Prices in an Open Economy

Absolute vs. Relative Prices

Cutting off external trade relations causes a dramatic change in the prices of traded goods. Less dramatic policies that restrict international trade such as tariffs and quotas also significantly affect the prices of traded goods. To lay the basis for our discussion through the course, we first consider how foreign prices are converted into domestic prices so that home consumers can compare the prices of imported and domestic goods.

Domestic price of a commodity (p$) = $/unit

Foreign price of a commodity (p€) = €/unit (or RMB/unit)

Exchange Rate e (dollar price of a foreign currency) = $/€ (or $/RMB)

Domestic price of an imported good

= p$ = e × p€ (or e ×pRMB)

= ($/€)(€/unit) = $/unit.

The Law of One Price: One price prevails, provided No Transportation Costs + No Trade Restrictions.

Given the exchange rates, one can obtain the dollar price of any good.

If p > p*, then import the good. Imports lower p until p = p*

If p < p*, then export the good. This raises p until p = p*

Assume N goods: 1, 2,...,N.

Absolute Prices: (p₁, p₂,..., p_N). N absolute prices.

Relative Prices: (p₁/p_N, p₂/p_N,...,1). (N-1) relative prices.

You may use another good as a standard.

2 good case. AP: p₁, p₂

RP: p₁/p₂.

HDTV = $4,000. Corn price = $4 per bushel. p₁/p₂ = 1000. Relative price changes over time. Now HDTV = $2,000, p₁/p₂ = 500.

One HDTV costs 500 bushesl of corn. oil price = $72 per barrel. p₁/p₂ = 18 (i.e., one barrel of oil costs 18 bushels of corn.)

Equilibrium in a Closed Economy

Figure 1
Autarky price = p^A; = (p¹/p²)^A; at autarky. At this price X = M = 0.

If p* > p^A, then export.

Export supply: X = X(p₁/p₂), + (positively sloped)

Import Demand: M = M(p₁/p₂), - (negatively sloped)

alarm clock
Findings

Commodity trade occurs because of differences in autarky prices between countries.
Goods flow from a low-price country from a high-price country. (add two demand and supply curves)

Equilibrium Price in the World Market

Figure 2

5 Cantaloupes, ranging from ¥10,000 to ¥20,000 per box. That is, ¥5,000 to ¥10,000 each (or up to $90)

6 Watermelon, ¥2980(or $25) each

Doha Round

WTO was established in 1995. Doha Round was supposed to have started in Seattle in 1999, and was going to be called the "Seattle Round," but such efforts were stymied by vehment demonstrations in Seattle. In these trade negotions, member countries send their representatives to negotiate the terms with others. They weigh the benefits and costs of their concessions, which are measured by consumer surplus and producer surplus resulting from the proposed concessions or agreements.


	This plate depicting the baptism of Jesus was included in the 151 vessels together with other vases and plates. Chinese factories received orders asking for specific designs from the European royalties. Christian missionaries were probably sent to China at the time.
Zwinger porcelain collection

Consumer Demand

Assume that a consumer's preferences are represented by a utility function, solely defined in terms of consumption goods. This idea comes from Jeremy Bentham, but it was basically derived from the Epicurians who believed in minimizing pains and maximizing pleasures.

For simplicity, assume there are only two consumption goods. Such a utility function is written as:

Utility: U(x₁,x₂)

Assumptions

Indifference curves are downward sloping (commodities are goods)
A higher indifference curve represents a higher utility (more is better)
Indifference curves are non-intersecting (otherwise nontransitive)
Convex to the origin (average bundle is preferred to extreme bundles)

Budget Constraint: M = p₁x₁ + p₂x₂.
The quantity of good 2 consumed can be written as:
x₂ = M/p₂ - (p₁/p₂)x₁.
Consumer Equilibrium: Tangency between the highest attainable Indifference curve and the Budget Line.
MRS(marginal rate of substitution) ≡ MU₁/MU₂ = p₁/p₂.
Figure 3
Change in Price: Law of Demand
Market Demand: a horizontal sum of individual demand curves.
Consumer Surplus (Marshallian) = Willingness to Pay - Price.
The area under the demand curve and above the market price. Figure 3. Consumer Surplus

Why are the paintings of famous artists auctioned for millions of dollars? Why do their prices always go up? Each painting is unique. The supply of each painting is limited to only one unit.

	Edvard Munch's Madonna (= mia donna (my lady) in Italian = virgin Mary), October 2002. Another painting with the same title, together with "The Scream" was stolen from Munch Museum of Oslo in August 2004. Munch painted five versions of Madonna.

	Edvard Munch, Girls on the Bridge

Producer

Profit: Π = pq - c(q)

pq = revenue

c(q) = production cost

c(q) = FC + VC

Profit maximization
p = MC, and p is above AVC.

p = price
MC = marginal cost
AVC = average variable cost

Figure 5, Revenue, Cost, and Profits

Supply Curve: the segment of MC above Min AVC.
It is positively sloped.

Market Supply: a horizontal sum of individual supply curves.

Producer Surplus = pQ - Variable Cost.

Total variable cost = the area below MC.

(The slope of the arrows is called the "derivative" in calculus.)

MC(1) = margnial cost of the first unit, and MC(2) = marginal cost of the second unit, etc.

The blue area in the above diagram approximates the total variable cost. The stairwise approximation yields some errors, because it does not exactly match the contour of the marginal cost (MC) curve. However, if the width of each step is made smaller, say infinitesimally small, then the area of the blue stairs is equal to the area below the MC curve.

Figure 6, Producer Surplus

Free Trade, CS and PS

Figure 7. Gains from Trade

A Numerical Example

S = 2 + .8q (supply price)

Here, S means supply price, not quantity!

D = 20 - q (demand price)

Similarly, D stands for demand price, not quantity.

At autarky, demand price must be equal to supply price, i.e.,

2 + .8q = 20 - q, or

1.8q = 20 - 2 = 18,

p^A = 10.

Quantity at autarky: 10 = 20 - q, and hence q^A = 10.

Autarky: CS = (10x10) ÷2 = 50
PS = 10 x 8 ÷2 = 40. TS = 50 + 40 = 90

World price: p* = $6

Domestic production: 6 = 2 + 0.8q. Then q = 5

Domestic Demand: 6 = 20 - q. Then q = 14.

Import demanded: 14 - 5 = 9.

Free Trade: CS = 14x14÷2 = 98. PS = 10. TS (total surplus) = 108

Gains from Trade: 108 - 90 = 18

Or, simply get the area of the triangle: 9 x (10 - 6) ÷2 = 18.

Lucas Cranach, Der Jungbrunnen [Fountain of Youth] (1546).

This painting shows the emergence of the middle class (which disappeared for about a millenium during the Middle Ages) in the 16th century.

Life expectancy was about 20-25 years during the time of Jesus. This painting shows that (as income increased) there were a considerable number of aged people in the population. Life expectancy rose to about 40 years around 1900, and then to about 70 years or more in some high income countries.