Question 1bThe above graph illustrates production possibilities of a given country that produces only two products, which are sunscreen in litres per month and food in kilograms per month. The trade off between the two commodities, that is sunscreen and food, is in such a way that more food is foregone if this country decides to produce only sunscreen. On the other hand, less sunscreen is foregone if this country decides to produce only food. The trade off is however different, if this nation decides to produce either 100litres of sunscreen or 100 kilograms of food.
If it decides to produce 100 kilograms of food, it will have to forego 100 litres of sunscreen. Similarly, if it decides to produce 100 litres of sunscreen, it will have to forego 100 kilograms of food. The amount of sunscreen to be produced so as to attain production efficiency can be calculated by first determining the equation of the line, which is given by y = a + bx. We first begin by calculating the gradient, b b = ∆Y/∆X Where Y denote sunscreen in litres and X denote food in kilograms.
Therefore, by choosing any two points from the graph, such as (300, 200) in the X axis and (0, 50) in the Y axis, the gradient of the line will be calculated as follows, 50-0 = 50/-100 = - 0.5200-300 The equation of a straight line normally takes a form of y = a + bx, where a is the adjacent point and b the gradient. By inserting the calculated gradient in the equation, Y = a – 0.5xTo determine a, we take any point from the graph, such as (300, 0), 300 represent a point in x axis while 0 represent a point in the y axis.
By inserting this two points in the above equation, a is found to be 150. Therefore, the equation of the line becomes, Y = 150 – 0.5X. From this equation, the amount of sunscreen to be produced, if 150 kilograms of food per month is produced, will be calculated as followsY = 150 – 0.5 (150) = 75Therefore, if the country produces 150 kilograms of food per month, it will have to produce 75 litres of sunscreen for it to attain production efficiency.
In order to calculate opportunity cost, it is important to first find the combination of goods produced and then determine the amount foregone, which is the opportunity cost. If one kilogram of food is produced, the amount of sunscreen to be produced so as to attain production efficiency will be, Y = 150 – 0.5 (1) = 149.5 litres, the opportunity cost of producing 1 kilogram of food therefore will be 150 – 149.5= 0.5 litres.
If on the other hand 1 litre of sunscreen is produced, the amount of food to be produced so as to attain production efficiency will be 1 = 150 – 0.5X = 0.5X = 150 – 1, X = 149/0.5 = 298, therefore, the opportunity cost of producing 1 litre of sunscreen will be 300 – 298 = 2 litres. Question twoa (i) Gross domestic product (GDP) is calculated asGDP = C+ I + G+ (X-M)Where C is consumption, I is investment, G is government expenditure and X-M is net exports.
From the table, government expenditure, G = 267, Consumption = 791, investment = 209, net exports, X-M = 322-366= -44 GDP = 791 + 209 + 267 -44 = 1, 223 billion pounds