Production Possibility Frontier: Concept, Graph, And Shifts

What is Production Possibility Frontier?

(a) Using the given data, below diagram shows the production possibility frontier for two commodities – Cars and Bicycle in Newland.  X-axis shows production of cars while Y-axis shows production of bicycle. This curve shows the best combination of these goods which can be produced by the country in the most optimum manner (Mankiw,2007). 

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 Production possibility curve is the graph which displays numerous production possibilities available to the producer to choose from when the resources are constant. It also displays maximum possibility of production of two or more commodities when the scarce resources are fully employed. This diagram is also a representation of the choices that an economy has deal with.

There are a few key assumptions for PPF are as follows:

  1. Resources are employed in the production of either one of both of the two goods produced by the economy.
  2. There is a fixed quantity of resources
  3. State of technology used in the production of these commodities remains the same or constant.
  4. All the resources are utilized in the most efficient and productive manner.

So, in this case, if all resources are used in manufacturing cars, an economy would produce 30,000 units of car (Point A on the graph); whereas if entire resources are used up for bicycle, it would produce only 5000 units of it (point F on the graph). In between these two extremities lie several combinations that an economy can produce with te constant resources. Joining these various combinations give us the smooth downward sloping, concave PPF curve-AF curve. This AF curve is the Production possibility frontier curve showing maximum combination of these goods- Cars and Bicycle that Newland could produce with the given assumptions. There is very much likely that a combination could fall below this curve. If this happens, it would only mean an economy is functioning at less than optimum level and some resources are not being utilized or remain underutilized. Marginal rate of transformation shows the rate at which substitution in taking place. Rather, it is a ratio of units given up to attain additional unit of the second commodity. So, in this case, marginal rate of transformation (MRT) is  the ratio of giving units of bicycle to attain additional units of car. So, MRT =  (Pindyck & Rubinfeld, 2006; Mankiw,2007).

Cars

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Bicycles

Changein Cars

Change in Bicycles

MRT

30000

0

   —

28000

1000

-2000

1000

-0.50

24000

2000

-4000

1000

-0.25

18000

3000

-6000

1000

-0.17

10000

4000

-8000

1000

-0.13

  0

5000

-10000

1000

-0.10

There are two main properties of PPF:

PPF curve slopes downward from left to right

As discussed above, PPF is the optimum combination of two goods that an economy produces with the resources being limited. This would mean that if we want produce one extra unit of the second good, we need to give up the resources used in the production of the first good so that the freed resources can be used in order to produce marginal unit of the second good. Thus, there exists an indirect or inverse relationship between productions of two commodities. That is, increase in the production of one commodity leads to the decline in the production of another commodity. Hence, the shape of the PPF curve is negatively sloped or in other words, slopes downward from left to right (Pindyck & Rubinfeld, 2006)..

Assumptions and Properties of PPF

Concavity of the PPF curve is due to the accelerating marginal opportunity cost. This means that one needs to sacrifice more units of the first commodity in order to receive additional unit of the second commodity. This implies that as we move downward from left to right on the concave PPF curve, the economy would give up more units of Y commodity to achievean additional unit of the X commodity. Hence, the marginal opportunity costs increases as we move down from left to right thus giving a concave shape to the PPF(Pindyck & Rubinfeld, 2006). Infact, the slope of PPF curve is actually a marginal rate of transformation (MRT) that increases as we move along the curve downward. The slope actually depicts the ease or the complexity in transforming one to another group (Mankiw,2007). Here, if we move downward, it shows how bicycles are transformed into cars while as we move upward along the curve, it reveals how cars are transformed into bicycles.

It is important to highlight a very important that PPF curve only shows numerous combination with which an economy would choose to function but it would never state exactly at what point or which combination exactly an economy is producing at. This would depend entirely on whether the economy is utilizing its resources to its maximum potential. Only in that case, it would be positioned on the PPF or AF curve here. Moreover, if the economy is operating inside PPF curve, it suggests that its resources are not operating at its maximum level and are underutilized. It can definitely not produce anywhere beyond PPF curve as such combination is unattainable and it’s beyond the current productive capacity. Thus, the above discussion implies that the economy can operate either on the PPF curve or inside PPF curve, which will be known as attainable combination and cannot operate beyond PPF curve, which is an unattainable combination(Mankiw, 2007).

(c).  Given that the demand has increased for both bicycle and cars, it is evident that the current set of resources won’t be sufficient enough to deal with this increased demand. Thus, these changes in resources lead to the changes in PPF curve, which could be in two forms-the entire shift in the PPF curve or rotation shift in the PPF curve across X-axis and Y-axis. In this case, there would be an overall shift of PPF curve to the right because we see that the demands for both goods have increased. 

