Macroeconomics Answers

(a) consider three consumers who care about the consumption of a private good and their consumption of a public good. their utility function are given by

Ui=XiG i = 1, 2, 3

where Xi is consumer i's consumption of the private good and G is the amount of the public good consumed by all. the unit cost of the private good is $1 and the unit cost of the public good is $10. individual wealth levels are w1=30, w2= 50 and w3 = 20.

(i) compute the marginal rate of substitution between G and X for each of the three consumers.

(ii) derive the samuelson condition for this model

(iii) derive the aggregate resource constraint and compute the optimal level of public good consumption.

(b) brief discuss the relevance of the samuelson condition in consideration to provide public goods in your country

The table below gives the CPI basket for 2012. Suppose that 2012 is the reference base period. (5 

marks each)

Item Quantity 

(2012)

Price 

(2012)

Price 

(2013)

Oranges 50 $0.90 $0.75

Bananas 100 $0.50 $0.95

Chicken 200 $2.00 $2.50

Beef 100 $5.00 $4.80

Bread 300 $1.75 $2.00

a) What is the cost of the CPI basket in 2012?

b) What is the cost of the CPI basket in 2013?

c) What is the CPI for 2012?

d) What is the CPI for 2013

1.    Given y = (x, z) = 6x² + 3xz⁴ where

X(B, E, T) = B² + 2E + TB

Z(B, E, T) = (ETB)¹ + B + E Then, find the partial derivatives of y with respect to B, E, and T.

Consider the market for loanable funds. If expectations about South Africa’s future economic

performance are negative such that firms cancel plans to build new equipment and factories, then in the

short run we would expect:

Briefly explain the weakness of the RSAs industrial development zones

1. Given C=20+0.8YD, I=20+5i, G=500, X=400, and T=200.

a). Derive the IS equation

b). Find the value of the multiplier

c). Find the equilibrium consumption

2. Assuming Government spending increases by 50% and investment reduces by 10%, what happens to the IS equation