Economics Answers

(a) If x is the sample mean, prove that the expected value of x,E(x) equals the population mean (μ).
(b) Describe the process of testing hypothesis about population proportion of a given attribute.

Sita expects her future earnings to be worth Rs. 100. If she falls ill, her expected future earning will be Rs. 25. There is a belief that she may fall ill with probability of 2/3 while the probability of remaining in good health is 1/3
Let her utility function be given as U(y) =y1/2 suppose that an insurance company offers to fully insure Sita against loss of earnings caused by illness against an actuarially fair premium.
(a) Will Sita accept the insurance? Explain.
(b) What is the maximum amount that Sita would pay for the insurance?

A consumer’s utility function is given as
U(x,y) = In (x+2y-y2/2)
,
)
Where x and y are two goods of consumption.
(a) Find the indirect utility function of the consumer.
(b) Examine if Roy’s law is satisfied by the consumer’s demand function for y.
(c) Find the expenditure function of the consumer e(p,u) where price of x = 1 and price of y
= p.
(d) Find the Hicksian demand function hy (p,u) for commodity y, where the price of x is 1
and the price of y is p.

(a) Distinguish between pure strategy Nash equilibrium and mixed strategy equilibrium.
When would you use mixed strategy equilibrium?
(b) Find all the Nash equilibrium of the following game:
Player1
Player 2
Left Right
Up (5,4) (1,3)
Down (4,1) (2,2)

An economy comprises two consumers, 1 and 2, with two consumption goods bi-cycles (b) and
wheat(w). Both consumers have the same utility function μ (b,w)=bw
Bi-cyclesandwheat are produced by two firms which use only labour according to the production functions
b =1b and w=0.5/1w
$!l%
Both firms are owned by consumer 1, and consumer 2 owns 200 units of labour.
(a) Find the production possibility frontier for this economy.
(b) Find the competitive equilibrium.
(c) Find competitive equilibrium if every consumer owns 100 units of labour and owns one
firm.
(d) Find the Pareto efficient allocations for this economy.

Assume that workers, employers and investors all believed that inflation in the coming year would equal the annualized rate of inflation experienced in the past 6 months. Also assume that workers had been receiving nominal wage gains of 5% during a several year period where the annual inflation rate was 2%. Now assume that a decline in the unemployment rate below NAIRU creates conditions where workers push for an annual real wage increase of 4%. Also assume that labor productivity growth declines to 1% per year as unemployment is squeezed below normal frictional & structural levels.

a) What rate of nominal wage growth will workers seek at the new low unemployment rate?

b) How fast will firms have to raise prices given your answer in (a) in order to protect profit margins?

c) If the rate of inflation in (b) occurs and the Fed allows AD to grow fast enough to maintain the unemployment rate below NAIRU for another year, what rate of nominal wage growth will workers
seek in the following year?

d) If the rate of inflation in (b) had persisted for 6 months or more, how large an increase in the federal funds rate would be needed to increase the level of real interest rates in the economy?

ABC limited has the following details for the period ended 31st December 2012.
Sales Purchases Expenses
January 100,000 40,000 20,000
February 120,000 25,000 28,000
March 150,000 30,000 30,000
April 200,000 50,000 42,000
May 280,000 120,000 150,000
June 400,000 150,000 180,000

The opening cash balance for the firm was Ksh.150,000/-,

Sales are made on credit and paid for as follows: 50% cash within the month of the sale
25% cash in the following month
25% cash in the third month

Purchases and expenses are made on credit and paid for as follows:
50% cash the month of purchase:
50% cash the following month
Required :
Prepare an analysis sheet showing the following:
i)Cash sales
ii)Cash purchases
iii)Cash expenses
iv)A Cash budget

1.Given the following monotonically transformed utility function faced by the consumer
U(X1X2) = X_1^0.5 X_2^0.5
The price of good X1 is P1 and the price of good X2 is P2. Derive the optimal demand (Marshallian demand) function for X1 and for X2.

2.Under a perfect competition the price as sh. 6 per unit has been determined. An individual firm has a total cost function given by C=10+15Q - 5Q^2+Q^3/3. Find:
Revenue function
The quantity produced at which profit will be maximum profit
Maximum profit

Given the following estimated demand equation Qdy= 3,000-py-5.6pw+0.4px+0.000003pz+0.004M

Where Qy is the quantity demanded of good Y, Py is the price of good Y, I is the income of the consumer, Px,Pw and Pz are the prices of good X, W and Z respectively. Py = 100, Pw = 300, Pz = 400, Px =100 and M = 40,000. Compute income elasticity of demand, own-price elasticity of demand and the three cross-price elasticity of demand.

Assume that a company intends to sale product in the market, at a selling price of sh.9 per
unit. The V C is shs.5 per unit and the T F C is sh.2000
Required:
i. Compute the B E P in units and in shs.
ii. Assume that the company intends to make a profit before tax of 20% of sales,
determine the number of units that must be sold.
iii. Assume that the corporate tax rate is 30% and the company has a target profit
of 1640 after tax. Compute the number of units that must be sold to earn this
target profit.
If the company expects to sale 600 units, compute the marginal of safety.10mks