Please I need the solution before Monday Petroleum Economics Due: Sept 19th, 6PM
ID: 1136130 • Letter: P
Question
Please I need the solution before Monday
Petroleum Economics Due: Sept 19th, 6PM Please submit your homework electronically through D2L's dropbox as a PDF file. You may use excel, matlab or any other program of your choice to answer the questions. 1) A company, Gadgeteering Inc, produces Widgets. During a given month, they need to pay $10 to lease their factory and pay for administration. Currently, they can produce up to 100 widgets per month at a cost of $1 per widget. They can produce an additional 20 per month at a cost of $1.50 per widget due to overtime a) Plot Total Cost, Variable Cost and Fixed Cost as a function of quantity for the current month in one figure Plot Marginal Cost, Average Total Cost, Average Variable Cost and Average Fixed Cost in one figure b) 2) Gadgeteering decides to hire more workers, so they can now produce up to 200 widgets per month at a cost of $1.25 per widget, plus an additional 40 widgets per month at a cost of $2 per widget. However, their monthly costs are now $20. a) Plot Total Cost, Variable Cost and Fixed Cost as a function of quantity for the current month in one figure. Plot Marginal Cost, Average Total Cost, Average Variable Cost and Average Fixed Cost in one figure. b) 3) If the current demand for a widget is 110 units per month, was Gadgeteering better off before or after they hired the additional workers?Explanation / Answer
Relative Prices, Wages, and Supply If the price of cheese relative to the price of wine is less than the opportunity cost of producing cheese P C /P W <a LC /a LW, then the wage in cheese will be less than the wage in wine P C /a LC < P W /a LW so workers will make only wine (the economy specializes in wine production) Production, Prices, and Wages If the price of cheese relative to the price of wine equals the opportunity cost of producing cheese P C /P W =a LC /a LW, then the wage in cheese equals the wage in wine P C /a LC = P W /a LW so workers will be willing to make both wine and cheese Production, Prices, and Wages For example, suppose cheese sells for P C = $4/pound and wine sells for P W = $7/gallon. Wage paid producing cheese is P C /a LC = ($4/pound)(1 pound/hour) = $4/hour. Wage paid producing wine is P W /a LW = ($7/gallon)(1/2 gallon/hour) = $3.50/hour. Workers would be willing to make only cheese (the relative price of cheese 4/7 exceeds the opportunity cost of cheese of ½)
11 Production, Prices, and Wages If the price of cheese drops to P C = $3/pound: Wage paid producing cheese drops to P C /a LC = ($3/pound)(1 pound/hour) = $3/hour. Wage paid producing wine is still $3.50/hour if price of wine is still $7/gallon. Now workers would be willing to make only wine (the relative price of cheese 3/7 is now less than the opportunity cost of cheese of ½) Production, Prices, and Wages If the home country wants to consume both wine and cheese (in the absence of international trade), relative prices must adjust so that wages are equal in the wine and cheese industries. IfP C /a LC = P W /a LW workers will not care whether they work in the cheese industry or the wine industry, so that production of both goods can occur. Production (and consumption) of both goods occurs when the relative price of a good equals the opportunity cost of producing that good: P C /P W = a LC /a LW 1-32 Trade in the Ricardian Model If the home country is more efficient in wine and cheese production, then it has an absolute advantage in all production: its unit labor requirements for wine and cheese production are lower than those in the foreign country a LC < a * LC and a LW < a * LW where * notates foreign country variables
12 Trade in the Ricardian Model A country can be more efficient in producing both goods, but it will have a comparative advantage in only one good. Even if a country is the most (or least) efficient producer of all goods, it still can benefit from trade Trade in the Ricardian Model Suppose that the home country has a comparative advantage in cheese production: its opportunity cost of producing cheese is lower than in the foreign country. a LC /a LW < a * LC /a * LW When the home country increases cheese production, it reduces wine production less than the foreign country would Trade in the Ricardian Model Since the slope of the PPF indicates the opportunity cost of cheese in terms of wine, Foreign s PPF is steeper than Home s. To produce one pound of cheese, must stop producing more gallons of wine in Foreign than in Home
