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### Question

**Task 1**: Production Choice and Opportunity Cost

(**a**) Consider a plantation owner in Brazil who allocates his 100 acres between growing coffee and grazing cattle. Suppose that if the plantation owner allocates all acreage to growing coffee, then he can produce 8,000 kg of coffee, but if he allocates all acreage to grazing cattle, then he can produce 15,000 kg of beef

(i) Define opportunity cost. What is the plantation owner's opportunity cost of growing coffee. Define the Law of Diminishing Returns. How does it apply to the plantation owner's net value of growing coffee? Hint: Rule of Two.

(ii) Graph the production possibilities frontier (PPF) for this plantation owner. What does opportunity cost imply in the graph of the PPF? What does the Law of Diminishing Returns imply in the graph of the PPF

(iii) What is the average coffee production per acre if the plantation owner allocates all of his acreage to growing coffee? What is the average cattle production per acre if the plantation owner allocates all of his acreage to grazing cattle?

(iv) If he allocates all of his acreage to growing coffee, then the production is 8,000 kg of coffee and 0kg of cattle. If instead the plantation owner allocates one acre to grazing cattle, choose an amount of the increase in cattle production, and another amount of the decrease in coffee production, that are each consistent with your answer to (iii)? Use these amounts to compute the opportunity cost of cattle production.

(v) Suppose that the plantation owner allocates a second acre to grazing cattle. Using your answers to (i), choose two additional amounts that are consistent with your choices in (iv). What does this imply about the opportunity cost of cattle production?

(vi) On your graph, indicate and identify three production bundles – one that is feasible but inefficient, one that is feasible and efficient, and one that is infeasible.

**b**) Suppose that at the end of last season, the plantation owner had 50 acres planted for growing coffee and 50 acres for grazing cattle. Converting land from cattle grazing to coffee growing costs $200 per acre, but converting land from coffee growing to cattle grazing costs $1500 plus $100 per acre

(i) What type of cost do the $200, $1500, and $100 represent? Hint: they may represent different types of cost. How much does it cost to convert two acres from coffee growing to cattle grazing?

(ii) Suppose that the $1500 cost were instead $2000. What effect, if any, would this have on the plantation owner's allocation of his acreage?

(iii) What are the components of the opportunity cost of coffee growing? Hint: Rule of Two.

(c) Suppose that, at the beginning of the planting season, the plantation owner expects that, when the coffee is harvested, the price of coffee will be $10/kg, and when the cattle are sent to market, the price of beef will be $20/kg. However, midway through the growing season, the World Health Organization (WHO) produces a study that concludes that coffee is harmful to human health. The plantation owner now expects the price of coffee when the harvest comes in to be $8/kg.

(i) Using marginal analysis, explain why this would make the plantation owner regret his allocation of acreage.

(ii) Show this on your graph from (a).

**Task 2:** Consider only the market for coffee. In this task, you examine the Long Run Supply Effects of Climate Change and Technology For this task, assume that the market for coffee is perfectly competitive.

(a) Create a standard and properly labelled supply-and-demand graph. Identify the equilibrium price and quantity, and the consumers' and producers' surpluses.

Climate change is a problem that is both global and intergenerational. In Topic 5, we will discuss possible solutions. For this part of the assignment, listen to this clip and consider the effects on coffee producers. Understanding these effects is essential to being able to evaluate the benefits of the possible solutions.

Clip: http://one.npr.org/?sharedMediaId=497578413:497715272

(b) On your graph from (a), show the effects of climate change on the market for coffee. Be sure to label the future equilibrium price and quantity, and show the changes in consumers' and producers' surpluses.

**(c)** Consider the changes in welfare.

(i) In your graph, identify and show the area that represents the new consumers' surplus.

(ii) Describe the sources of changes to consumers' surplus: Hint: Rule of Two.

Technology marches forward. Watch this clip. For many herbs, vegetables, and fruits, scientists are developing methods of growing them in greenhouses or on rooftop gardens. By controlling the environment, it will become possible and less expensive to grow these foods in different climes and periods that are out of the usual growing season. Suppose that this happens for coffee.

Clip: https://www.youtube.com/watch?v=LM60P6WvbTs

**(d)** What will be the effects on the producers of coffee in Brazil and other economies that produce coffee? Suppose that Brazil's politicians try to counteract this by implementing an export subsidy. In Brazil (the exporting country), what are the consequences of an export subsidy? Who is helped and who is harmed by it? How, if at all, is the government affected by such export subsidies? What are the long run effects of export subsidies?

**Task 3:** Long Run Demand Effects in Coffee and Other Markets As the world's economies develop, more people rise out of poverty.

(a) Define a normal versus an inferior good, and state which you think coffee is. What do you expect to happen to the market for coffee as the world's economies develop?

(b) List the characteristics of a perfectly competitive market. Which of these does the market for coffee growing satisfy? Which of these does the market for coffee shops satisfy?

(c) Define a substitute good and a complement good. Choose either a good that is a substitute for coffee, or a good that is a complement with coffee. For the good that you've chosen, state which it is. From your answer to part (a), what do you expect to happen to the market for this good, ceteris paribus, as the world's economies develop. Show graphically

(d) Suppose that the price of coffee today is $4 and the quantity demanded (which equals the equilibrium quantity) of the good that you've chosen is 20 units per week. Choose a new price of coffee that is consistent with your analysis from (a) – ignore any effects from Task 2. Choose a new quantity demanded of the good that you've chosen that is consistent with your answer in (c). Compute the cross-price elasticity

**Task 4**

(a) Suppose that the demand for coffee in Australia is Qd = 20 – 2P, and the supply is Qs = c + dP, where c>0 and d>0. Choose a value for c and a value for d.

(i) Derive the equilibrium price and quantity.

(ii) Choose a value for the world price that is less than the equilibrium price that you determined in part (i). Determine the new equilibrium in Australia: the price, quantity produced in Australia, and imports.

(iii) Suppose that the effects of climate change are realized, in Brazil and elsewhere where coffee is grown, including Australia. Choose new values of c and the world price that are consistent with these effects. You do not need to re-solve.

### Solution

**Task 1:** Production Choice and Opportunity Cost – Solution

(a) (i). Opportunity cost is defined as the cost of foregoing one choice or opportunity over another choice.

The plantation owner's opportunity cost of growing coffee is 15,000 kg of beef production he will forgo.

Law of Diminishing Returns is referred to as decrease in incremental output production of a firm as a single factor of production (say, labour) is increased while the other factors (like capital) stays constant.

15,000 kg of beef production in the vertical axis and 8,000 kg of coffee production in the horizontal axis. Let’s say the initial production is at point B in the graph here the opportunity cost implies if we move the production of beef from 7,500 kg to 11,250 kg the coffee production drops from 4,000 kg to 2,000 kg. So the opportunity cost of the additional 3,750 kg of beef production is 2,000 kg of coffee production forgone.

(iii) According to the PPF graph in (ii) if the plantation owner allocates all his acreage to growing coffee, i.e. 8000 kg (which implies 0 kg of cattle) to the given 100 acres of land he will produce an average of 80 kg of coffee per acre.

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