Explain these microeconomics questions
. . . 3.20 Development of a new deluxe version of a particular software product is being considered by Ravi Behara's software house. The activities necessary for the completion of this project are listed in the following table: Normal Crash Time Time Normal Crash Immediate Activity (weeks) (weeks) Cost Cost Predecessor(s) $2000 $2600 W 1 1 2200 2800 3 500 500 A WaDOWNA 4 2300 2600 A 900 1200 B NNW 3000 4200 1400 2000 D. E a) What is the project completion date? b) What is the total cost required for completing this project on normal time? c) If you wish to reduce the time required to complete this project by one week, which activity should be crashed, and how much will this increase the total cost? d) What is the maximum time that can be crashed? How much would costs increase?I{ltusstion 1 Consider the linear regression model given by y = xb+ a . where E(') = all! a) Explain the assumptions of the linear regression model. [5 marks] b) Derive the ordinary least squares (0L8) estimate of :5. Explain the steps involved in the derivation. [10 marks] c) Show that the OLS estimate of b is unbiased. [5 marks] d) Consider the following data set with three time-series observations: 1.53 1 1.84 y: 0.25 ,x= 1 1.5 _ {1) 0.75 1 {1'1 Use the OLS formula derived' in part (b) to estimate the coefficient .5 using the data on the dependent variable y and independent variable x in equation {1). Show all calculations [20 marks] 1. [Market Equilibrium I - Consumers and Producers Surplus, Price Floor] Find (a) equilibrium price, (b) equilibrium quantity, (c) consumers' surplus, (d) producers' surplus, and (e) total surplus for the following markets. Qd21252P Q,=45+8R What is the surplus or shortage if lhe government imposes a price oor of P = 20 in this market. 2. [Market Equilibrium II - Comers and Producers Surplus, Price Ceiling] Find (a) equilibrium price, (b) equilibrium quantity, (c) consumers' surplus, (d) producers' surplus, and (e) total surplus for the following markets. QM+W=O lygmzo What is the surplus or shortage if the government imposes a price ceiling ofP = 2 in this market. 3. (2) Consider the supply and demand model below Demand: g=-p+3+4x+e, Supply: p=q+1+6, a) Find the reduced form equations for p and q. b) Suppose that x - 2. Find the equilibrium p and q (i.e., the values if e, = e, = 0 ). c) Suppose that x - 5. Find the equilibrium p and q (i.e., the values if e, = e, = 0 ). d) If we have / observations on p, q, and x, can we consistently estimate the reduced form equations by OLS? Why? e) To illustrate part (d), note that the slope of the reduced form curve for p is equal to Ap/Ar . Using the values from (b) and (c) compute Ap/Ax . Is the value equal to the reduced form coefficient for p? f) Do the same thing for Aq/Ar . Is the value equal to the reduced form coefficient for q? g) If we have A observations on p, q, and x, can we consistently estimate the supply equation by OLS? Why? h) To illustrate part (g), note that the slope of the supply curve is Aq/Ap. Using the values from (b) and (c) compute Ag/Ap. Is the value equal to the slope coefficient for the supply equation? i) . If we have / observations on p, q, and x, can we consistently estimate the demand equation by OLS? Why or why not
