ECON104: Consider the demand and supply curves 𝑄! = 𝛼 − 𝛽𝑃 𝑄” = 𝜇 + 𝛾𝑃 where 𝛼, 𝛽, 𝜇, and 𝛾 are suitable positive constants: Microeconomics Assignment, UC, Singapore

Question 1 

• Consider the demand and supply curves 𝑄! = 𝛼 − 𝛽𝑃 𝑄” = 𝜇 + 𝛾𝑃 where 𝛼, 𝛽, 𝜇, and 𝛾 are suitable positive constants.
• Find the equilibrium price P*, and the corresponding quantity Q*.
• Suppose a tax of $𝜏 per unit is imposed on the producer. Find the new equilibrium price. How does it change?
• Compute and compare the total revenues obtained by the producer before the tax is imposed (R*) and after (Rˆ).
• Use diagrams to illustrate the difference between the two market equilibria.

Question 2

• Given 𝐴 = – 0 0 0 4 0 0 10 5 0 2, find 𝐴# , 𝐴$, 𝐼 + 𝐴 + 𝐴# and (𝐼 − 𝐴)(𝐼 + 𝐴 + 𝐴# ) where 𝐼 denotes the identity matrix of order
• Use the results in (a) to find (𝐼 − 𝐴)%&.

Question 3

Let 𝑈 be the n × n matrix where all the elements are 1. a. Show that (𝐼’ + 𝑎𝑈)(𝐼’ + 𝑏𝑈) = 𝐼’ + (𝑎 + 𝑏 + 𝑛𝑎𝑏)𝑈 for all real numbers a and b. b. Use the result in (a) to find the inverse of 𝐴 = – 4 3 3 3 4 3 3 3 4 2. 4. Let the IS equation be where 1 – b is the marginal propensity to save, g is the investment sensitivity to interest rates, and A is an aggregate of exogenous variables.