Solve The Equilibrium Price And Quantity Of The Markets Abov

Solve the equilibrium price and quantity of the markets above you should show your work

Given the demand function QD = 20 - 2P and the supply function QS = 2P, the task is to find the market equilibrium where quantity demanded equals quantity supplied (QD = QS).

To find the equilibrium, set demand equal to supply:

20 - 2P = 2P

Combine like terms:

20 = 4P

Divide both sides by 4:

P = 5

Substitute P = 5 into either the demand or supply function to find equilibrium quantity:

Using demand: QD = 20 - 2(5) = 20 - 10 = 10

Using supply: QS = 2(5) = 10

Thus, the equilibrium price is P = 5, and the equilibrium quantity is Q = 10.

Graph the market above

[Since this is a text-based response, a graph description is provided.]

  • The demand curve can be graphed with the equation QD = 20 - 2P, which intercepts the quantity axis at Q = 20 when P = 0, and the price axis at P = 10 when Q = 0.
  • The supply curve is linear, with the equation QS = 2P, intersecting the quantity axis at Q = 0 and rising to the right.
  • The point of intersection of the demand and supply curves is at P = 5 and Q = 10, which indicates the market equilibrium.

What is the consumer surplus in the market at equilibrium price P = 2?

First, note that the question asks for consumer surplus assuming the market is at P = 2, not the equilibrium price P = 5. Hence, we need to calculate consumer surplus at this price.

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay, summed over all units bought. It's represented graphically as the area of the triangle between the demand curve and the market price, from Q = 0 up to the quantity demanded at P = 2.

Calculate quantity demanded at P = 2:

QD = 20 - 2(2) = 20 - 4 = 16

Determine the maximum price consumers are willing to pay when QD drops to zero:

Set QD = 0:

0 = 20 - 2P → 2P = 20 → P = 10

This is the choke price (the highest price consumers are willing to pay). The consumer surplus is the area of a triangle with base (Qd at P=2) and height (difference between maximum willingness to pay and market price):

Consumer Surplus = 0.5 × QD × (Maximum price willing to pay - Market price)

= 0.5 × 16 × (10 - 2) = 0.5 × 16 × 8 = 64

Bonus: Tell me an appropriate joker

An appropriate joke: Why did the economist bring a ladder to class? Because they wanted to reach the high demand!

References

  • Mankiw, N. G. (2020). Principles of Economics. Cengage Learning.
  • Krugman, P., & Wells, R. (2018). Economics. Worth Publishers.
  • Perloff, J. M. (2019). Microeconomics. Pearson.
  • Samuelson, P. A., & Nordhaus, W. D. (2010). Economics. McGraw-Hill Education.
  • Pindyck, R. S., & Rubinfeld, D. L. (2017). Microeconomics. Pearson.
  • Varian, H. R. (2014). Intermediate Microeconomics. W. W. Norton & Company.
  • Frank, R. H., & Bernstein, D. (2020). Microeconomics and Behavior. McGraw-Hill Education.
  • Hubbard, R. G., & O'Brien, A. P. (2018). Microeconomics. Pearson.
  • Landsburg, S. (2010). The Armchair Economist. W. W. Norton & Company.
  • Friedman, M. (2002). Capitalism and Freedom. University of Chicago Press.

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