# Economics 461: Partial Equilibrium

conomics 461                                                                       Name___________________________

International Economics

SU 2016

Class Action:  Partial Equilibrium 2 X 1 Model [200 points]

AUTARCHY [47 points]

Imagine two regimes—Celtic Gaul and the Roman Empire

1. Celtic Gaul (22 points)
2. In Celtic Gaul,

consumers demand wine

D:  Q = 60 – 2P

Transpose this schedule into P = form, showing your work clearly:

And domestic producers supply wine:

S:  Q = -24 + 1.5P

Transpose this schedule into P = form, showing your work clearly:

1. Determine the equilibrium price and quantity of wine in Celtic Gaul, showing the set-up as well as the work:

PCeltic Gaul = ________________

QCeltic Gaul = ________________

1. Graph Celtic Gaul, carefully revealing all intercepts appearing in quadrant I, as well as labeling

the equilibrium price and quantity with PCeltic Gaul and QCeltic Gaul on the vertical and horizontal axes, respectively.

1. Then, identify (by outlining distinctively and labeling clearly) for domestic agents:
• The willingness to pay—WTP
• The total expenditures—TE
• The consumer surplus—CS
• the total revenues—TR
• the opportunity cost—OC
• the producer surplus—PS

Directions:  Mimic the procedures used to portray autarchy in Celtic Gaul, now for The Roman Empire.

1. The Roman Empire (22 points)
2. In The Roman Empire, consumers demand wine

D:  Q = 90 – 3P

Transpose this schedule into P = form, showing your work clearly:

And in The Roman Empire, domestic producers supply wine

S:  Q =  34 + .5P

Transpose this schedule into P = form, showing your work clearly:

1. Determine the equilibrium price and quantity of wine in The Roman Empire, showing the set-up as well as the work:

PThe Roman Empire = ________________

QThe Roman Empire = ________________

1. Graph The Roman Empire, carefully revealing all intercepts ‘appearing’ in quadrant I, as well as labeling the equilibrium price and quantity with PThe Roman Empire and QThe Roman Empire on the vertical and horizontal axes, respectively.

Then, identify (in distinctive colors) these ‘domestic’ events:

• The willingness to pay—WTP
• The total expenditures—TE
• The consumer surplus—CS
• the total revenues—TR
• the opportunity cost—OC
• the producer surplus—PS

1. Summary (3 points)

An opportunity presents itself.  [Strictly speaking, it is not an arbitrage opportunity, because that implies risk-free, and trade routes—whether by land or by sea—are never clear sailing.]

Assuming that transportation costs are negligible, an trader could buy wine cheaply in _________________(The Roman Empire/Celtic Gaul) and sell it ‘dearly’ in _________________(The Roman Empire/Celtic Gaul), making a profit per unit, the price differential: _______________ per unit.

1. Economic Integration [16 points]

Assume that the ‘law of one price’ prevails, that all arbitrage opportunities are exhausted promptly.  For the moment, it is as if the two regions have economically integrated, becoming an economic union.

1. Aggregate the two regions’ demands for wine.

Qd The Roman Empire + Celtic Gaul  =

1. Aggregate the two regions’ supplies for wine.

Qs The Roman Empire + Celtic Gaul  =

1. Determine the equilibrium price and quantity for wine, assuming economic integration.

P* = _________________

Q* = _________________

Note:  In free trade, P* will become the ‘one price to rule them all’ –the world price or the international price–preempting any local price. In this context, the equilibrium, market-clearing quantity is the TOTAL quantity produced (by Roman and Celtic firms) and the TOTAL quantity consumed (by Roman and Celtic consumers).

1. GRAPH THIS SYSTEM IN THE TOTAL SPACE PROVIDED, indicating all possible positive intercepts as well as P* and Q* on the appropriate axes.

In actuality, each region maintains its political sovereignty.  But with free trade, with full economic integration, wine will be exchanged as if the two nations are one in the sense that one price, to ‘rule them all,’ will prevail.  Provide the equations, in “eQ_” form, showing your setup and the answer.

1. The Celtic
2. EQD for wine =

And, in the event P* = 20 prevails, EQD for wine = _________(specific number)

1. EQS for wine =

And, in the event P* = 20 prevails, EQS for wine = __________(specific number)

1. The Roman
2. EQD for wine =

And, in the event P* = 20 prevails, EQD for wine = __________(specific number)

1. EQS for wine =

And, in the event P* = 20 prevails, EQS for wine = ___________(specific number)

1. Graph–Trading Space: Plot the excess _________(demand or supply)  schedule for Celtic Gaul against the excess (demand or supply) schedule for The Roman Empire—choosing the CORRECT schedule, consistent with the story).  On the graph, reveal, again, the ‘one price to rule them all’ in free trade—P*– as well as the equilibrium quantity—the quantity traded, Qt (not to be confused with Q*, the TOTAL quantity produced and consumed jointly).

1. In effect, the Celtic ______________________(shortage/surplus) of wine will become the _______________(exports to/imports from) The Roman Empire; At the same time, the Roman  __________________(shortage/surplus) of wine will become the _______________(exports to/imports from) Celtic Gaul.

The Celtic ___________________(negative/positive) EQD offsets the Roman ___________________(negative/positive) EQD, so that their sum is zero.

The specific quantity traded, at the ‘one price to rule them all’ proves to be _______________.

1. (49 points)

Graph the Celtic national diagram all over again, this time to illustrate the free trade scenario.

Assuming free trade prevails, identify (by outlining)

• The willingness to pay—WTP
• The total expenditures—TE
• The consumer surplus—CS
• the total revenues—TR
• the opportunity cost—OC
• the producer surplus—PS
• import expenditures–IE

Then calculate and report the values for each variable, before and after trade, for Celtic Gaul.

 Celtic Gaul Autarchy Free Trade Change (+ or -) & magnitude Price Domestic Qd Domestic willingness to pay Domestic total expenditures on domestic product Import expenditures Domestic total expenditures Domestic consumer surplus Domestic Qs Domestic total revenues on domestic product Export revenues Domestic total revenues Domestic opportunity cost Domestic producer surplus Quantity traded internationally

1. (49 points)

Graph the Roman national diagram all over again, this time to illustrate the free trade scenario.

On the new The Roman Empire graph, identify (by outlining distinctively and labeling clearly) for domestic agents:

• The willingness to pay—WTP
• The total expenditures—TE
• The consumer surplus—CS
• the total revenues—TR
• the opportunity cost—OC
• the producer surplus—PS
• export revenues–ER

Then calculate and report the values for each variable, before and after trade, for The Roman Empire.

 The Roman Empire Autarchy Free Trade Change (+ or -) & magnitude Price Domestic Qd Domestic willingness to pay Domestic total expenditures on domestic product Import expenditures Domestic total expenditures Domestic consumer surplus Domestic Qs Domestic total revenues on domestic product Export revenues Domestic total revenues Domestic opportunity cost Domestic producer surplus Quantity traded internationally

1. (8 points)

Finally, in both the national free trade spaces and in the Trading Space, use a color to outline and label

• The net national gain to The Roman Empire from free trade, assuming all resources rendered jobless by free trade are absorbed in their next best pursuit, in both the Roman graph space and the Trading Space.
• The net national gain to Celtic Gaul from free trade, realizing all resources employed in the expanding export sector are obtained from other sectors and paid their true opportunity cost (their value in that next best pursuit) in both the Celtic graph space and the Trading Space.

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