IB Economics - Linear Supply Functions

This study note for IB economics covers Linear Supply Functions

Supply Function

Qs​=c+dP

A supply function represents the relationship between the quantity of a good supplied (Qs) and its price (P). When expressed in a linear form, it takes the equation:

Qs=c+dP

• Interpretation of terms:
  • Qs: Quantity supplied of the good.
  • PP: Price of the good.
  • cc: Intercept term, which represents the quantity supplied when the price is zero (usually not realistic but theoretical).
  • dd: Slope coefficient, which indicates how much the quantity supplied changes in response to a change in price.

Plotting a Supply Curve from a Linear Function

Example: Qs = −30+20P

• Interpretation:
  • Intercept (cc): -30
  • Slope (dd): 20

To plot:

• Set different values for PP (e.g., 0, 1, 2, ...) and calculate corresponding QsQs​.
• Plot these points on a graph where PP is on the x-axis and QsQs​ is on the y-axis.

Slope of the Supply Curve

The slope of the supply curve is determined by the coefficient dd in the supply function Qs=c+dP

• Interpretation:
  • If d>0d>0, the supply curve slopes upwards (positive slope).
  • If d<0d<0, the supply curve slopes downwards (negative slope).

Impact of Changing the Intercept ( cc term)

• Shift of the Supply Curve:
  • When cc changes, the entire supply curve shifts.
  • An increase in cc shifts the supply curve to the right (higher quantity supplied at every price).
  • A decrease in cc shifts the supply curve to the left (lower quantity supplied at every price).

Effect of Changing the Slope ( dd term)

• Steepness of the Supply Curve:
  • The slope coefficient dd determines how steeply the supply curve rises or falls.
  • A higher absolute value of dd (whether positive or negative) means a steeper supply curve.
  • A lower absolute value of dd means a flatter supply curve.

Glossary

• Quantity supplied (Qs): The amount of a good that producers are willing and able to sell at a given price.
• Price (P): The amount of money that buyers pay and sellers receive for a unit of a good.
• Intercept (c): The constant term in the supply function, representing the quantity supplied when price is zero.
• Slope coefficient (d): The coefficient of the price variable in the supply function, indicating the responsiveness of quantity supplied to changes in price.

Related Topics

• Elasticity of supply
• Non-linear supply functions
• Equilibrium in competitive markets

Worked Example

Example: Given the supply function Qs=50+10P

• Calculate quantity supplied when P=5P=5.
• Plot the supply curve.

Solution:

• At P=5P=5: Qs=50+10⋅5=50+50=100Qs​=50+10⋅5=50+50=100
• Plotting points like (0,50),(5,100),(10,150)(0,50),(5,100),(10,150) gives the supply curve.

IB Economics Essay Questions

1. Discuss the relationship between price and quantity supplied using the concept of a linear supply function.
2. Analyze how changes in the intercept and slope coefficients of a supply function affect the supply curve.
3. Compare and contrast the implications of a positive and negative slope coefficient in a supply function.
4. To what extent can a linear supply function accurately depict real-world supply behavior? Discuss with examples.
5. Evaluate the impact of government policies on the parameters of a linear supply function.

Model Answer:

Evaluating the Impact of Government Policies on the Parameters of a Linear Supply Function

Introduction

A linear supply function is expressed as Qs=c+dP, where QsQs​ is the quantity supplied, PP is the price of the good, cc is the intercept, and dd is the slope coefficient. Government policies can significantly affect the parameters ccand dd of this function, thereby influencing the supply of goods in an economy. This essay evaluates these impacts using real-world examples.

Impact on the Intercept (cc)

The intercept term cc in the supply function represents the quantity supplied when the price is zero. In reality, this is a theoretical construct, but it captures the base level of supply influenced by factors other than price, such as production costs and technology.

• Subsidies: Government subsidies can shift the supply curve to the right by increasing the intercept cc. For example, the U.S. government provides subsidies to farmers to encourage the production of certain crops. In 2020, the U.S. Department of Agriculture offered subsidies to soybean farmers to mitigate losses from trade tensions. This financial support allowed farmers to produce more soybeans at every price level, effectively increasing the intercept cc in their supply function.
• Taxes: Conversely, taxes on production or sales can shift the supply curve to the left by decreasing the intercept cc. For instance, carbon taxes aimed at reducing emissions increase the cost of production for industries that rely heavily on fossil fuels. The introduction of a carbon tax in the European Union raises production costs for energy-intensive industries, reducing the quantity supplied at each price level and shifting the supply curve leftward.

