantity unambiguously rises — both shifts push it up. Price is ambiguous: the demand increase pushes price up while the supply increase pushes it down, so the outcome depends on the relative size of the shifts. On an exam, state the ambiguity explicitly; claiming a definite price direction here is a classic error.

Problem 5

In the market from Question 1 (P∗=25P^* = 25), the government sets a price floor at P=30P = 30. Calculate the resulting surplus.
Show worked solution
At P=30P = 30: quantity demanded is 200−4(30)=80200 - 4(30) = 80; quantity supplied is 50+2(30)=11050 + 2(30) = 110. The surplus is 110−80=30110 - 80 = 30 units. The floor binds because it sits above equilibrium. Quantity actually traded falls to the demanded quantity, 80 — sellers cannot sell what buyers will not purchase.

Problem 6

Explain the difference between a "change in demand" and a "change in quantity demanded," and give one cause of each for the coffee market.
Show worked solution
A change in quantity demanded is a movement along a fixed demand curve, caused only by a change in the good's own price — for example, coffee prices fall and consumers buy more. A change in demand is a shift of the entire curve, caused by something other than own price — for example, the price of tea (a substitute) rises, shifting coffee demand right. Mixing these up turns otherwise correct analysis into a contradiction.

Problem 7

In the market from Question 1, the government pays sellers a subsidy of 6 per unit. Find the new consumer price, the effective price received by sellers, and the quantity traded.
Show worked solution
Sellers now supply according to the price they receive including the subsidy: QS=50+2(P+6)=62+2PQ_S = 50 + 2(P + 6) = 62 + 2P. New equilibrium: 200−4P=62+2P200 - 4P = 62 + 2P, so 138=6P138 = 6P and consumers pay PC=23P_C = 23. Sellers receive 23+6=2923 + 6 = 29. Quantity: 200−4(23)=108200 - 4(23) = 108. Relative to the original equilibrium at 25: consumers gain 2 of the subsidy, sellers gain 4 — the less price-responsive side (supply, slope 2 versus demand slope 4 in absolute value) captures the larger share.

Problem 8

For the demand curve QD=200−4PQ_D = 200 - 4P, calculate the price elasticity of demand at the equilibrium price P=25P = 25, Q=100Q = 100. What is special about this point?
Show worked solution
Point elasticity: ϵD=dQdP⋅PQ=−4×25100=−1\epsilon_D = \frac{dQ}{dP} \cdot \frac{P}{Q} = -4 \times \frac{25}{100} = -1. Demand is unit elastic exactly at this point — which is the midpoint of this linear demand curve. Above the midpoint demand is elastic (∣ϵD∣>1|\epsilon_D| > 1), below it inelastic: elasticity varies along a straight demand curve even though the slope is constant. Slope and elasticity are not the same thing.

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