# Slope of Demand Curve - Techniques of Analysis - Past Exam, Exams for Economics. Guru Ghasidas University

## Economics

Description: Slope of Demand Curve, Value of Intercept, National Output, Cobb-Douglas Production Function, Breakeven Quantity, Disposable Income, Marginal Propensity to Consume. I invite all economics student to visit my files and find different subject's past exam paper. Correct name of subject is given in file title.
Showing pages  1  -  4  of  6
Ollscoil na hÉireann, Gaillimh
GX_____
National University of Ireland, Galway
Semester 1 Examinations 2008/2009
Exam Code(s)
2BA5
Exam(s)
2nd B.A. (Economic & Social Studies)
Module Code(s)
EC222
Module(s)
Techniques of Analysis
Paper No.
1
Repeat Paper
External Examiner(s)
Professor Robert Wright
Internal Examiner(s)
Professor Eamon O’Shea
Mr. Stephen McNena
Instructions:
questions from section A and 6 questions from section B.
Duration
No. of Pages
Department(s)
Course Co-ordinator(s)
Requirements:
MCQ
No
Handout
Handout of formulae to be distributed at St. Angela’s
College, Sligo
Statistical Tables
Yes, to be distributed at St. Angela’s College, Sligo
Graph Paper
Yes, if students request it
Log Graph Paper
No
Other Material
No
SECTION A MATHS
Answer any 6 of the 8 questions. 15 minutes per question.
1. (a) Consider the demand function represented by the equation: Qd = 50 – 5P
(i) Express Total Revenue (TR) as a function of Qd.
(ii) What is the slope of the demand curve? What is the value of its intercept?
(iii) Sketch the demand curve.
(iv) At P = 6, calculate the quantity and the total revenue.
(b) Consider the following production function: Y = A f (K, L) = 10AK0.5L0.5
where Y is national output, A is technological knowledge, K is the capital stock,
and L is labour.
Transform this Cobb-Douglas production function into a linear model using
logarithms.
2. (a) A firm that makes paint sells their product for 7. Their cost function is
represented by the equation: TC = 200 + 5Q.
(i) Calculate the breakeven quantity.
(ii) Determine the Total Revenue, Fixed Cost, Variable Cost and Total Costs.
(iii) Sketch the Total Cost and Total Revenue curves.
(b) Consider the following demand and supply equations:
Demand: P = 100 – 3Q
Supply: P = 10 + 2Q
(i) Solve for the equilibrium price and quantity.
(ii) What are the slopes of the two curves?
3. Consider an open economy described by the following equations:
C = 300 + 0.9Yd Govt spending = 600
I (autonomous) = 400 Tax rate = 20% of incomes
Exports = 800 Imports = 27.5% of disposable income
Note that C, Y and M are endogenous, and I, G, t and X are exogenous constants.
(a) Solve for the equilibrium national income, Y.
(b) Then calculate disposable income, consumption and imports.
(c) Determine the Marginal Propensity to Consume and the Marginal Propensity to
Save.
(d) Calculate the expenditure multiplier.
(e) If an injection of extra autonomous expenditure causes national income to rise by
400, calculate the size of the extra expenditure.
4. Consider the demand function represented by the equation:
Qd = 30 - P
(a) Express Total Revenue (TR) as a function of Q.
(b) Determine the equation for Marginal Revenue.
(c) Using differentiation, calculate the quantity where TR is maximised.
(d) Calculate the price where TR is maximised.
(e) Calculate the maximum Total Revenue.
5. Assume a Total Cost function of the form: TC = 30Q - 15Q² + 3Q3
(a) Derive a function for Average Cost (AC).
(b) Derive a function for Marginal Cost (MC).
(c) Find the levels of output that minimise AC and MC.
(d) Calculate the minimum AC and the minimum MC.
(e) Using algebra, confirm that AC = MC when AC is at a minimum.
6. A firm faces the following demand and Total Cost functions:
P = 125 – Q
TC = 500 + 5Q + 0.5Q²
(a) Determine the equations for Total Revenue, Marginal Revenue, Average Cost,
Marginal Cost and Profit.
(b) Derive the profit-maximising level of output.
(c) Calculate the maximum profit.
(d) Derive the price and Marginal Revenue at this level of output.
7. A monopolist produces a single good (X) but sells it in two separate markets. The
cost function is TC = 120 + 8Q. The demand function in each market is
P1 = 50 – 4q1 P2 = 80 – 3q2
where P1 and q1, P2 and q2 are the prices and quantity in markets 1 and 2. Find the
prices and quantities in each market that maximise overall profits.
8. A firm has a Cobb-Douglas production function as follows: Q = L0.3K0.7
The price of labour is 3 and the price of capital is 15. The firm faces a total cost
constraint of 150.
Determine the values of L and K for which production is maximised, subject to the
cost constraint.
SECTION B STATISTICS
Answer any 6 of the 8 questions. 15 minutes per question.
1. (a) Your sell newspapers at 1.80 each, breakfast rolls at 3.50 each and textbooks
at 40 per book. During one day you sell 150 newspapers, 25 breakfast rolls and 10
textbooks. What is the weighted mean selling price?
(b) You invest some of your savings in a managed fund. The annual percentage
returns earned by the fund for the last 5 years are outlined in the table below.
Calculate the geometric mean annual return earned by the fund.
9.4% 13.8% 1.7% 11.9% 4.7%
(c) (i) Calculate the mean, median and mode of the following set of numbers.
0, 9, 9, 6, 9, 7, 9, 3, 3, 2, 1
(ii) Explain carefully why the median is sometimes a preferable measure of central
location than the mean.
2. (a) A student is taking two courses: maths and economics. The probability the
student will pass maths is 0.75, and the probability of passing economics is 0.90.
The probability of passing both subjects is 0.70. What is the probability of passing at
least one subject?
(b) A firm uses two types of machines, the S40 and the S60. The probability of the
S40 machine being available is 0.90 and the probability of the S60 being available
is 0.80. What is the probability that both types of machine are available? What is
the probability that both types of machine are not available?
(c) If you ask three strangers on campus, what is the probability that:
(i) All were born on a Wednesday?
(ii) All were born on different days of the week?
(d) Sarah is the owner of a convenience store. Sarah collects data on how many items
each customer purchases, as shown in the table below:
X = no. of items
P(x)
0
1
2
3
0.10
0.40
0.30
0.20
(i) Compute the mean and standard deviation for the distribution of number of items.
(ii) If a customer enters the shop, what is the chance that they buy at least 2 items?