Impact on the Slope (dd)

The slope coefficient dd in the supply function reflects how the quantity supplied responds to changes in price. A higher dd implies that quantity supplied is more responsive to price changes, while a lower dd suggests less responsiveness.

• Price Controls: Government-imposed price controls, such as price ceilings or floors, can affect the slope dd. For example, rent controls in cities like New York have led to a less responsive rental housing market. By capping rents, these controls prevent landlords from adjusting rents in response to changes in demand, which affects how responsive the quantity of rental properties is to price changes, thus flattening the supply curve.
• Regulations and Standards: Regulations that impose stricter production standards can impact the responsiveness of supply. For instance, stricter environmental regulations in the automotive industry, such as the U.S. Corporate Average Fuel Economy (CAFE) standards, have increased production costs. This reduced the slope dd of the supply curve for cars, as manufacturers are less able to increase the quantity of cars supplied in response to price increases due to higher production costs.

Real-World Example: Pharmaceutical Industry

In the pharmaceutical industry, government policies on drug patents and pricing can significantly impact both cc and dd. For example, policies that extend patent protections can increase the intercept cc by ensuring that pharmaceutical companies have higher returns on their investments in drug development. This encourages them to produce more drugs, shifting the supply curve to the right.

However, if the government imposes price controls on medications, this can flatten the supply curve by reducing the responsiveness of drug supply to price changes. Price controls can limit the ability of pharmaceutical companies to adjust prices in response to changes in production costs or demand, thereby affecting the slope dd of the supply curve.

Conclusion

Government policies play a crucial role in shaping the parameters of a linear supply function. Subsidies and taxes influence the intercept cc, affecting the base level of supply. Price controls and regulations impact the slope dd, altering the responsiveness of supply to price changes. Understanding these impacts helps policymakers design more effective policies and assists businesses in anticipating the effects of regulatory changes on their supply strategies.

In summary, the effects of government policies on the linear supply function are significant and multifaceted, influencing both the quantity supplied at different price levels and the overall responsiveness of supply to price changes.

Multiple Choice Questions on Linear Supply Functions

1. Which of the following represents the correct interpretation of the slope coefficient dd in the linear supply function Qs=c+dPQs​=c+dP?

   a) The amount of the good supplied when the price is zero.

   b) The change in quantity supplied for a one-unit change in price.

   c) The maximum quantity supplied at any given price.

   d) The intercept of the supply function on the price axis.

2. If the supply function is Qs=40+15PQs​=40+15P, what will be the quantity supplied when the price PP is 4?

   a) 40

   b) 100

   c) 1000

   d) 160

3. What happens to the supply curve when the intercept term cc in the supply function Qs=c+dP increases?

   a) The supply curve becomes steeper.

   b) The supply curve shifts to the right.

   c) The supply curve shifts to the left.

   d) The slope of the supply curve becomes negative.

4. Which government policy would most likely result in an increase in the intercept term cc of the supply function Qs=c+dP?

   a) Implementation of a tax on production.

   b) Introduction of a price floor.

   c) Provision of subsidies to producers.

   d) Establishment of stricter environmental regulations.

5. If a supply function Qs=−20+10P is modified to Qs=−20+20P, how does this change affect the supply curve?

   a) The supply curve shifts upward.

   b) The supply curve becomes steeper.

   c) The supply curve shifts to the left.

   d) The supply curve becomes flatter.

Answers

1. b) The change in quantity supplied for a one-unit change in price.
2. d) 160

   Calculation: Qs=40+15×4=40+60=100Qs​=40+15×4=40+60=100

3. b) The supply curve shifts to the right.
4. c) Provision of subsidies to producers.
5. b) The supply curve becomes steeper.

   Explanation: Increasing the slope coefficient dd from 10 to 20 makes the supply curve steeper, indicating that quantity supplied is more responsive to changes in price.