How Changes in Resources lead to PPF Shifts

To meet this increased demand for cars and bicycles, the economy may explore more options for new resources. The three possibilities that would enable Newland to deal with the increased demand are as follows:

As the present world is dynamic, there has been constant search of new resources as the economy is very quickly exhausting the present resources. Thus, discovery of the new sources of the resources would lead to the increase in the productive capacity of the economy.

It may also invent new technology which would produce more goods with the same level of resources. A technological discovery would help the economy make a huge leap in dealing with the increased demand with the limited resources. In fact, discovery of the new technology along with new resources would go a long way in enhancing the productive capacity of the Newland.

The economy may also look for innovative methods or technique which would improve the efficiency and productivity of the current machines or labor and in this way; it would be in a position to meet the increased demand in an effective and efficient manner. 

(a). The market price is 65 cents per bag and the equilibrium quantity is 145 million bags per week as the quantity demanded equals quantity supplied at this level.

(b). As the rise in the demand for new dip increases the demand for the potato chips would lead to the rise in the demand while the supply being constant. This would lead to rightward shift in the demand, indicating higher demand at any given price level. This would lead to rise in the equilibrium price and quantity. 

(c). This leads rise in the demand and supply curve. As shown in the below diagram, the equilibrium price is 60 cents and the equilibrium quantity is 180 million bags per week. Demand curve shifted rightward while supply curve shifted downward , both indicating rise in the quantity demanded and quantity supplied.  

(a). Income elasticity is the ratio of % modification in the quantity demanded due to the% change in income. Here, it is given that the percentage change in the demand for concert ticket is +15% while for bus ride is -10%.

% change in income = (170-130)/130 =0.307

(i). Income elasticity of demand for concert ticket = 0.15/0.307 = 2.05, implying it’s a luxury good as it is a positive income elastic greater than 1 suggesting increase in income would lead to rise in the demand. Income is highly elastic for concert tickets

Methods to Deal with Increased Demand

(ii). Income elasticity of demand for bus ride=  – 0.10/0.307= – 0.325 suggesting it’s a necessity good and that income elasticity is lower in this case.

(b). Cross price elasticity relates to the ratio of change in the quantity demanded of good 2 on account of changes in the price of good 1. So here, given that the demand of soy has decreased by 2% as the price of Sushi has increased by 5%, the cross elasticity of demand is 0.4.

cross elasticity of demand = % change in quantity demanded for good 2 / %change in the price of good 1

= 2%/5% = 0.4

Since the coefficient is positive, it indicates that these two products are substitutes, however not very close substitute as the value not greater than 1.

Price elasticity of Sushi = – 1%/5% = 0.2

(c). Price elasticity of demand for domestic beef = -1.30

Percentage change in the quantity demanded for beef = +6.5%

% change in the price of the domestic beef = 6.5% / -1.30 = -5%

Cross elasticity of demand = % change in quantity demanded for imported beef / %change in the price   of domestic beef = -4%/ -5% = 0.8

This suggests that imported and domestic beef are substitutes as the coefficient is positive`. 

With price floorings, it sets the price above the equilibrium level in order to support farmers thus making it expensive for the consumers. KNF is the initial consumer surplus while LFN is the producer’s surplus. With price flooring, consumer’s surplus has decreased to KAB and producer’s surplus increased to ABYL, however causing a deadweight loss to the economy depicted by BYF. This phenomenon occurs when there is a difference between the equilibrium price and buyers ‘willingness to pay. It is the sum of the losses of the consumer and producers’ surplus.

(b) Here PFT  is the world price for beef PQ  is the import quote set above the world price level. With this new price, imports would reduce thus reducing the overall domestic supply and raise domestic price. Here, ABCD is the consumer surplus, A is producers’ surplus and C is the deadweight loss. Thus, consumers would be worse off as it raises the price of the imported as well as substitute goods. Producers would be better off as they are receiving better price

(c) .With this quota, there is a reduction in the total supply from the market, thus leading to rise in producer’s surplus and loss to consumer’s surplus (ABCD), government revenue is D   

CS1 = 0.5* base*height = 0.5*    625 * (15-4) = 2812.5

CS2 = 0.5* 500* (15-5.6) = 2350

Consumer’s loss = 2350 – 2812.5 = – 462.5 

PS1=0.5* 125 * 2= 125

PS2= 0.5*250*3.6= 450

Producer’s gain = 325 

Tariff Revenue = 250* 1.6 =  400 million               

Amount of deadweight loss= (625-125)*2 – (500-250)*3.6 = 1000-900 = 100  

References

Mankiw , G  (2007). Economics: Principles and Applications, 4th edition South Western, Cengage Learning India Private Limited. 

Pindyck, RS & Rubinfeld D. (2006). Microeconomics, 6th edition, Prentice Hall.