Joseph C. answered • 05/12/19

Former grad student in economics with 6+ years tutoring experience

a) Autarky equilibrium prices & quantities — for each country, simply solve the system of two equations in two variables, given as demand & supply for each country, by whatever method you like (substitution, Gaussian elimination, Cramer’s Rule, or plug it into your TI-84):

country A:

P + Q/25 = 40

P – Q/125 = 10

country B:

P + Q/25 = 40

P – Q/375 = 10

b) There doesn’t appear to be a way to upload pictures into a post, so I’ll have to assume you know how to create a graph from the given equations & the equilibrium solutions you found in (a).

c) A lower initial price in country B will increase quantity demanded in A beyond what domestic producers are able to supply at the new price, and exports will flow from B to A. Conversely,country B’s consumers will reduce consumption as A’s consumers bid up the price relative to B’s old equilibrium. Country B’s suppliers will increase production in response to A’s demand for imports, and A’s suppliers will reduce production as their price falls. A new, common equilibrium price will be reached in both countries, above B’s old price but below A’s. To calculate the common price and the new quantities, modify the supply & demand equations by adding or subtracting the single equilibrium export amount, as follows:

country A:

demand — P = 40 – (Q_{A} + N)/25

supply — P = 10 + (Q_{A} – N)/125

country B:

demand — P = 40 – (Q_{B} – N)/25

supply — P = 10 + (Q_{B} + N)/375

where Q_{A} and Q_{B} are the quantities **produced** in A and B, respectively; and N is the net amount exported from B to A. We now have a linear system of four equations in four variables:

P + Q_{A}/25 + N/25 = 40

P – Q_{A}/125 + N/125 = 10

P + Q_{B}/25 – N/25 = 40

P – Q_{B}/375 – N/375 = 10

Solve this system by your preferred method (I highly recommend using the TI-84 or other calculator, if permitted by your instructor). On each graph, the new common market price will appear as a binding price constraint: a ceiling (below the old equilibrium) for country A, and a floor (above old equilibrium) for country B.

d) Consumer & producer surplus can be calculated from the graphs. Each country’s autarky consumer surplus is the triangle extending from the demand line down to the equilibrium price, and out to their intersection; similarly, producer surplus is the triangle below it, from the supply line up to equilibrium price, out to the same intersection. The common market equilibrium, however, does not look like an equilibrium on either graph. In this case, consumer & producer surplus is calculated the same way, but the intersections of the common market price with the demand & supply lines are no longer the same. A’s consumer surplus grows larger, while its producer surplus shrinks; and the reverse happens in B.

Autarky:

CS_{A} = ½(40 – P_{A})Q_{A}

PS_{A} = ½(P_{A} – 10)Q_{A}

CS_{B} = ½(40 – P_{B})Q_{B}

PS_{B} = ½(P_{B} – 10)Q_{B}

Common market:

CS_{A} = ½(40 – P)(Q_{A} + N)

PS_{A} = ½(P – 10)Q_{A}

CS_{B} = ½(40 – P)(Q_{B} – N)

PS_{B} = ½(P – 10)Q_{B}

To find the change in surplus for each side of the market in each country, **always** subtract the autarky value **from** the common market value. If a surplus decreases from autarky to common market, the change in surplus will be negative. Check your signs carefully. For example, suppose PS_{B} = 1500 under autarky, and 600 under the common market. The change in surplus for producers in country B is therefore

600 – 1500 = –900.