13 Fig. 3-2: Foreign s Production Possibility Frontier 1-37 Trade in the Ricardian Model Before any trade occurs, the relative price of cheese to wine reflects the opportunity cost of cheese in terms of wine in each country. In the absence of any trade, the relative price of cheese to wine will be higher in Foreign than in Home if Foreign has the higher opportunity cost of cheese. It will be profitable to ship cheese from Home to Foreign (and wine from Foreign to Home) where does the relative price of cheese to wine settle? 1-38 Trade in the Ricardian Model To see how all countries can benefit from trade, we need to find relative prices when trade exists. First calculate the world relative supply of cheese: the quantity of cheese supplied by all countries relative to the quantity of wine supplied by all countries RS = (Q C + Q * C )/(Q W + Q * W)
14 Relative Supply and Relative Demand If the relative price of cheese falls below the opportunity cost of cheese in both countries P C /P W < a LC /a LW < a * LC /a * LW, no cheese would be produced. domestic and foreign workers would be willing to produce only wine (where wage is higher) Relative Supply and Relative Demand When the relative price of cheese equals the opportunity cost in the home country P C /P W =a LC /a LW < a * LC /a * LW, domestic workers are indifferent about producing wine or cheese (wage when producing wine same as wage when producing cheese). foreign workers produce only wine Relative Supply and Relative Demand When the relative price of cheese settles strictly in between the opportunity costs of cheese a LC /a LW < P c /P W <a * LC /a * LW, domestic workers produce only cheese (where their wages are higher). foreign workers still produce only wine (where their wages are higher). world relative supply of cheese equals Home s maximum cheese production divided by Foreign s maximum wine production (L / a LC ) / (L * / a * LW)
15 Relative Supply and Relative Demand When the relative price of cheese equals the opportunity cost in the foreign country a LC /a LW < P C /P W =a * LC /a * LW, foreign workers are indifferent about producing wine or cheese (wage when producing wine same as wage when producing cheese). domestic workers produce only cheese Relative Supply and Relative Demand If the relative price of cheese rises above the opportunity cost of cheese in both countries a LC /a LW < a * LC /a * LW < P C /P W, no wine is produced. home and foreign workers are willing to produce only cheese (where wage is higher) Relative Supply and Relative Demand World relative supply is a step function: First step at relative price of cheese equal to Home s opportunity cost a LC /a LW, which equals 1/2 in the example. Jumps when world relative supply of cheese equals Home s maximum cheese production divided by Foreign s maximum wine production (L / a LC ) / (L * / a * LW), which equals 1 in the example. Second step at relative price of cheese equal to Foreign s opportunity cost a * LC /a * LW, which equals 2 in the example
16 Relative Supply and Relative Demand Relative price of cheese P C /P W 2 = a * LC/a * LW RS 1/2 = a LC /a LW L/a LC L * /a * LW Relative quantity of cheese Q C + Q * C Q W + Q * W 1-46 Relative Supply and Relative Demand Relative demand of cheese is the quantity of cheese demanded in all countries relative to the quantity of wine demanded in all countries. As the price of cheese relative to the price of wine rises, consumers in all countries will tend to purchase less cheese and more wine so that the relative quantity demanded of cheese falls Fig. 3-3: World Relative Supply and Demand
17 Relative Supply and Relative Demand When the international price is strictly in between the two autarchic one (eq 1 in the figure), the two countries completely specialize in the product in which they have a comparative advantage. But this is not the only possible equilibrium. Also 2 could be one Gains from Trade Gains from trade come from specializing in the type of production which uses resources most efficiently, and using the income generated from that production to buy the goods and services that countries desire. where using resources most efficiently means producing a good in which a country has a comparative advantage Gains from Trade Domestic workers earn a higher income from cheese production because the relative price of cheese increases with trade. Foreign workers earn a higher income from wine production because the relative price of cheese decreases with trade (making cheese cheaper) and the relative price of wine increases with trade
18 Gains From Trade We use two approaches to show the gains from trade: a) International trade allows and expansion of the consumption possibilities set b) International trade considered as an indirect method of production is more efficient than domestic production Gains From Trade a) Without trade, consumption is limited by what is domestically produced Consumption possibilities expand beyond the production possibility frontier when trade is allowed. With trade, consumption in each country is expanded because world production is expanded when each country specializes in producing the good in which it has a comparative advantage. In Fig 3-4, the lines TF and T*F* (whose slope is given by the international price) limit the consumption possibility set. Both of them are external to the PPF Fig. 3-4: Trade Expands Consumption Possibilities
19 Gains from Trade B) Think of trade as an indirect method of production that converts cheese into wine or vice versa. Without trade, a country has to allocate resources to produce all of the goods that it wants to consume. With trade, a country can specialize its production and exchange for the mix of goods that it wants to consume A Numerical Example Unit labor requirements for home and foreign countries Cheese Wine Home a LC = 1 hour/lb a LW = 2 hours/gallon Foreign a * LC = 6 hours/lb a * LW = 3 hours/gallon What is the home country s opportunity cost of producing cheese? a LC /a LW = ½, to produce one pound of cheese, stop producing ½ gallon of wine A Numerical Example The home country is more efficient in both industries, but has a comparative advantage only in cheese production. 1/2 = a LC /a LW < a * LC /a * LW = 2 The foreign country is less efficient in both industries, but has a comparative advantage in wine production
20 A Numerical Example With trade, the equilibrium relative price of cheese to wine settles between the two opportunity costs of cheese. Suppose that the intersection of RS and RD occurs at (P C /P W ) INT = 1 so one pound of cheese trades for one gallon of wine. Trade causes the relative price of cheese to rise in the home country and fall in foreign A Numerical Example without trade, Home can utilize 1 hour of labour to produce 1/a LW = 1/2 gallon of wine with trade, Home can utilize 1 hour of labour to produce 1/a LC = 1 pound of cheese and trade it for wine at the given international price. It obtains (import) 1 gallon of wine Home gains from trade In general, Home gains if: (1/a LC ) (P C /P W ) INT > (1/a LW ) or (P C /P W ) INT > (a LC /a LW ) This is always true when the international price is in between the two autarchic prices A Numerical Example without trade, Foreign can utilize 1 hour of labour to produce 1/a LC = 1/6 pounds of cheese with trade, Foreign can utilize 1 hour of labour to produce 1/a* LW = 1/3 gallons of wine and trade it for cheese at the given internatinal price. It obtains (imports) 1/3 pounds of cheese. Foreign gains from trade
21 Relative Wages Relative wages are the wages of the home country relative to the wages in the foreign country. Productivity (technological) differences determine relative wage differences across countries. The home wage relative to the foreign wage will settle in between the ratio of how much better Home is at making cheese and how much better it is at making wine compared to Foreign. Relative wages cause Home to have a cost advantage in only cheese and Foreign to have a cost advantage in only wine Relative Wages Suppose that P C = $12/pound and P W = $12/gallon. Since domestic workers specialize in cheese production after trade, their hourly wages will be w = P C /a LC = $12 /1= $12 Since foreign workers specialize in wine production after trade, their hourly wages will be w * = P W /a * LW = $12/3 = $4 The relative wage of domestic workers is therefore $12/$4 = Relative Wages The relative wage lies between the ratio of the productivities in each industry. The home country is 6/1 = 6 times as productive in cheese production, but only 3/2 = 1.5 times as productive in wine production. The home country has a wage 3 times higher than the foreign country. In general: a * LC / a LC > w /w * > a * LW / a LW
22 Relative Wages These relationships imply that both countries have a cost advantage in production. High wages can be offset by high productivity. Low productivity can be offset by low wages. In the home economy, producing one pound of cheese costs $12 (one worker paid $12/hr) but would have cost $24 (six paid $4/hr) in Foreign. In the foreign economy, producing one gallon of wine costs $12 (three workers paid $4/hr) but would have cost $24 (two paid $12/hr) in Home Relative Wages Because foreign workers have a wage that is only 1/3 the wage of domestic workers, they are able to attain a cost advantage in wine production, despite low productivity. Because domestic workers have a productivity that is 6 times that of foreign workers in cheese production, they are able to attain a cost advantage in cheese production, despite high wages Relative Wages and gains from trade We can use this framework to show the gains from trade in a third alternative way: In Home the real wage in terms of wine in autarchy is: w / P W = (P C /a LC ) / P W = (P C / P W )/ a LC = (1/2)*1= 1/2 In Home, the real wage in terms of wine in free trade is: w / P W = (P C /a LC ) / P W = (P C / P W )/ a LC = 1*1 = 1 Hence with free trade a worker in Home gains since its purchasing power increases in terms of the imported good and it doesn t change in terms of the exported good